What is the evidence that sound tnz-s du; oj.w8ravels as a wave?

What is the evidence that sound is a form of enerk;93w ldjjy 7zan1ns2 q8xj9fgy?

Children sometimes play with a homemade “telephone” by attaching a s)ndik;06:wxft j 3qp atring to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, tp n)jw ;dtf: 06ia3kqxhe 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 watwd;;d+9 ag smfer, do you expect the frequency or wavelength to ch;9fm d;d sga+wange?

What evidence can you give that the speed of sound in aiqraubt4e,tmrwm0 8;o e) * 3cyr does not depend significan 3mroye;0e )*t4bmqu8w,tc ratly on frequency?

The voice of a person who has inhaled hetczj-he147mmb :9x: 8c67r bhfbohc klium sounds very high-pitched. Why?

How will the air temper pwr+;ll/ng xw3pdd ;mjz i6+/ature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to redu5+of6117a1 ugzo c; zpprey nsce the amplitude of sounds in various frequenp+11 pz56yz;1rooneg f7scua cy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 1ejxhr 8 oo6cs;*thx 582–30) spaced closer together as you move up the fingerboard toward thec6e hs;xh*8 roxo5j8t bridge?

A noisy truck approaches you from behind a building. Initiall27,;e(fdql 1ra 0ktkwcv wbb4y you hear it but cannot see it. When it emerges and you do se4b7erwwl1d bq,(0 k 2ktvfac;e 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,” wh6ojvi) f5+ ggjny1 8h9zrnxh0bbwu . 0ereas beats can be said to be due to “interference in time.” Explan08+y)bjuhrj1w h v ig 5fxzb0on9.6 gin.

In Fig. 12–16, if the frequency of the speakep1p5 du4k. wvtrs were lowered, would the points D and C (where destructive u.dp4pwvk 5 t1and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who wooyd6, a1c 8z hm.8hysjrk in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relativelyhom. 8c 1jdyh8yzs ,a6 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. Ead.idhd61 d)l*ix: kyach wave can be thought of as a superposition 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? Expld)*ddy61h: i lkdi ax.ain.
(12-31)
(12-18)

Is there a Doppler shift if the fnfv6m4 l5jc) source and observer move in the same direction, w v m5)lcnf4j6fith the same velocity? Explain.

If a wind is blowing, will this alter thecb + b-1xw 2z dvufu1z,c2xy4z frequency of the sound heard by a person at rest with respect to the 1+f2zx,dc 1wc zyb2 uub-4zvxsource? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on mq ( lja-mh0g3zgm(w :a swing. A monitor is blowing a whistle in front of the child omwjz a:g l-((gh03q mmn the ground. At which 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 lake by listening for the echo of her sht +-yt/ mu0;).g,g h wiebruvtout reflected by a cliff at the far end of the lake. She hears the echo- e;v ut.rbiy+mw /hg)tt, 0gu 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship qfop;3ivhua 8f (+ 5pajust below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of soun3aua(p+pf;vi o8fh 5q d 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 gqz5edfqii.mwh5 5: (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 istgt:q bcz0sft-l4 y 4/ drifting just above a school of tuna on a foggy day. Without warning, an s tfy04-tltb 4:z/gqcengine backfire occurs on another boat 1.0 km away (Fig. 12–33). 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 9fe.z jg779m g4k b6t 5 z)rolgcuumi/top of a cliff. The splash it makes when striking the water 9 g tmem/j9r. c g7k fgzoiulzu7b4)65below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, seureq ouin1s 1rhka,44 zfd,/ 5es a huge stone strike the concrete pavement, u1onq 1r ei, uhf/rs4z45dak. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rava f ;b5)(fqlule” for esti)a5(baf f;vql mating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound atp k*-n6m- cdlbnf .d6j 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 i3bmun1f:f( l es $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB 8q2er w .f:xtewhen fired simultaneously at a certain place, what will trw8fee .q2x:be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certai g gj5 (p3xh9tk69 tcm.nzxp*yn distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level wouy t9m *kg9thgzx 6jcn(.53ppxld 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 have a signal-to-noise ratio ofau 7)junjd+ wqq(nr)2 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities o(u dnruwaj) +7)nj q2qf 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 b)lplbrk(..f fxt n/ph* q9.uspeaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphkr9f.p)fx q.b(*l/tph n bul. ere 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 str3z 3ygdl.c nlv8m;w /vikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier gg+)n g)gnms5B is ratngng s m)+g5g)ed at 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 regi;i.z;f9wxfn onyq66b,au. nx stered 130 dB when placed 2.8 m in front of a loudspeakynw9xq anf6bni , .;o;x.uf6zer on 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 detect a difference in sound level of 2.0 dB. Wm/lp7:cv3xlryqm x) 6 hat is the ratilm6vq3yx r/lp:mx )7co 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 fac7.r-ducz,-im vh5kft: i sj (dtor will the intensity increase? Increavkctzj(-- ,h rsu:dm.75 dfiise 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+5;pjg, uts,te o lvrget p.g25wu4l) the frequency of t ejw)t5pu, g 5tps.lgo ut+lvge;2,4rhe other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound waveue3o4 3, afcgj q:*tkt in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hc4: egt3oqt3u kja*f ,z?    dB

  A 6000-Hz tone must have what sound leve 9lqj y 6es9eolidd 7:-r;ro8ll to seem as loud as a 100-Hz tone that has a 50-dB sound level?orlodl js:el96r;7iey d8q-9 (See Fig. 12–6.)    dB

What are the lowest anc ;-u.vj,zjt ld highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. uj; -t.,cljzv 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the rak*g( d9hjy:erj9)bnr+ . mi natio ofrd+) mba9nrjenk9 ( h: y.gi*j 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 lengz.x++.c9 hr.cosgx q w+, kf0m ,adhhuth of the vibrating p+ . g.xqa+dh c0r9fzu,khwc.h+os,x m ortion is 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 cm long. Wha*w v1qk6d 1 3yjhhunr1t are the fundamental and first three audible overtones if the pipe i rj*h1nw116u hqdyvk 3s
(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 frequen/s)j,jnhfoqt8, s8i 5pxfj f 9cy would you expect from blowing across the top of an empty soda bottle fjo9s q,jp8fx)8 js fnti ,5h/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 pipesv4a1e+k/b1 ji*z1wwai 7tbtf spanning the range of human hearing (20 Hz to 2af t w14b1i e z7wj1kbi+/tav*0 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 a frequency op/is -9yd4hvgkj 6y*z f 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 length?6syvyphi /-4zk9d j*g    Hz

  An unfingered guitar string is 0.73 m long and ijvsslw( z+ .nfte*uk9 :hp/t4s tuned to play E above middle C (330 Hz)zsvjlhtt+n:(kp9 *s.u f e/w 4.
(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 lengt9s5/s e3l9trz x*slh2olrn mu0a:rz ygi;;l4 h of an open organ pipe that emits middle C (262 Hz) when theyiz ssen mr24llha:lslr;3 0uxo9/t9z;* r5g temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20rg/d jzw 6f-me464icq9*g yc e $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exam /p7eev6ad xb sv5rm-1ple 12–10 should the hole be that must be uncovered to play D abov6rmep b/51exa- v7 dvse 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 re6 2uchq/cuf7g sonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a7h2uu cq/f6cg 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 bot:r2 k390f8xqx r8h 5ftjb8rwhoi/k ky4il .whh ends. It resonates at two successive harmonics of frequencies 275 Hz an 0i rw8k xk jh/ow8if 328:rq5.br khtflx4hy9d 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 zw17nhiw8lg,iez /eep-2b 8z$^{\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 pres )ks,8a*sfof13sobepg;h .yfent within the audible range for a 2.14-m-long organ pipe at 20 f.sepfbh s;a8gsykf o,o31)*$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It zyum ;8 7+ofsuerxd. 6is 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 theu +.fd xeuz76 ;sym8ro 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 tryi5 znf p ps(qvth3z f8bb/fl1;zyb0s 5.ng to adjust two strings, one of which is sounding 440 Hz. How far o nt1z05hf.8bpf 53 /yz v fbbszq;s(lpff in frequency is the other string? ±    Hz

  What is the beat frequenc4y7 .pm0epvw* qda 9niu tk6w*y 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, whilexz z+:*bo: bse another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played se:z ezb:o+ bx*sparately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded fc: p4wdhzs g24(1 qltwith a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your rea tz2glh c: w4p(f1d4sqsoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. (0.g.qmsblwdThe tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two stri s(.wgmq0 .bldngs are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each tocctg5 wn r8;z3 x,fb2*hk;tn ry to play middle C (262 Hz), bub53;2c,nn*z htf 8ro ;c gwkxtt 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 frequency o.(a: cioc/k dq i,nm7sf 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, ta.: sd,7qi cmc(/k niohe 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 stands 3.00 m 8x-w )g8bmd dgd4euo 4from one speaker and 3.5g-e g 8d) dbm4xwuo48d0 m 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 vd;l2b2yq- 2ri g ,yrgcibrating at 132 Hz, but a piano tuner hears three beats every 2.0 r,d yi2g2gq-b2ry ; lcs when they 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 m aoing0 dw5o1 q*nd 2.76 m in air. How many beats per second will be h 0gnw i1*oqdo5eard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a x .uew8q1qol/g0v m sz8l+w-dcertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if yom 8lqu zxo 0w+dqls v1w.-/ge8u 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 engine whose s*d; g:)psnz3 pm1pp rwiren emits at 1550 Hz moves at a speed of 32 m/ssd*p1pppm3r w :;z)ng
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source istly +v s9b/mb;hs u:nhi*-x5m moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencbtisbm+ /u: ; -hh* mn9lvsy5xies 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 singi4yih 7bpo1j* le frequency horn. When one is at rest and the other is movinyo4j7biip*h 1g 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 50.0 kHz and receives them i2xgro+-p;*fg4i vhggx ,sn0(d -oow returned from an object moving directly away from it at 25 m/s What is the received sound frequency? n-og(vo*2,og4 di; gwgfxpr0 x s-+ih    $ \times10^{ 4}$ Hz

  A bat flies toward am( 1ekg kj/ j9ww87esm wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic 8 j/7wgkws 1j(em 9kemsound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was play*q6 o(jrp*mlr ed 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 freque(plmoj* 6 rq*rncy was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloou lzq2m5nm *lyq, p:u5d-flow speeds. Suppose the device eml*ln , y52zqu5uqp:mmits 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 in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wavesvi 8 xx8,mg60fqk4 rx( qze9-gt prx9u of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity isd wim(ynkv(3 bg-(pkl4. z3ls 12 m/s from the( y kp g((l-3kndw3zlismb. v4 north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving r ng(rgt5p+oo e-pp b0b8 n43fon land 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 t iu gfuw:tu.(-he speed of sound is 310 m/s (a) What is the angle the shock wave makes with:uw.i-f gu(u t 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 hlddw h-t8)1k the thin atmosphere of a planet where the speed of sound is only about 3l1 hw) t-8kddh5 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 strikes the ocean. Determine the shock wave angljdq m0;)2mu vofjv)d6 e 0u2m jd)qjvod6mf; ) vit produces
(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 e/vfw3/bhieak )h+2+k1byge$/theta$ 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 pv2)ti*v aaodwx; tpm:/14i wground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 1aw 2/miitvox; vp a)41tp: *wd2–34. 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 v b8cot*/oqaw m ;tr+cv2 en- h+tym;:device that sends 20,000-Hz sound pulses downward from the bot*vtaryn+oqt2 +m-:/vhm woc bt 8; c;etom of the boat, and then detects 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 aud*u ;.qz 1xdsb+7w,t9cgx bkxe ible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display-3,zjg7q lr.fp9l pwn called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both endqlpgpjz7w 3nrl 9f.-,s.
(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 th3vw lmy8p zxn/ 15.vgbv5p9x je threshold of human hearing (0 dB). What will be the sound level of 1000 vp8 /x n3px59gzbmwl51vv y.jsuch mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound anh.utz4 9to:e 3+gfe ;kq7fq pod an 87-dB sound are heard simultaneoot pq3oezte+ fkf ughq .794:;usly?    dB

  The sound level 12.0 m from a loudspeaker, pl/tdf:j -u 5+u;t oxulq irv6xs q02ia7aced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direc26-d5 :uu;i ua0 tsv/r lxi7q+oqx tfjtions?    W

  A stereo amplifier is ratem o: (e8;trkntd at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What 8n(ot tm e;kr:is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devicegpm5g-( oaw33am d6vcs over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an gw3cd m3p o(-5m6avag 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 systems, the gain,h30 t uvl7vra1 $\beta$ 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 viol jxk7gp:kg;)min is tuned to 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 violinhnz4*6,nb r i*vy 3yao is 32 cm long between fixed points with a fundamental frequency of 440 Hz n o,n3*vr*a4i6y byhz 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 vertical open tube filled with 87zw/b3mq.j olj ety50 7zltg water (Fig. 12–35). The water level is allowed to drop slowly. As 53 z.jzm77weg l8qtyl b0 t/ojit 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 frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube thk . f *w8isdwd/i351ls xjku60i;ygpfat 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 fundamen.;3i8sskw1jp lid 6ui /f5wdgk0*xfytal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatb80)6i -: yijmcmpht7xcx .zz e 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 500–10x0t wkek nz7 ,9ex fe: z:i:vz)vhr;4f00-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the persvhzfv 7kie: 9r0nz wfkx: ;, )txe:ze4on 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 stativ*zo.jm7e6y i u( d0deonary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the.(dziu7de oey v jm*06 moving train?   m/s

  The frequency of a steam train whistle ah+b.v f-cx7* p vm ,bjjv)yx,as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constan+ hyxbp*7)jm f.vacbv- ,vxj,t velocity)?    m/s

  At a race track, you can(6 lk lkm01xrk v;jq j:80tkyz estimate 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 a0;1v8lk :kty0(zrkj6 qlmk xj 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, ppug. ,-xc(ay1 wexak-li*h+ sounding together, produce a beat frequency of 11 Hz. The sxikcpe ,l-a xu(wg a1-+hp *y.horter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a f9hq(hk5)u 6u 8t ibuystationary obser(ufiu 9u5qb)6 t 8hyhkver at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) 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 wh - p7dbvyez4n*at beat frequency would you expect if 5.50-MHz ult p-e*7zdvbn4yrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth ykij33 hcv9z-kb)h0 q oc tte3wa3( *kat speed 6.5 m/s while the moth is flying toward the bat at sqi hz ybcv9(*jo- 33)e 3kttwc0ahkk3peed 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 frtr )4 zcemi+l,e ,6pdfequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How ee+, z,ld )ptm4c6 rfifar 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 t)msh- 69e)q4xz sjwwsignals from one 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 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- w)6wje4z )tx9mssqh close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the prese0rxqqd1q(d/ ec 7rdalho4a4,p t + mh2.3kxzunce of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4mdq4a aqtdhho (d.el30 pr74k1x z/xu+r cq, 2.0 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 “sing5e xfu*2bq e(iba*( ifm.k ,,izdgl8wing 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 rod can be made to “sing,” or emit a clear, loud, ringi*,ed( zx8e5k2iim l.*fuqb (i fagw,bng 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 the human ear at a fr+dmmotdkd3 gn7 ch-,2 equency of aboutd dck23t+o7 ,g dmmnh- 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 obsefcp;;6 s zvonc+n a9d1rver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the pl;v1nd s ocpnac6+;9fzane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbon 7brlbkk; 0g5at 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