What is the evidence thamp d x) 4800awwkyie/kt sound travels as a wave?

What is the evidence that sound is a form of energy-v44xesf pu-t ?

Children sometimes play vq1 8zxu rr7d g45qaa*with a homemade “telephone” by attaching a string to the b a4*1x 7au8vgq5drzrqottoms 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 travels from one cup to the other.

When a sound wave passes from ai o*+5dl.r9 ,w- b5i4a2em;ams cltnzc bujl;jr into water, do you expect the frequency or wavelength to chamruj-2bje4m clsw*;; 9a 5o c.+nt5blz,idalnge?

What evidence can you give that the speed of sound i)tj6eb g:z9dl4 qc rql3.n2 pzwm)en, n air does not depend significantly on freqmzeb34 :ljpn 2t6zr9l, nq)cd) ewqg.uency?

The voice of a person who has inh-.m5iom7d b1 hwz1 y18wkdd zraled helium sounds very high-pitched. Why?

How will the air temperature in a room affy6 ms;vaq awc;a3l5.d4c+k kyect the pitch of organ pipes?

Explain how a tube might be used as a filter to l(;oucj e9+sd reduce the amplitude of sounds in various frequency ranges. (An example is o;ju(9c s +dlea car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you moo4rybk/c*- o5iey huv3 *d/aeve up the fingerboard toward the hae 3rc* dvu eo/b-*k /y45oyibridge?

A noisy truck approaches you from behind a building. Initially+ 9tejt21w-yquxn c* ,c h-(urqk1xyi 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. Explain. [Hint: See Sectkwyqyiu j-u1e+n9*1 ,cxtt h(xr2 -qc ion 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wherea)p g-e)w(/x8x;cippfh r *irps beats can be said to be due to “interferenc h p ppwr-(xxe*fg8pci)r; i/)e in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poi;vo-h z-u uq(tnts D and C (where destructive and constructive interference occur) movt(ohz ;-u q-vue farther apart or closer together?

Traditional methods of f., ypwm(hawdem g /i/s 9-8p(2lz dtnprotecting the hearing of people who work in areas with very high noise levels have colfw, n sd-i(mzdp/( /.pgt ah982m ywensisted 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 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 thoughttawwmi ( npeedn *3,;f8q .;mw of as a superposition of two sound waves with slightly different freq *q3,(pmnwm.e;e;8anf d t wwiuencies, 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 obs8d bt/) lp; 2pvq7tptlerver move in the same direction, with the same8lptbq/t2v tpd7 p; l) velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound hear f8 n-/lilvh9jd by a person at rest with respect to the source? Is the wavelength or velocity changed /-98fjni lhvl?

Figure 12–32 shows various positions of a cabs8kq2 4hc c hc2d+(ihild 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 whistle? Explain your reasoning. +k42cb hc(hia28dqs c

  A hiker determines the length of a bl4n /*oct-lyd)k:qslake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hys:q-*bo l4)ckt/ ndlears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears th gpwosx25d/ )gyo;ae *e echo of the sound reflected from the oceap)ges ;o*d5g ayo2 x/wn 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 smm+j t)q9p7) x8bb5 :1riu mnjxtax2in 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 scho7:w,l,a0l ekj cavu8 z( vice5ol of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). H,ul: v elzwvc(a,ek5c8i a07jow 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 cli/b91sol:z bj 8p0o+c s3;lmkamwsfw5 ff. The splash it makes when striking the water below is heard 3.5 sws3pmlws 5 o ksj/+:cb1 0b 8zfmal9o; later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike thf h- fwqkp8 h;23cs5fde concrete pavement. A moment later two sounds are heard from the impact: one traw85-3;h fhfcf pk2dsq vels 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 mi6knfxem.w lk2g si;f3s800z;p o3. h rbo;igole of distance by the “5-second rule” for estimating the distance from a lightning strike i;ersoo 6;8i2 x3f3 wlogi.kgf.km0;z bnhp 0sf the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at tl -fx wjqm+qwo*1 nh.(:i5 fnohe 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 let x7xurpl9 o8 7:rnqf0e:u5yw vel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soundhuu76wv (7lk1 ke bj6e level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add inteke6w7blj v6uk he(7u1 nsities, not dB’s.]    dB

  A person standing a certain d4 i9gdva8u+skistance from an airplane with 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 engiauk84+dg 9s vine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-t:lt ddu3 c 1*q/hhwnds01 by(do-noise ratio of 58 dB, whereas for an0ld( hy:* dw3sq/ dhu11 dtbc CD player it is 95 dB. 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 a person speng1 pug,dr+ 9jaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uni+j gu9 pd,rg1nformly 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 wh7mefvgbl,/+n a7me )cose 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 )l-e pu6dq x3abicpar:6b3b*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 froarlp:cp b36 i -b36 a)eb*uxdqm 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 regimo 1sg i+9w.ggstered 130 dB when placed 2.8 m in front of a loudspeaker on the1+gso mi9g w.g 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 deuu99j7z f:j;ottu 5detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hz;u f9u5j79 d:utot ejint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what n46nlg ;c)e(hi 5c(vbusvp)n factor will the intensity increa(pc 5 siblv(;n4ch))neug6 nv se? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement aill o b4:ucx;6w-ebkk3b m5-hmplitudes, but one has twice the frequency of the other. What is the ratik-bo 3ecb h4;l:wm 5i-ulx6 bko of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds tsk)2v /;k cbdho k;k)2/hvcb dsa displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seemnz-j 7;mc9f vu as loud as a 100-Hz tone that has a;7-vnc m9fz ju 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencygt wv*e fj8oj;hw8; (ies that an ear can detect when the sound level i;(y h8oew;v8 fjwt* gjs 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rangeussw) 9hb+j6 t 5d)k5z ixx ;5ytz-pte of sound levels. What is the rayzs je5)55;k xszpb)xdu + hw9 6-titttio 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. The length v-jzxxnnfd8gl: (6 k- of the vibrating portion is 32 cm, and it has a mass of (x:-n-zxvdgkn 68lj f 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fdrt1x ,i431h 9hzdgf 4o qvc7nundamental and first three audible overtone g97,df 4t4ozh3v 1chxqrndi 1s 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 expec 2;hfwf5)thq7 k 5.m4xay5 /fg tlztart from blowing across the top of an empty soda bohaxqzl /wt 5ht7ftaf4g5 ) 5f;k.y2 rmttle 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 ww1z ibo mvt5m(51ho3f+:cy9d r1se2pk fhz 0gith open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pr1tz shcd5m 0(+k 2 15 p9: hbovy3f1mizgwfeoipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hlq atpz-y;42dz as its third harmonic. What will be its fundamental freque -ztapdq2y ;l4ncy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above 8 ppuv52;3sig i(,f xfcvy1gu middle C (330 Hzv25iufivpg p; s8c gx1u( ,3fy).
(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 opk+:a* mnr djmuef5;5j en organ pipe that emits middle C (262 Hz) when the temperature i :u mj;en*aj5md+5 rkfs 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 ie,qn.i da// 8jlrm)j:b-kpd20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Examplezlrv 8j+0dy/i 12–10 should the hole be that must be uncovered to play D ab / 0rd8l+zjyviove 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 26 :-64kwvurnsrnn15gn 4 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a clok-5:6 gn1vrsnn w 4unrsed 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., -i+ nm68hxtg8m llfk fj6r:f It resonates at two successive mn+h: f 8tj86-lm kgr6ffxil,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 e8 b /dxwe+wbvd1 vc0+$^{\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-m-longdvqu65zls cip sh9 907+azs ,g organ pip+s7dz5q szah,0p 6 vu9cgli 9se at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is7 ;a y)h5zuelp 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 canal. What is the relationship of z5eylh)pu; 7ayour 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 everlcx6yqn9;q+tp ;jr( i y 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in freq lc9 ryjpx tq+(qni;6;uency is the other string? ±    Hz

  What is the beat frequency if middle C (1s he*x,t (x,x af5ged7ze;xf262 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 aq zv bxg ayxvm6 24w o9-x-e-kh*6nb+pnother (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, estimat- + g4-*-ex6b wvnvpxxo2hzy6 akmb9qe the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork atf1 w3hut u0crf(360u2wuqel nd 9 beats/s when sounded wi wf tweluuu0(3tcr12u0f6hq 3th 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 tensiof9zdzy :0gfvyd q e(, ywsi-* ;st;g7an in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings i(fde,*fqdw: yz ;z;7g9yyts v-as g0are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try t d pjo2maev k*ri:m:;*b* tp5to play middle C (26o5ebpjmm:v2p k t*d*; ri:*a t2 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequ+ia xgvfu1nk a2yv2s,:n 2ehy , 91uddency of 441 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 4 Hz. What are the possible frequencies of A and C? What beat frequencies a va1 k2dny,v +u:9 h122,xdyegfs niuare 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 + ()f ts.mseknar p90lperson stands 3.00 m from one speaker and 3.50 9l(f.nmp st sr)a+ke0m 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 vibrating atgk4o62b xw l(u 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 6xlbu o2g4 w(kHz, 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 and 2.76 m4f 0 f0diehq.x*o(k rsfpmeo r8s7 mzf050+yk in air. How many beats per second will be heymfs os0z0 +mfee f 4krd0xo f*50 7pk(qhi.8rard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cern)vglk,g0x)dytz9w 1 tain fire engine’s siren is 1550 Hz when at rest. What frequency l1z k)0g)nxvyt,9w gddo 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 dete2 rki 7;f ty7cxcu qb3 wpylde:dh4*0+ct if a fire engine whose siren emits at 1550 Hz moves at a speed of 3 r 7eyc7fluxqd* bk0w:c ;h4t2diy3 p+2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is 4cjzvxh7ko 84m3 sak9moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies cm7a483j zh94kovxks 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 oh*lhh0:iku ;;; mj awlne is at rest and the other is molh ai*k;uhwm;0;:jhlving 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 at 50.0iqg-g0g b3o(b m2:xgb x-f-a/sk ,yqh kHz and receives them returned from ano-/bg0 h-bbxgsy(x- aq igf,mk32: g q object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at xg1.o/5kd4.1reqj/ i sunefaa speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with fr gi.a1d /4s ke/j5rqouf.ne 1xequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler ez+h9b f*w/jqpxperiments, 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 the railway station. What beat frequency was heard if the train car approached the s9/ b+hw jfzqp*tation at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speedsse1* burz yg.4. Suppose the device emits sound at usery 1gb *z4.3.5 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 in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using nnram -wa/kpt9y*a 06 i 8-z+egcuw;oultrasonic 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 frequencv3x nw164gai u0 0vmj:wz:uyuy 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hewm6 i3 zgv0n xwuu:jvua4y1 :0ar 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 if sl9vdb2v:v(5j nu u g5its 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 wherejwm: .qe3zgi0 ch;inn-ql.7r the speed of sound is 310 m/s (a) What is the angle the shock wave h;lcne .n7m.3z qi0:g q-rjiwmakes 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 souno t-5x xr1)v2h +g9vk(pppee ed is only about 35 m/s +)vh1g ex9 2-evpp 5pxer(tok
(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 strikes the ocean. Determ7m6gxcc 2)rzjmayj5f+ x m(:nine the shock wave angle it pro 2m:a 5ycfjc7()rz+n6j mgm xxduces
(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 a0tyyu-wva;3hfurl v+2 : c*y $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead t:4r.r2x8qkr 5i+p8l h ks a-i khfdc9and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By tkk. fdli5c+8x 8phs-khr9r :4i t2aq rhe time you hear the sonic boom, the 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 20,000-Hz soundygmdxws(u k;9/t2 gl1jf9 fr/ pulses downward from the bottom of the boat, and then de k1sfj m/w(9 92g;rul/gytfxd tects echoes. If the maximum 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 octaves are there in the human audibl4rrppc8 / v0 ,ksy5zhqe range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pi1ztrz c j v azd2,sw7l0;n2a7(eamq w.pe symphony. It consists of many plastic pipes of various lengths, which are open o 7 n.zma,2sw(2t;a1 jqwe cl0azzr7dv n 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 soundq :dzpy/bb u -wuzs5vq3( 8dd8,ekb. w close to the threshold of human hearing (0 dB). What will be e8y . 3wqdp-zkbds/v5b ub:8 d(zqu,wthe sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sounb-hxa55wbct ca6r 1 .wd are heard simultaneob15cw.wh6a bx5atrc - usly?    dB

  The sound level 12.0 m from acmz)).1 kj rpd-zj h:owl,q,w loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all wj1hjlw-p)mzkd,:qorc z .,) directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hzt ca(n axl-vptb/li y a.p77-lw06p/m. The power output drops by 10 dB at 15 kHz. Whati wll .cmp-t xv(-n/7apb 0/lty67apa is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically weg;i**kdb 4k btw2gi:,of3kt gar protective devices over their ears. Assume that the sound level of a jet gk*i4b*3d;t:wg obi ,gk kt2fairplane 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 from a jet airplane engine?    W

  In audio and communications sy1s:8m fv/ mjdwvc.ag 9stems, 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 tv06qr,p t b9mko a frequency 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 fundaazu .eqwu;h/c-6yuep -0 plv,mental frequenu,qwc-vp 6hza; upel/y0u e-. cy of 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 into vibration above a 2ebc+0ini id*vertical open tube filled 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 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 fren d+i20 ie*cibquency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tub0p yp;0y*hj+r eao; bo(pn3uxe that is open at one end and also 75 cm long. How much tension should be in the string if it is to yxnujor;0 0;pp+*ob yeph(3a produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observvz-sk*s*nuv6q b3no 4ed to 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 coming f 3xcg-txclsyl (,8mbmfw:x:p95 ;gye rom two sources. The sound is loudest at powfmy xmg;,5:txby9g8l slcc-p(x :e 3ints equidistant from 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 whistles. One train is s spqm/ 6p1l9kvtationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the otherpp9q6kl ms1v/ train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches youb*w vk3r;j9c2 )vmd lg jeq-v5 is 538 Hz. After it passes you, its frequen*3-ewld;j vc9q kvg)mj b 52vrcy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can asz9caem9dmrl 6 4r ((estimate the speed of cars just by listening to the diffelcz9r4(m6rsaa (m 9e drence 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 together, produce a beat frequency of 11 H3:r ztmrciwi3 mu m*(4z. The shorter one ir:zcu wt m4(iim33rm*s 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends (vowhr-;u;owof a railroad car as it moves past a stationary observer (o;; uorh v-wwat 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) 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 ao9m52 isgsubkto ; 7yv k:)r(ezrta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and ref okzksrb2t( um9e i gy5);s:7vlected 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 tcygm *eguh qqa71z8+ 7oward the bat at 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? aq8zmq ug71+h ge7yc*   kHz

  A bat emits a series of high frequencym62p xz4bziee* t ;bu3 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 detectpbui42m 36e*;zebzxt ed 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 useda 2;y0rntdd/dd;/ykl:xee;w,dkl y 3 to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. W3wyyt2k; ;dedd e, xr//dy;ll0kn ad:hen 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 .r2vz z4vzv .bbe compromised by the presence 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.r.zb vz4v v2z. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstratp lwmfdy)y46 39.;x7gat,zi tn5 eoez+n tw9o ion, called “singing rods,” 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 w)x4nay7etopze t +gd,w o 936mt.;f59inzyl rod can be made to “sing,” 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 hearing for tfwrcgz0+y uds6 *u;d -gzq4u2he human ear at a frequency of about 10004z2;g*0+ u fr6 cguz-uysdwqd 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 gr+. sq7u cx+a.yc7bwt cl4dc9tound hears the sonic boom 1.5 min after the plane passes directly s+4tat +.9ucb7q cylw dccx7.overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbp 8s2-ppjrbs9 oat 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