What is the evidence that sound travels a+n whyd,/8 m cr y7emrvz3)fk*s a wave?

What is the evidence that sound ix(ms7torli9:q w g j .4*s,dkxs a form of energy?

Children sometimes play with a ho qwcu3.d6gcum95g g- xmemade “telephone” 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 travels fro59gxuwum.6 d c-cg3gqm one cup to the other.

When a sound wave passes from air into water, do you1i+ i5fch t3g; h-oyr7gag w;q expect the frequency or wavelengrw75oi gggcy aqtihf;;h -+ 31th to change?

What evidence can you give that the speed ofqmop6 ,nzk /+p sound in air does not depend significa/, +kmp6z qnpontly on frequency?

The voice of a person who has inhaled helium sounds very8o*xppgerg///)azq z, wv8 jo high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipes? *bz)je,gb8wh z7zr x5

Explain how a tube might be used as a filter to reduce the amplitude of8z fbjmlrd ox-;l (,. skcx5xg3(y8yq sounds in various frequency ranges. (An example is a car muffler5d .,jx;kl8 og (z(lyc qxmfybrx8-3s.)

Why are the frets on-is o a../whvwm;3iwm a guitar (Fig. 12–30) spaced closer together as you move up the finger3wi ov/sw.. ;i-awmmhboard toward the bridge?

A noisy truck approaches you from behind hoznp ,q:s0 +y/cgqqsuh (6 4na building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequengns,n/ h(:qs + 0uhy4qpo6cqz cy noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats sbj 8 -8wsxr5 8pqwxh1can be said to be due to “interference in tibs8 5 8q81xpjswx w-rhme.” Explain.

In Fig. 12–16, if the frequency of the speakers were lower nh1y gs 7m fv))ez;1):npktxfed, would the points D and C (where destructive and constructive interference occur) move farther apart or closer mt y1 nxv:1sz nf)khp; egf7))together?

Traditional methods of protecting the hearing of people who work in ar q;5lftsv7 8vhch:ws .8:x ehleas with very high noise levels have consisted mainly of efforts to block or reduce noise l sfs8ec v:q hl;7h8ht:lx.wv5 evels. 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 thougcw s ejv9;f oiy s3+yg44)j4mwht 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? Exp)fwwjs+9o e jm44g 4yv y3ci;slain.
(12-31)
(12-18)

Is there a Doppler shift if the sougz0:6-bhhxe qw6v6u mr. ln7q rce and observer move in the same direction, with the same eqv6rln. u :7h0wqhm-g b6zx 6velocity? Explain.

If a wind is blowing, will4*:uzf)u)s(j:y pe+h7: k ubw pkmxeu this alter the frequency of the sound heard by a person ep pyuuk) um::*z(eb s7 k:w4uj)f+xhat rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monip;ltr 77g wg(gtor is blowing a wt7pg7gwr( g l;histle 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.

  A hiker determines the length of a lake by listeniu x1eb1l5kn5i(1wp0lhc et q9ng for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the leng0nuil5 kh(plb qw 911cxet15eth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the d-mt 8k dx.yvb8db;/ y +h34id8 bgvqnside of his ship just below the waterline. He hears the echo of the sound reflected from the oceg. n-id/dyb8 d3x8dbvv bhy;k4tm8 + qan 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 warq61x k +cviai,0 kv.dvelengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on azi )r smvee+r15 w6rp; foggy day. Without warning, an engine backfire occurs on another boai;m61rer ps+ zwvr5)et 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 top of a cliff. The splash it *urlf6-xayw s6p2) h1 :yidtymakes when striking the water below is sd rt-l6uyiy xw6 *:2f ah1yp)heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone *1z b ;5: zwmr4arcsp/y ;wlltstrike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. Ho;*rm;a wzw5yr: sl4t1lp /bc zw far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of d 1ctj*tbff8)x:m 4 xztxb0k.g istance by the “5-second rule” for estimating the distance frbtc)jftx *1x8k 0x4g.b tzmf:om 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 lebl) r0 )d2.w4oevdhd uvel 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 b:o9 qk hw(g+7s6szkwis $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslya87o q) (a (awytdu,eb at a cereaq8,7b)atd wuo ((y atain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distanc-x brj8g1/s zze xu( )wl6fea)e from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sou ewsxa/el zguj)r18b6-) fx (znd level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, -oh,bsm2j ui; whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eac,joum -2ishb; h device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the pow nq46r34gux kger output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformlnq4 3xgruk46 gy over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose arp07gscwejc-4;na )p t ea 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 Aosw95kssn9g.5 lu yz0);fswyml ) 8dn is 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 3w 5 s o5w l;zkn)fygn8 msdsy9ls90u.).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 regyt. l zs;* cru*jbid60istered 130 dB when placed 2.8 m in front of a loudjbui t*cd y6*zs;0rl.speaker 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. Whx :58g+qhst bhat is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hx ts8bh hq:g+5int: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (ay;o8cd h52m xnp ;pei*) by what factor will the intensity increase? Increase c; n;pe2 yi5hpxdm*o8by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equ fpizm5zm :zqt e9k0 bw36.-xqal displacement amplitudes, but one has twice the frequency of the other.m :qi.zmwz -fxeb0kq 6 3tzp59 What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspdr;v +.,wy7ss+.e iebpt30j o9qivj zonds to a displacement amplitude of vibrating air molecules oide, o7jr q3 .ev+psjy0zsw;9bti+v.f 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seek wvl5c n k2-3(u-wkvhqw (js)m as loud as a 100-Hz tone that has a 50-dB sound level? (See F-k(v2qkljk su)(5 wv-ncwwh 3ig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detectx5mzj/1. ;exwx.+ ,gov jj utd when the sound level is 30 dB? (See Fig. 12–6 1 jmxgotu vw,/ zjd.xe+.5jx;.)

  Your auditory system chnf. +3gpj1ncvzt d y 7ilc(pth9,7 *oan accommodate a huge range of sound levels. What is the ratio of highe3jc i7 nd1nvz ,tchpyhp.+9g( ftl*o7st 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 cj9,pp2lzn+4 epn u7tHz. The length of the vibrating ,zu p4np9 ctnp 27jle+portion 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. What are the fundamental a( n2f0kpxwo7 3pt/nxhnd first three audible ov3 nhf7w02ox/t xp pkn(ertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the topqivm5mb0 m8vyw0er.- of an empty soda bottle that is 18 cm deey8m0m i.50-vwrvebmqp, 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 pipelt ,-3*rd/:tviwqu ik organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengthriq3 /w-id ktv t*:u,ls of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a f*6 u w2udfwd9 w0ofw.qrequency of 540 Hz as its third harmonic. What will be its funduw ww2od 0.fuwd9q6*famental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m l86ii:sb 8 bixcpf,s1 3 l 9z(fye1caoz/ vjo4uong and is tuned to play E above middle Clb6,xs4/j1o 9 8fbz(vp1cuzi yfo3e8si :ai c (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 length of an open ,a-4xp f6a graorgan pipe that emits middle C (262 Hz) when the a ap,ax-gf4r6 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 jih4v rv- kkreq6)y,zp7g68tt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be a2ix+6fgzjjn-w3f - q h x1oa.that must be a3n xwi+o-ff2 a-.x1q jh zg6juncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz,*m6fdx i(m +gl1f9 a;ei- xogw 440 Hz, and 616 Hz, but not at any other frequencieseiim flw;axmf 9*(ggx o16- d+ in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 0jrkgvz/ ;h+ im long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Wik +/; jvghz0rhat 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 p a0-nqbz,rah5 o 8:2im,sj lt$^{\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 au/p ydh74)(m rtgno n00bzi5j skcgy0/dible range for a 2.14-m-long organ od)m/jb n5gsty(4h7z00gn i/ kc0pr y pipe 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 is open to l1fdyn 0;oxo q3:4e l4elidrnh5) s9 fthe 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 your answer to the information in nfi s1 4:eo 0;eqdd95hl)ry fxlol3n4the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears onef 8/ u*1qo2ehr 2c5u gy,)f1j mcuf oo,xqjqa/ beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is x/c,c e,/huj5 2jrf q 2myu1)81oqqufg*ofoathe other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andnnt/0-: zwxjf $C^＃$ (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 opde o3p tg:o1:zerates at 23.5 kHz, while another (brand X) operates at an unknown freq:e :dpz1o og3tuency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hzh f1 iczv:bml zexy,1-q go.2 c99da)w tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain youryg9b.mdvfl:wz 9) zxqi1ea1,h co- c2 reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in odk*h ma,y 5df.v3q s4vne string mk,3 dahq y 4v.fds*5vis then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to plf, llxy9( s4hcub-5r jg2a+2mvhod/may middle C (262 Hz), but one is at 5.0°C and the other c g(,jafbl5mu - 922hrv lx4so/hdm+yat 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fork)dn;/zgi* pt(gt pof* s, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a dgn/ * z (;)*iptgpftobeat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m fl :f.vg2rowk0em qn (6rom one speaker and 3.50 m0r 2m evnq:(k6w.fg ol 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 vi+34rsx n99jz6*f8cyxtl .tzun q2 mgkbrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If oneckgj. +28yulzq xn*mrs 6xt9 n4z 39ft 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 and 2.76 m in air. How many beatj jbjgna5 (:*t q3g0hts per second will be heard? (Ast j*jgthnqgb: 53(a0jsume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cl (hq7mf 2te705s skowertain fire engine’s siren is 1550 Hz when at rest. Wh0 7e ft lkqm5so7hw(2sat frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire k9zx6qo4dvpcn70 t.i q +n6whengine whose siren emits 6wkqivop .06 hdtn9z7cq4nx+ at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towaazk6.i.)r3gvjn v y 0urd you at 1u v6ik.y) jr3vng az.05 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single fr:4bg-b.t oa4kw1 nolayjq o/1equency horn. When one is at rest and the other is moving toward the first at 1o 4l.1ojo ak/a:bnqgwtby4 -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 recek 8yxx7y8)p dcives them returnckx d7y8 px8y)ed from an 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 a speed e) e.m0ygah;k of 5 m/s As it flies, the bat emits an ultrasonic sound wave with freque.) 0e;g ehkamyncy 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 platvl z,i.:hz13uds* vxyed 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 station at a sd.:*, iztxhs3vu1 lz vpeed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to :nmf6wcu myna gyzj ,9k5* g4*+2mvndit 7wl. 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 in large leg ar: nf au nzjcik6g7n+mwt,v5y*4.g*mdm9ly w2 teries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency 6a*b6o zj7pse (hl*y v$2.25 \times10^{ 6}$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 veloci3q j27djoowr0i 4q/zmty is 12 m/s from the north, what frequency will obserdo mj0 rw4i7qq23ozj/vers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on fg z 9wb)v 22 oy;zlshwq286meland 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 is 6 pl6w;gdfxxk4g*jw9310 m/s (a) What is th4f xd; p69k6wgwlgx* je angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thiehxi qs j2,- 1m;(snfbn atmosphere of a planet where the speed of sound is only aboum ;s sf-e xijnq1(2b,ht 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 strikes the ocean. Determine the shock wave ang2ui9(c u-bb sble itb sub2-9i(c bu 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 ro)vm.3; soj r;ia; x kcy,d7l$/theta$ 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 thenx 0 r*rha l8b474vbr,r+wzo p ground flying faster thanb v7l, zrr4bho p*8+0 xaw4nrr 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. 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 sym5c) na 7o(vozvcdl1+ pz,t)ound pulses downward from the bottom of the boat, ant cz+)7n, o1zy(cpmv a5 )ldvod 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 therzb7a ag5f(p4: dnhig )j0qb, me in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dih6ohw0kce u: tfd 48ex 2af7r;splay called a sewer pipe symphony. It consists of many plastic pipes of various len8 e6ufkt 7e24x:hdafw0hcor ;gths, 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 p-b kp3 oxvwbwq(:3xvt-c*h -aerson makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 hwv3-(x:x a tq p-cw-bkob*3 vsuch mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound a /ko wuxur2qk(//t.mare heaar/.k/ou(mwut/ qx2 krd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the openu.iaq mf*(9y. k3z nzi, is 105 dB. What is the acoustic power outpua .z39y *(.kmzni qifut (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outpn pdb:b)twioc589 i9mehv/6q ut at 1000 Hz. The power output drops by 10 dB at 15 kHz. What m b)qei: bh85d9t9/vw icpn6o is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wea rsci , tvwd0,ez77x4e ;s/gwur protective devices 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 effective radiusesxi;4 dw 0tzg r,/ s77wecvu, 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 communicati 9nnkoikvzg h3su45aw97n.* qons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to+m6yxr 0ozikvk :+8 .wqwwp+; to jji. 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 violpkl r m64pp54gshn* ,* tg12gx(gfuad in is 32 cm long between fixed points with a fundamental frequency of 440 Hz andp1t*sug( r h6f4x l,gm42*5gg pkdapn 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 0kpj (eg y40jhk05yz bfilled 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. Whathp(y0z k40gkb5yejj0 is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass rig+s1gv n 9r92.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the strin gn+1grrisv 99g if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lok+p 3p7-cv)bjgknii + op ($\frac{1}{2}\lambda$) 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 from op+h 2o0kexqho3x*i j1/zj q+ two sources. The sound is loudest at points 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 souriko*+qp2xq0ez xhj/ h 1+ojo 3ce than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stati6o fo+fu 3t ntpb;h*(monary. The conductor on the stationary nobo ; utht(3mfp 6*+ftrain hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as /4y+( iuttg dft39iahit approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movinah+t g3(fdi 49/ui yttg (assume constant velocity)?    m/s

  At a race track, you can estimate the speed ofhgg3pj citcgspt1 )-,,2 b-; /pr pffu cars just by listening to the difference in pitch of the engine noise betwee3 ,g2gfhg -tcpt1 ;rf uipc/ppsj-b),n 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 11olb6iz1; bf( d Hz. The shorter one is 2.40 m bid bofl;1z( 6long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it ida9wq yq2/m(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 f /mqdi29yw(aq requency 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 ao4md,g stnz(*cf0o9e+ hx p,qhrta is normally about 0.32 m/s what beat fre4,* zdtshfp+ oge(9,hm0 ncxqquency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while 9c-kbira n1m 6.9 rlolthe moth is flying toward 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 that1bra lcinlk96o9r. - m wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it a v7bz8v9 nfro,pproaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emv9,7vb8orn fzitted?    m

The “alpenhorn” (Fig.f ba7)ug; 4qbb 12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity lg7bb4bfa)q u ;oss, 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 caem6wy33sl)6xk rcg7 en be compromised by the presence of standing waves, which can wkegy3 m3x6lse6c r7)cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involvn os/ jo+c0l3gup p0s(es a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the ojso+(3u pn0g oscp0l/ther hand. With a little practice, the 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 the human ear at a frequendn -uuo4r fd-e, r0d5pcy of about 1000 Hz i50 - dd- or4dnpurfeu,s $I_0$ = $1 \times10^{12 } W / m^2$ 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 atm3h e;jle7i8 b,kknwls;j yv gr p1(5- Mach 2.0. An observer on the ground hears the sonic boom 1.5 m mn5bkwk,l1el(j3pg8 -rsye;7h j v i;in after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat dyo :qdr6 vfr(7b- *24pnghui 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