What is the evidence that sound travelz v8agka a8o13uw (bylux.2z.s as a wave?

What is the evidence that sound is a form of .c p-mgckjy85 h,4a beenergy?

Children sometimes play with a homemade “teh-n;0/6o pcof ir( gpyymg *n8lephone” by attaching a string to the bottoms of two 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 trave80 -rfgi* cgnyhp yo;pnm/6o(ls from one cup to the other.

When a sound wave passes from air into w9d30i+) :sgows u.r+imj k gjgater, do you expect the frequency or wavele+ w0ori g ju9g.k+3s:js)idg mngth to change?

What evidence can you give that the speed of sound in aibt5 lx9: en sco4h-mr,r does not depend significantly onblho-sec,49mt:x r5n frequency?

The voice of a person who has inhaled hel pw +qenq)0 yh6j je39bwep2x:ium sounds very high-pitched. Why?

How will the air temperature in a room a8.zm:ec0oz raffect the pitch of organ pipes?

Explain how a tube might be used asie2jrm q,*dh7cz*f ( b a filter to reduce the amplitude of sounds in various eiqjrb, 72f*c *(mhzdfrequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig.us;2p l +hnbd 2cb+d*j0a,gqa0ah *oq 12–30) spaced closer together as you move up the fingerbq b+*a,d+0d a2 ;hsoujqh0bgpc*2al noard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it bvms8n 8( ;n1cde(dfck ut cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffractiofn 1n8v c(dk;(se8cd mn.]

Standing waves can be said to be due to “interference in space,” whereas zw*7 r5)+6nrad:3 triddgsio beats can be said to be3d* ir or:i7 t6+)zagd5rdwns due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speak n2bf0d9rr550tnx h kxers were lowered, would the points D and C (where def9nb02k5rn ht dxrx50structive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting;o ;o0gsfvmi 5l)gk ui jtx38* the hearing of people who work in areas with very 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, inver8go0;5i*i st;kful3mgovjx)ts 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. 12–37s/xa;8/pgpd kogus 0 1. Each wave can be thought of as a superpos ossk0x /; pp7g/8agduition of two sound waves with slightly different 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 7)/c7l4poirsmdjh) omove in the same direction, with the same i7j)lp rs/4 7) doochmvelocity? Explain.

If a wind is blowing, will this alter the frequency of ohi;ok ay6+ z8lvvm/hzjd (9 5the sound heard by a person at rest with respect to the source? Is the wavelelk ojaio+; v (zh/z6d m95vyh8ngth or velocity changed?

Figure 12–32 shows various poe t z2p+ih0hhz;jty -u 9+ydu-o kl*x)f7zqv 2sitions of a child in motion 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 whisth0y y2 f2 u++zuhqv;7tjk l- *-xoizedh )9ztple? Explain your reasoning.

  A hiker determines the length of a lapb*ap, x(q 5qc5oh1o+i kun2wke by listening for the echo of her shout reflected by a cliff at the far end of tp5ouwpixa o( 1bn2,5c *hq q+khe lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of h9kms4 *vblpaq pp*/0 s: ib+uvis ship just below the waterline. He hears the echo of the sound reflelppvp *vsqi4b* kb0+ ua 9m:/scted 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 24+snx 6mh8i vz0 $^{\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 sc v-*zsgusud , -7eyh:shool 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) by the fs,gss e7dvu*- u:hz- yish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a)0pw9v ncsl6v cliff. The splash it makes when striking the water belowv vp9wnsc6)l 0 is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge sto g.qrf jb;: 10m3kyllvne strike the concrete pavement. A moment later .k1b jv: f ;r3lq0glmytwo sounds are heard from the impact: 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 erhvrv nvno9793 .vt6vi*a0htsror made over one mile of distance by the “5-second rule” for estimating the distance fro 03vvv*ns 9htt9hvri. ov n6a7m a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain le 4fy7nw ;2,qp-oseab vvel 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 hgs+9 myu1gx .rwwl 82sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when0t(arw5aq;m, nzg7 kwae m (rf:bxn+9 fired simultaneously at a certain place, what will be the sound level if only one is expla x,w5n:zar(t9b m k0e(r7nmqwf;+ag oded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane witfjk3. ncd 1fkp*3p4geh four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [H3*d1fkcjngkp 3. pef4 int: Add intensities, not dB’s.]    dB

  A cassette player is sa:hr,d5u scj6wl pz3;hryo ,0bid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities z; o y0shh5 rdwu jcp,:3lbr6,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 speaki us:. c2y: qlobk (dx3qf,r7zjng in normal conversation. Use Table 12–2. Assume the sound sqcsb7z y:x2 rlqkfdj:o u3.,(preads 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 st 2,0d lwfnwo-u.t d5(u4ak fyqrikes 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 ad5r62w, r7 gtwo-qycemt,. f+/xyyj rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a lou-xe,t 2rao /yfd,w+gtq 6r.m 7wjyc5ydspeaker 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 registered 130 dB when placed 2.8 ny 57svhw5j3vf e(jg3 m in front of a loudspeaker gvwy7e j (sn535v f3jhon 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 d,1 oz8qtre qpdp+nd+o,o(70 hsyh5 saetect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this am( q o7 z,+ohser1p,a 0pd5h8 ns+yoqtdount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (aak;f9t9jmvyy7;mia u(o 0v u)) by what factor will the intensity increase? Increase by a j ot a;uyu)av0mf(7;mv9 9ykifactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eqpvq )kc8z, u jf0)jdy i05yiu*ual displacement amplitudes, but one has twice the frequency of the other. Whatfd j*c8kj 5, )ziui0p)qyvyu0 is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspo60 :a+kd) hivw nazd7hnds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 hw)+ha daz0:i dv76nkHz?    dB

  A 6000-Hz tone must have what sound leo2hvzyfq w 5pu7gh0;)vel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12wh)gh2qz;o5p y0uv 7f –6.)    dB

What are the lowest and 1b0 5sg3sgf+d 2aha gphighest frequencies that an ear can detect when the sound level is 30 dB? ( 2s3s b+g05a1hgpgfadSee Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels.ku7zjvc 2 8 p1b9ea8ec What is the ratio of highest to lo98zce 7k 1ju82bceapvwest 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 ofeu*bm xcs w;6:aw k,5z 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Und6amzeu w x *s;5wcb,k:er what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental andxo2scgidze x--5 + x: pdl-5z9lw;gyj first three audible overtones if the pipi sj-olz:g yglw+xzd x9d;c2p5x --e5 e 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 wo/5trg3,nw 45tscgyioqcn4; puld you expect from blowing across the top of an empty soda bottle tt 4 5wg/tying 5 ;on,s3pcq4crhat 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 rang*6- xhhdta* iqe of human hea6*iqha* x-d htring (20 Hz to 20 kHz), what 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 oyv-jol:lp-wlj, wl g mnl(ee; 8z81 r3t7a; ja frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original -wvg z:lllnpa78-j w18ye (jto,ol 3lm;r;j elength?   Hz

  An unfingered guitar string is 0.73 m long and is tuned kp1 n)+gt0jscto play E above middle C (cngsj )kp0t1+330 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 lenh tld7au: mzl.p 2fp.6.t1yuugth of an open organ pipe that emits middle C (262 Hz) when th2p. u 6. p7f.hd tlumt1ya:zlue 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 a c4c24.()ss8afz3 fzxuvms dgt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of tfz6q3i xy2 ,g1rx:oimhe flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz? oxi: gy,qxz m3fi1r26   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 reso0-bz (aobm r u8hjk - )f(8rb(omlwj;lnate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (akubmlajh ;8 rjo mrb (f)(o(b-zwl-80) 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 ends. It resonates at two suvj1py-m:*vp dq .adk.xb7. uxkahl 5 .ccessive harmddvlpp.j.*xqm :aab17k.hx k5 . vyu-onics 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 4swib+ ba-ll/at) y3r$^{\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 present within the audible range for a 2.14-a++p6/60 9i7sspht)l wpg/ xn dmf q w2aic5dkm-long organ pipe at s iw/k/w52h +ap0q7nptc p +6)mdxg6ld fa9is20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lolmr3b7 lhswv;8u5:f png. It is open to the outside and is closed at thhsmrbf w:7 lluv ;385pe 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 2.0 s when trying to adjust two strings, one7a:8(d jabg: hjf l1mu of aajbjd u(lhf:m:8 71gwhich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (f,ndau k2or- 1262 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 another (brand X) operates at2e+xr ijr:j6 k an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz +:rj 6jix 2erkoccurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz+e-c 6utv0:bhb, b oow;mkogz/ : ;xcc tuning fork and 9 beats/s when sounded;,ozgccev+; :c -:w 0xkou/tmbo6b hb with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are dhd2+e0g 2og e0qtgwar 9r2ye;n/ri.tuned to the same frequency, 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? [Hint: Recall 2 degdg09.aqgey2e r+it/rr0wh 2;on Eq. 11–13.]    Hz

  How many beats will be heard if two identical fluted.n/lby8 yh;d3iet4wjj ( sr*s each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25j.e( ;ilnd/sb yd*4rh83 ywtj.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of5h3 zgd)b00)hsajb/sf x eb+d 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz zbb/e+js )035agf dbd hxh0)s 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 person st0gpw3/em hfirjtp 3:5ufw)9cands 3.00 m from one speaker and 3.50 mw p pc 3i9h0)tgf:w 5urfej3m/ from 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 lv*v*zlgc;bt -:vvm/ vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when theyt;l-vg:/m *vlz b *cvv are played together. (a) If one is vibrating 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 86pjpl (rq+gmm and 2.76 m in air. How many beats per second will be heard? (Ap j 6(pmq+r8glssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at 0,w cj+e .j+g5/eidroy na-u+lh:hj orest. What frequency do you detect ifr: eo.hjudgjc o-l+y 0 j,e+anih5/w+ 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 fire enginkib d4)4ug94bowk0(a8ro)upp ( txuq e whose siren emits at 1550 Hz moves at a speed of 329ikp 4 b)wa0ux(48ouq() r bd4gpkuto m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shiftkt7ez:g w ,3xk in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are th zgkx,we3tk7:e 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. When o gctg7yxqg9m-4mh 1s, ne is at ret-c,q hysx7 914gggm mst and the other is moving toward the first 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 sound waves at2bclrdg f(9u. 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received soun9gbfd ru( lc2.d frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/pumb-1er l(nt96/y ixs As it flies, the bat emits an ultrasonic sound wave with fmlxnt yu1b-6(9rei p/requency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments,ig sczj(-q ,1l a tuba 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 g ,i1cz (qjsl-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 ultrat+fr/e3wj ;d4ck*g6hei o v+ dsound 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 expected beat frequency if blood is flowing *3gv4 hitd+ec+wo ;d6fje/kr in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using )pgtb3wwvq.rhy 5k-v:c 1 )h5f 9iidcultrasonic waves 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 fre cw9nk:-;oo j-sk lzqs yokcl/5fl/8 *quency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are los c/l5k-- ock k8n:sq9w;lj ylzo*f o/cated, 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 landgdfobg d x;,*9 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 speed of sound i: fet+c6 d354dwhvr*k1rezets 310 m/s (a) What is the angle the shock wave makes with the direction of tht4:t3 6refvrw*e +cdh1e z k5de 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 z3mestw7+lyw3 f.4j lspeed of sound is only awf4 +z l3yljs em37tw.bout 35 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 8500 m/s sbpx-yxbzp*f+jg 1w.;rhg+a;42 t d mbtrikes the ocean. Determine the shock wave angle it prodambg ; ;r+gdx21.zbh+pp bx4t- wfjy* uces
(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 tj -(si 8 q4dio1ecivx2b)j-z$/theta$ 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 exactly 1.5 km above the ground f*77aqy7m5 k xvrro, )v2ulewq 1snze2 lying faster than the speed of sound. By the time you hear the sonic boom, esx,qv ulr1 5y 72aervn*o7qk2 )7 mzwthe plane 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 that sends 20,whw6sexjd 9b( 0jdp3r;f:)e z000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the max(j e x hp0: wwsr63defdbj9;z)imum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octvvp(qn47q m rekxdy;8:xx a)0 aves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists ooruc)m bf2j+ ;f many plastic pipes cmr;b 2f+)juoof 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 the thresholdmbrwyfk.m 776 of human hearing (mkf677byw.mr 0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound a6 jf5jx1 + d:vdjl/muxnd an 87-dB sound are heardjjmj5 /fv +d: lx16uxd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whano: d :qki8i/ot is the acoustic power output (W) of the speaker, assumin8d kiqoin /:o:g it radiates equally in all directions?    W

  A stereo amplifier is rated t475m0k ogo3 ykw)ax71lvvpd at 150 W output at 1000 Hz. The power output drops by 10 dB at 177tvko 0pyo gl3v w4d51am kx)5 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears.x 3m8ktp (3uc gpf(nov+d,t7e 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 re kt3ufv8( pg3 ,m7tocxdp( n+adius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sy;. .bodj6y veze,n7tyw2yw 1 qstems, 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 freqwu ,;fzqprd ) 3i:9bnaeus29 wuency 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 l vrm, 7kp8p6ahong between fixed points with a fundamental frequency of6 mpa,8 rphk7v 440 Hz and 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 zxr ,as6+,h.a uoh.ccinto vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the aiz .h ,x6.shou+a ,cacrr in the tube above the water level is heard to 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 2.10 g is near a 9s (dsc12iysi 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(is 2i1ds ysc9) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed p2qp(l+ 35r ;fuyizjhto resonate as one 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 500–1000-Hz range commxo-ql2 e4rj y f;wi7(ing from two sources. The sound is loudest at points equidistant from the two sources. oj2q eiwxmf;l4(y 7r- 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 whistles. One train is stationary.n( 7 oveay,y(i The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. W,(oany e7( ivyhat is the speed of the moving train?   m/s

  The frequency of a steam train whistle a5o*:q x+f b2zcsb5fxm s it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. Hcfzox* 52 xm s+f:qbb5ow fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimatqi+/qnb;gjs dj/--yt e the speed of cars just by listening to the difference 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 straigqn-itbsjyqd;/g j -+/ htaway. How fast is it going?    m/s

  Two open organ pipes, soundin+t3ka7fh 7u) 5s yecnyrr7a:tg together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long.kcnt 7:s7+ a u5r7h3ft )ayrye How long is the other?    m

Two loudspeakers are at opposite end,fiu y,a(ly*ds 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 wheyl,u, i(*dafy n (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 beatceu/2o1hbhi -s*v*a a frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Aeu* 1*b ah2/hcivs-o 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 yrd )h 3wfd4*al9mm:a the bat a9m3lya:d)4* dr fawm ht speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approoxpjmq(vq , e.rfi *29aches a moth. The pulses are approximately 70.0 ms apart, and eari (p,2*joveq f9m.qxch 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 emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from oncg d;lt9g:/ u;dvf6 m4y:owbe e Alpine village g6wbmgu: vfcdy; e: dlto;/94 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 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 prese(2n 2.x6b hmj, 8v1ojcyy bxipnce of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, b2ihxjj.pbv2yo 86m c (y, x1n4.0 m wide, and 2.8 m high. Calculate 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, slendehoah(-3 *rws.zf+azfr 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 “singofa*aw. h fs+zh3rz( -,” or emit a clear, loud, ringing sound. 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 hearinnw3nqp 1 im/kh0. ;.b-ilzqjc( lrj v kr:(,ycg for the human ear at a frequency of abou 1mcqlkkn,r:c. i /q 0(byp3l-hjzi( ;jrwn.vt 1000 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 observer on the ground ht1f n j.esj8:mears the sonic boom 1.5 min afterftm1.8jnjse : the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbog60bm .sa d/rzat 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