What is the evidence that sound travels as a wavee+vh/fz es1 5eces4 4p?

What is the evidence tha5zmz h/k ztlo/cfyst6:; jz f)n;*2a3nckb5s t sound is a form of energy?

Children sometimes pla h5 o psbqflo1-t2;n4ny with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched an4hn2pf; o-nq slt51 bod a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do 9aa; rin xrtuta6e-yy(6 q23nyou expect the frequency or waventu(qra i-ry x ;26 3ytn9eaa6length to change?

What evidence can you give that the speed6pytq (6m d6q- dmr0pmzmz9y7 of sound in air does not depend significantly on frequenc6q6r(d-pdmy9 y q0m m7pzzmt 6y?

The voice of a person who has inhaled helium sounds very high-pka: *mww0 c.yttro2u-k cs))qitched. Why?

How will the air temperature in a room affe 2;jt7e6tmzv bes8r5y6z 9e7sw,fgf q ct the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the ampl ;.;f8riec yyditude of sounds in various frequency ranges. (An examp.8ficyy;d; e rle is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tog hb-3 h)m m0aycsjde./ether as you move up.m0c hy-m)/behd a3js the fingerboard toward the bridge?

A noisy truck approaches you from behind a buildingl2b( vahor -y2. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. 2oal2r yb(- vhExplain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,*u356*uvz gy+x rpv ymeq gb95” whereas beats can be said to b x+uug*z5bpqvv39gey6 y5m *re due to “interference in time.” Explain.

In Fig. 12–16, if the frequenv qd )-jq9o1+you*1u yaq6beqcy of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farth*uqeyy+oau9- 1q1j6qo )bd v qer apart or closer together?

Traditional methods of protecting the hearing of people w 5ftrbz;d-:p +pgfsb, ho work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise level:b,+-sff5tpp z dgr ;bs. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thoug7wg*q3ywo+:3 yu lm 3ex9fx kzht of as a superposition of two sound waves with slightly do+xm:3ku* ezl3w7wxyq 3 9gfyifferent frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the svfno39 hffgr0db8m 1*d toe zb. ,;qv5ame direction, with the same velocity? Eenhfrt8vz01dobbmov 5 g*f,93. ;fdqxplain.

If a wind is blowing, wizk h ---lhrxdz0 *0q(pe35*m gtq-m3kzcwkecll this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity 5c-ez3hrqpg -kd * -zmlq00et3w(-c mk*hzx k changed?

Figure 12–32 shows various positions of a child in moti5*vgkp7yx4 h.f. kmewon on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasonhxwf.p 7y.v45mkekg *ing.

  A hiker determines the length of a l:f ,i4mfyekj2 b vxpt(;dn/4rake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate t,f rvpnym (/fd kxb4:;4ie2tj he length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just bev * 6ati*x ,jrz;+qxb6mo eky3low the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary signamjtxr 36ybq oi* e kx,;vz+*6ificantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at ls:x)j /g/knu 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat isx ang4( 8yobpj*r9 p5h drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) bjrx459 onp (p a*by8hgy the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking*y ,y5c,a.tixp8r hsf th,,8pxhtc5 r.ayys i*fe water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grounz1ll.rch j-y 0d, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. y1zllc-rjh0 . How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance b 4rcidow5 (f7ey the “5-second rule” for estimating the distance from a lightning strikerdfiw e5c7o4( if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thd/mqb7 87wulsj9* auf e pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intens 9t 8fw8lz, l1r( wnynfnde.; v1wg2q ubo8zt4ity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB z46kb8bra(kq la g 84nwhen fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: n6q( 48aklkr g zb8ba4Add intensities, not dB’s.]    dB

  A person standing a certain distance frbd rj/-quh ;d+om an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would tb;+ rdj u-/dhqhis person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rati 92mq ,5fwa2iajqz- l)cy/ru zo of 58 dB, whereas for a CD player it is 95 dBfr/2 a2,j i5yz)qlm9wq -ucz a. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from s*xx+lgp q1dcd9,.q ga person speaking in normal conversation. Use Table 12–2. Assume the so *cg9+qx.px1ld gsq,d und spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strike*c3g iah *q+3jhzt2bfs an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest ampl :. /w,dsqr)w+3o zg zorneq,lifier B is rated at 40 W. (a) Estimate the sound level in decie, 3l ronw:oz+qzr w./)gds,qbels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter regisl :9w6msl8e iv0 buao:h6 d,intered 130 dB when placed 2.8 m in front of a loudspeaker oeohlws ad 906lbu:vmi:i8,n6n the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detgi t.17 vjz 5)vz0pcfpect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levepci7tjp vz5f 1v.0) gzls differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by w4q52.r,pbl*c i c0jred,i2e 8yuxtmqhat factor will the intensity increase? lpu,*exb eyr4 c .q2,52itdjm8 0cq riIncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the k.zmd9iu1 auvy t9(b.frequency of the other. What is the ratio of their intensit y1ua k.(miuz9td9. bvies?   

  What would be the sound level (in dB) of a sound wave in air that corresponds)du qs8 qei);qeh: ry:3ee. nw to a displacement amplitud.nhi8e qeuy:q;w):3r)qd e s ee of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem ast e*w,p aknz10k(sjom3z2-mf t /e cu; loud as a 100-Hz tone that has a 50-dBk0ma w ftmep*j; 1-z o(tczsu3n2e,/k sound level? (See Fig. 12–6.)    dB

What are the lowest and dvlet5r;+r -fq7 q5np highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–5nd vr qp-7rt;fq5e +l6.)

  Your auditory system c ort/6hn+s r1gi/an w,,0jqmz hd,)2n8o bc zqan accommodate a huge range of sound levels. What is the ratst rzoqdo+g/nhaq ,iznn 8jb/6 0c1rw) hm ,2,io of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. Thedgrq* ;nsk msm)/mw4/m m8r-q length of the vibrating portion is 32 cm, and it has a m*/)m8s s; 4r/ qnr-wmdgkm qmmass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are thet+lrxgh0*s mgyd,.z2 fundamental and first three audible overtones if the pipe z2t,y0xhr*gl.gsd +m is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across th;fp j 2a5x9bdsd:g 0qlmt5-tve top of an empty soda bottldxs 9 ;tj0afd5:v2mlgbp q t5-e that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range ua;(qm ur2e j8of human hearing (20 Hz to 20 kHz), what 2ea (m8uruj;q would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hpn3v2 e:sl9iez as its third harmonic. What will be its fundamental freque e:23viepl 9snncy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long a7nw q9aa-cpg4 nd is tuned to play E above middle C (330g 7awqapc4 n-9 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pidetg5v fxvok w 7o9.*n-/m p4lpe that emits middle C (262 Hz) when tv vxk7/poolw 4-ng edm5f 9.*the temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 2apa +t n.l7o6t0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shou;mdaxc 3b:1kjk4r ox hy (+7vrld the hole be that must be uncovered to play D kxrya3( 7o xkmj+h4 ;rb:1cdv above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe cancu(50krflyfwm)56w yd3e i 3g resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. l rw)um3wc(e 0gk35fi5dy6 yf(a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both en)c-t6m7yk 0b w7qmzrywx8y*h ds. It resonates at two successi0 -7)7rmbmtcyw z6xwqy8hy k*ve harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 e ,g6fv/nk)*n s2jjh2gimda1$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are tep tx,e384expresent within the audible range for a 2.14-m-long organ pipe,e 8t3txxepe4 at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is apm 9 :vwer-6qnh 3vbpb )ds.,ckproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear ca-p bk nd69.ceq 3 ,b:)rvvmhwsnal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s whi,zq*tpk tqkg(k-v.- en trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ± qz* v-p,.t-(kg tkqik   Hz

  What is the beat frequency ih m + bfhc43ph,x21kocf middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.r at ;4.kk;g4ujt *hss5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operatis4tu*r;tk4.kh jg sa; ng frequency of brand X.    kHz

  A guitar string produces 4 beats/sen;u u5h vh8,j when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your re, hn58jhe ;uuvasoning.    Hz

  Two violin strings are tuned to the same fam q z6ph0:jg;requency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hj:0g pam; qz6hint: Recall Eq. 11–13.]    Hz

  How many beats will be 4+vjqrs x4 cr0 bs.7d5i0btgkheard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C aq70g drv4xibst kb. jc40sr+5 nd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 44 q7oxechn5:3 c1 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is c5oh:x q7nc3e4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from onej:zdc ;1woi.qc6qm 6s speaker and 3.50 m from ts6c; zd :j.wo qm6icq1he other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 *a50lhn9r l6zkyrj3 /1suyx4kva , wz Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the y1 jak hxn3ru wz,ks4yrz 6l/59a*vl0other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How mada qv4k /.e 3oup;s2drny beats per second43/ oa2sekd;r qdpv. u will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire.lj3qpjl(+(;s a.zserd wh3 x engine’s siren is 1550 Hz when at rest. What frequency dqjhz 3.. l(ad; 3xs(+lwr sejpo you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a firlqf8h jn6q4 :q: jsu u-l0u1ine engine whose siren emits at 1550 Hz movn8:usnl-hq qjiq41u6:jf 0u les at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you at 1d (f5df3ce3d m5 m/s versus you moving toward it at 15 m/s Are the two frequencies e5(d3d3c emdffxactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped wih.kt:y :o(a-uk1 nbm:ruvt9eth the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency (h1 vk uamyt:btro: :.9eku-nof 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.; dy:1 h;rkfp aad lmj*)cz2 xix83ov;0 kHz and receives them returned from an object movi;i f z;x*:)crdhko28jxdp 1 alamv 3y;ng directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wal:jxzf ;m/o g2 n02gntd+ pm3nql at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frdn3t g2 ;/:njqm xn20pfm +zogequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubay7s2dku/ 0yy m-yf b1e was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency wasby7yu10s d yf2-/y mek heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppos/ isvs 3*i6rdumx2ff6o5j- ea e the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s Wha fs 23v d6six6 f-j*iaoemru5/t is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wavewypc8a 8y/q2x s of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hhnok9)sy:zejeod 2 zp4;gy ;5z. When the wind velocity is 12 y4s; n92y:gozde z;ehp j5k) om/s from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land86gb,djc/*ocosscb/ijvs ba76b- 0mbz 3h 7e if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the sped+rw+96kb6, ogcat dzed of sound is 310 m/s (a) What is the angle the shock wave ma++, wo 9dtkbgd cr66azkes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of soun*jw0fa*lt yb*m2ocry j8xk 01u t-pe.d is only about 1t 8yco a*.r-um*pj20* jyflxbk0wte35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling .b;*w b)-)d fbmakcf 1 lvx,sr8500 m/s strikes the ocean. Determine the shock wave angle it produ*-mr )k;,bfad) c1.bbslwxvfces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle qmc)vsiief qp9 j 42czw5g7e )vo649e$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a vo) q7plndz kzp- 4rpy3ms)/fo7m dk g+5s 97qplane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distancep 3md/dsgko -)l7kvqpr 4 mqpfzo7y n+ 5)7sz9 of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound p0c39q*roe trymm;bzexr -kl6) 4mj2 mulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minir 94t 3;)*e0mbm m6q zcylkerjromx2-mum time between pulses (in fresh water)?    s

  Approximately how many octaves are23fpkoiv9 3i e there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a s+zxk, sm0rs b mv4t2qa5- i2zkewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. z42m bvqt,izm0skskr2- + x5a
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to t1is3ivdcq.,v1kob q0t4iuk ,he threshold of human hearing (0 dB). Wcib3 dtuivskq1qo 4.0 v ,,ki1hat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB so2 x wzd(x n lugqw 2r7qpiy;)g-qfp-02und are heard u 2xqq--gdiw0lz2x7g)fnpp( 2;r qyw simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. ;oq.mh7vh/af2b b84bm:njya 6mu f9n:d 3 vhsWhat is .o haajmnm 2/u:v94h bym6n f;bv73sqh:fb 8 dthe acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rjk 8hbs.mn :tz9lujc.4u- r2q ated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz?-2qz.cun hrjt48. sjlk9 : mub    dB

  Workers around jet aircraft typically wear protective devices overhu)d-t5t q rk 44og*ps their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m fo-sq4tp5 4)d g*ht rukrom a jet airplane engine?    W

  In audio and communicationspw+0z8ks3 l l5dl*7bw44tvve 8v ik sh systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frepr +ow(.uuwf+x z/3guquency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violip9yxml ek r +d4 cik5 0f),2uhnti*g0tn is 32 cm long between fixed points with a fundamental frequency of 440 Hz a4lkethkm002* ,ictuf+gxd5 n i)r 9py nd a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fi2: dyenhf1( hgdzo7 +alled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonataeh(od7h2 g + 1fyn:zde with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a b 8qfah:7(6ftat*owl tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamea fa:8 l7qo*b(f 6ttwhntal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop (9cv a zf:+6f-ytfmrsk044u bl$\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in 6 ukv,6glt*6xk yv6t(igy.c fc 3s7ydthe 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency i si y67 uvvcxt6.kf,gg(k6dy*3 ctyl6s, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Onepi/w8r 8 hhbg9ss5.ge train is stationary. The conductor on the stpebwghh i9s rs.8g/8 5ationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. ; 1asur+vvqr-; 6qiee After it passes you, ;ar;v-sq q6ue+vr 1 eiits frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimq i 2c*tdl5(onate the speed of cars just by listening to the difference 2(nql*to cdi5 in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding to6* ,ies-pk0b dh*zs ,lbqhil3 gether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How longkbib ,3ph,ssl dheq* *i0-zl6 is the other?    m

Two loudspeakers are at oppos(;bmj2dybfc,m0ej o 3ite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) hcj3,;bojed 2(b 0m ymfe listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood2 0,twud w;zo*e pt0 :*byqsez flow in the aorta is normally about 0.32 m/s what beat frequency wouls ;0ypot*we*z:d te0quzb2 w, d you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward thej- v3ms(-c 1w rzqayf,;,rtza bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the w zs;1-qv- awjtymrfcr,az, (3ave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequdcd9caadsa;fh x6 za9*y5+ ;dency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected b +99dd *ad;cxza6asa5 h;ycf dy the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine v4f/as 5o5wj ya n*fwz9illage to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the f a/n5wa9 jw54fsyzo *overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the p1xq, xqhimpso bq89*-resence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room bqo918x,shq pi*-qm x.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rodoa4xfk+tbd wvc; n;yw(dmb 7. fwj-82 s,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. ;+.ajxbybwvd dwm ;2nw4f7ktc8(f- o For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a freque*2 x;y*l:/frib6uib sq ecm2 oncy of about 1000 Hz is ;m 6e *l2/:2cy*sfbixiur qob$I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observuy,) glo72y z5i*9yal g9zxyser on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Wha l og9xgyly75zuz9*yyi2a) s, t is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 1dxudk7 0tnc9$^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h