What is the evidence that sound travels as a wavv:nh ) g7waf;kbpqf6;h9cy5w e?

What is the evidence that znzuhp 6 g8d9s, fkk(e2,4fccsound is a form of energy?

Children sometimes play with a homemade “telephone” b 5ovyvdyy(n:t :lz8r1 y attaching a string to the bottoms of t ry(zy85:1y vlo: tndvwo paper cups. When the string is stretched and 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, up88 ek +at3rpdo you expect the frequency or wavelength to chang8e+urapk t 38pe?

What evidence can you give that the speed of soosxqa p)3qn9ppyc dl,u g; /7/und in air does not depend significantly on frsu aq qc/xg,9po7pdy npl3 ;/)equency?

The voice of a person who has inhaled helium sounds c6g0w*2 egll(/ e4km x.zwcz fvery high-pitched. Why?

How will the air temperature in a room af7()9vk9n 6, u x)ck hjlmogofsfect the pitch of organ pipes?

Explain how a tube might be used as a filter jzdi1f /oj ,g-to reduce the amplitude of sounds in various frequency ranges. (An example is a car mufj-o, /dgfjiz1 fler.)

Why are the frets on a guitn*wlyss 38 ft32igy)cg,wmb/r )zt. tar (Fig. 12–30) spaced closer together as you move up the fingerboarmg/tl.gs8w3yi, f ysn3*zt ) wb)2tr cd toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it bu je1 ;nd0ptvoj7yg* -qt cannot see it. When it emerges and you7o egnt0q*j -dy vp1;j do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beatfs(a3 q(yu /nis can be said to be due to “interference in tqf/nu(ys( 3 aiime.” Explain.

In Fig. 12–16, if the frequency of the speakers were lom ojl3n 2u1x5cwered, would the points D and C (where destructive and constructive interference occur) move farther apart or mj32 1x 5onclucloser together?

Traditional methods of protecting the hearing of people who work in areas with v(jz xz,bihal4d9 3 +ekery high noise levels have consisted mainly of efforts to block or reduce noise levels. 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 additaj (z9l4eb,k+x hdiz3ion to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves nf-cryi ( zw0w1/ j +)enktad/xvin53shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fiz y-knfw wv/5ninec+d01tj ix )/ra3(g. 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 qq7o9) 0x*irpm jz-*usib- hgobserver move in the same direction, with the same velocity? Explai * mpujo 0i7ghrsqib-* 9zq-)xn.

If a wind is blowing, will this alter the frequency of the sound heard bym(n6as017b (k pxaoqe . x;/8xyhqhrh a person at rest with respect to the source? Is the wavq y/saaq1h.h ;( x60 phbe7xoxn(8kmrelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mozwtr2nib 7fx, giv+2pf m2j+ +nitor is blowing a whistle in front of the child on the ground. At wh+gb22 rf7jtzi2m ix +,fnpw+v ich position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lakot8 s dkb5l/m(ea61b.smfr .- g)bgbde 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 afrmal . 851d/g bk bb) t.bo(md-g6fsester shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlineo gr1 rhpg(()t. 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 ther(h( r1g)togp speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavevc: tt6tq hh8/e aga nv;+oh7*lengths in air at 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 is drifting just above a school of tuna on a f ;)uefv / qn1c0zhrah)5zg(uuoggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–/han )ef u)qr0zh5;uv(uz1gc33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliffk9 ;8sl;gtqls+p / ckn. The splash it makes when striking the water below is heard 3.5 s later. /q9kln;+sstl8c ; kpgHow high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike thtp jfmtiup*/ od7:s--e concrete pavement. A moment later two sounds are heard from the impactfo:t 7mdt p/i-pj-u*s: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one micg.xm:10ysu qp (o;1fth ojg,le of distance by the “5-second rule” for estimating the distance from a lightning strike if thgj.uho ;p m fco(g:10qyst x1,e temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound zh iu0hj,)/lxyf 0 1umt,hw4 fat the 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 intensity m4h-f /(nrx 8v jltrg4is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soundbm mf wjmyz/y8eq z. vn503nyu63:*he level of 95 dB when fired simultaneously at a certain place, what will be the sound level if:ymnjhb*f8numev.yy 33/5m e 06wzq z only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airp 9e;ytrg/8ky lcnmfeu)p2:p, lane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound lever/9l p):mtekyuc ,ge ;pyn f82l would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hhaa5zm6durls 3 t x+/.ave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of int56st/hzu+axa d3.r lmensities 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 a person speaking )b9lnm3ko icvvwy ,xg6/: as +in normal conversation. Use Table 12–2. Assumg9,lw:s by xv3/o+ kma) 6cvnie the sound 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 strikes an eardrum whose are6 3o9cn ;k s7dhesoqx5a 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 mode ovy8d+bhdz q)hl8 ,u3st amplifier B is rated at 8bh8+odyu 3,d qzhvl)40 W. (a) Estimate the sound level in decibels 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 registered9nj 9c qd/uyv9g6xp; v 130 dB when placed 2.8 m in front of a loudspeaker on the st /p ducynxjg; 6999vvqage.
(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 detect a difference in sound level of 2.0 dB. Wce,6 mffumb+f3gw9z*b u3mh v9 fqw4 7hat is the ratiomff6b* bmu93cghe vwqf,7z+u9 3mfw 4 of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fp jy o7c1l0-c mhoeq:,80uaspactor will the intensity increase? Increasyp j -a co7h1u:esmq08lc,0poe 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 fretw5it. 1exzj; 5 zek-hquencyz1ix5.jh;z twt5-ek e of the other. What is the ratio of their intensities?   

  What would be the sound5 xe7zs/-tpxpt 8v53kf42 b:fovvzzw level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 m5 e7zx 8zff3 p-ovsw/4ptvv:2 btzxk5 m at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loudv8et h/l d35rc/wx p*qwq 09vmm8pw*x as a 100-Hz tone that has a 50-dB 59cqlw3epv/hw/q 0 m8dwx *8m xr*tpvsound level? (See Fig. 12–6.)    dB

What are the lowest and highest lwp2)(oy odx;v6m: anpw3tz: frequencies that an ear can detect when the sound level i(l mo 3dy)wat nzw6:;pvoxp:2s 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge oix7h; fqv fz r:)w bo 89)y;*/xaeblz u4*iuerange of sound levels. What is the ratio;x v buiaez)) o* we/u;*io8f:blxfhr9qy47 z 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 fuq(1e58c*qiaq- *- d e vqejuhbndamental frequency of 440 Hz. The length of the vibrating portion isd*u-c1 eeq*jqvqh-a5 8bqi( e 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 ck.z6g )jz me+kdp/e +f*w1tlim long. What are the fundamental and first three audible overtones*ekg+ l6f)m p w.t je+1/kzzdi if the pipe 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 the top o0v lbq0p rie+-f an empq-pei00 b rvl+ty soda bottle 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 of.*xn+ d,p6f 0jn gasdw human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requ 0fsw ,.* nj+npd6gxdaired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as 3+6 m4ea)b;opeo um laits third harmonic. What will be its fundamental frequency if it lep+6 ea a3m ;mou4)obis fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is t 0jh6 dbzg-k6quned to play E above middle C (330 Hz). zqd 0gkbj6 -h6
(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 pipe that emits middlonit g zd-4(f5w j3xz1e C (262 Hz) when the temperaturj 3xf5t-w 4(d1oizng ze 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 a 0 q8;06 w1n cx.qzvhc*minjbqt 20 $^{\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 should the hole bemfb zfiomh:5u6x1 6 +s that must :z 66i ms +1huxoffb5mbe uncovered to play D 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 can resonate at 264 Hz, 440 Hz,eelass+n* )i2 ib265 eae ad,l.ht0ul and 616 Hz, but not at any other frequencies in between. (a) Shsah2+.i i6)e* tlebl2aa ,u50 edselnow 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 ends. It resonazgd hjqg3+ d vc+to4*v.2(xif tes at two successive harmonics of v +jgdhgq(o+f.4zd3 t*c2ivxfrequencies 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 1 3thcx(fjwiz p7e 3.r$^{\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 presen ywuv/5qy6(bho 8wu0t t within the audible range for a 2.14-m-long organ pip/y w5 o uwbhuvt8q(y60e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm h wtkbq7 +4d4e baud.-s9ob)tlong. It is open to the outside and is closbk-ads.hwdte+4uo 9b)7 q4b ted at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. 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 ou;:) z79e dp enxqb1/u* piup2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the otiu1 *podzp/9b7)x;: une uqe pher string? ±    Hz

  What is the beat frequencyb1 ;8 j9cr8wy jz4zqgg if 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 23.5 kHz, while ane(tq/ x1 +nd)n xic:kk0m)7*ukxhx n/ 6ooizfother (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 1x*/o +mk0ex /)kqktcoznx( id6n7f xh:)ni uwhen they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4.91bwxg0hiw5g96jbm 2iy x dn beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded 6mwxg bxb y25h9j1 ii0wgn.9d with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensifv2yf ;rd5yri e;u,/pdzzg+ skyw(,7 on in one string;ffe,57zs, r(/gry 2dk;vy+dui wy pz is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to placei34j lm *c57j.)edq qcqan( y middle C (262 Hz), but one is at 5.0°C and the ot37ejeaci)lqq5 q c m(n.c*jd4 her at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; whendj45;; mna etv A and B are sounded togethe ;t;dav4jen5m r, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 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 6 bs:9:uvbnbrperson stands 3.00 m from one speaker and 3.50 m frob v:b9r:nusb 6m the 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 vibratindgr: +h7icn62 nat5wv g at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is v+nri6g7v5h2aw n t:cdibrating at 132 Hz, what must be the frequency of the other ?   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 an vg) ;qcs osouke,dgj1c0l6 1)d 2.76 m in air. How many beats per second will be heard? (elc1s)gdqu g j6cs)o01kv,o;Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of aq/7qfnys6 o.v; dteh/ certain fire engine’s siren is 1550 Hz when at rest. Whano7yqs;tdfv/ hq/.6 et frequency do 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. Whqpno s3,em 97r -ozxa4at frequency do you detect if a fire engine whose siren mo nxpez9a ,o 3q7r-s4emits at 1550 Hz moves 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-zaqx1nn30 wce8.e1hf -kzxe 2 Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/.w3 c 8zz1an-2qenxxef0hk1 es Are the two frequencies exactly 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 with the same single frequency horn. dh x6kn*zsa :*o0dm*bWhen one is at rest and the other is moving toward the fir6 d*z:0 h kao*xnbdm*sst at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sounw+f: 5 q+fdxuhd waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequenc+duqfh5 x:fw +y?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 mn iozf g.x(- q+0pbv5x/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in z p5. oiq+nxf(bgx0v-the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, qhp peag5jr h;.v;x0 u l09w7qa tuba was played on a moving flat train car at a frequency of 75 Hz,vpu;lgwqhh0p795ex j0 ;rq .a and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ulo3sevzmox s*d5 kp/,dzd. ) 2ae3/yu mtrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expecuo*/a.d e3d ,)xm5epvzo3k s2dzys/mted 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 wau vzan .:sp,3nves 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 570t:a1 aus(/fhpz,,wvb 9bp p i8 Hz. When the wind velocity is 12 m/s from the north, what frequenc8,us1z fbt/p: b9 a(hwiv,appy 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 land i7d,rzf g3rpu 5f 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 :)mc;iy47o w og; xqtmbzl+wz:g50yqMach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock gmotxi cy);05 7:;q4w bl g:z wzyq+omwave makes 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 s,cj1r*z w23drh3 wmhypeed of sound is only about 35 hwc12rrd 3hj*ymw ,3zm/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 8500 m/s svc 68/siw x/zttrikes the ocean. Determine the shock wave angle it produces x86vz/sc/twi
(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 z192bh 86nrutvyqzo 9$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane e,5ksc/v f hgs2xactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the , g/fhsskc 52vplane has traveled a horizontal distance 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 zj-axu*hz 6y+that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to wo*za +6y juhzx-rk is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in*b f9(wvrt) z xtitj-(e+7gwu the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe syq:*-dc +xw5le bozn5lmphony. It consists of many plastic pi -5 : l5wzqdxob+*ecnlpes of various lengths, which are open on both ends.
(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 k zhtg3f,n7xu c3f bon)3rr(: the threshold of human hearing (0 dB). What wi() b3 3tfk3gxf,r :crohnzu7n ll be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 8egp-e7;l k pm52-dB sound and an 87-dB sound are heard simue ;5g7plmpk-eltaneously?    dB

  The sound level 12.0 m dd7p1r/m3py musq(b 4from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions? pud13mm/rqb y(4 pd s7   W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pow8 , ct;eko :1n;y5x leup+peqfer output drops by 10 dB at 15 kHz. What is the pok eopxeu5+:l ct, ; n;yf1p8eqwer output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over theiywz i-b p c.2 z,.hhkod):mkk-r 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. Wzbkohypm.d -c.kwi kh - z:2),hat would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatioe1f;qcpn20 u1osm*gm s7i h; pns 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 frequencz xet7( vg)8 sd6/n;npcwvbl;y 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 violin is 32 cm long between fixed points with a st9 :zob(bw*: inn0sazuiq gs.)3g,f fundamental frequency of 440 Hz and a mass perntg)qs:9*iz,z of .:as0i3g n wbu(sb 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 filled with wate zkckah22s g) wxw(u-0r (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 z-2au ( )kkwc xg2w0shto resonate 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 2xo8*j zvl:i +, p3aqsw.10 g is near a 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 fundamental mode) with the t a8svxpw,q z+3oji*l :hird harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as ok):g w1x6q e6o,qnz6mra r+dpitf3f2ne full loop ($\frac{1}{2}\lambda$) 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 the 5tt t 1jmk76:4b ub3ine00–1000-Hz range coming from two sources. The sound is loudest at points equidistant k76b b j43 t1:ntmeitufrom the two sources. To determine exactly what the frequency is, 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 b)j x:9ml bzru9g we(z 4*rj5jwhistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the mol(j:5ruxebb4jmz) 9* gj r z9wving train?   m/s

  The frequency of a steam train whistle as it approachk1s6gq -ca5k i9 ltnahn+0*zn es you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant vetn hak10in-+cz*5kn96q alg slocity)?    m/s

  At a race track, you can estimate the speed ofl t;8ccf2pn kw- trx ,vkp08rz4hm8,z cars just by listening to the difference in pitch of the engine noise between approachingth 8cnxt2 p0clm,v4;kf rkzrz8p,8w- 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 together, produce a beat fren 6-ljrvd1v+c8l yj b/quency of 11 Hz. The shorter one is 2.40 m long. How lonl jc+ rvl81-j/by ndv6g is the other?    m

Two loudspeakers are at opposite ends of a railroad l+mnkg y r 4lto4gcx3w2la7f/h:)x5 tcar 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 observewmtaxr4n7 tllkg/lg 3f4)5: +yc hx 2or when (a) he 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 blood flow in the aorta is normally about 0.32 m/s what q6s f2;it4ugs w64 dcfbeat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from 42wc4 q fgd6t6iu;sfsthe 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 theswg054ih;x 3jq .sybd moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is thbdh w.s5ys0 gqj;4ix 3e frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high 7 40zlmow*7rto yj imj)jap;8 frequency 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 by the bat so that the echo from one chirp returns before the next chirp is ej8tyjop7m7w m ;irj)z*l4a o0mitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one6xzx+ peu;.p q5gabn2 Alpine village 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 overtones is resonating. The most ponue 2b6 ;+xp5.gzxqa ppular 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 presence of stan4mxb r+9r*a+ g- xsknxding 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. Csra xrxg 9x*+4b knm+-alculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slenderkxqmejx6jgm ;l((4u 3 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 sg64xe(;q uxm jm ljk(3ound. 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 eardm 8.iw 0ixti5 at a frequency of about 1000 iw.5ti8i0 dmx Hz is $I_0$ = $1 \times10^{12 } W / m^2$ 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 oyft eqwdzik9 bk28)3keh,v-qs7lc8;bserver on the ground hears the sonic boom 1.5 min after the plane passes directly o-k,f t deqq9evyl8)h 2;k 783wcszkbi verhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat: 4t.p*f 6ubyo xfwu8o is 15 $^{\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