What is the evidence that 4qyv2llr12zf7m c im 7sound travels as a wave?

What is the evidence that sound is a form of energyj9ni 1lxuh z y4ctz((6?

Children sometimes play with a homemade “tele kx4:qz.18 cnswnnj 5uphone” 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 clean8x n4n 5c jsuk:qw1.zrly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequenn(0 bs);edmqtpw 4s3p cy or wavep( p;m nw0t)desq4b s3length to change?

What evidence can yon.1aqm f4 ax svy;84leu give that the speed of sound in air does not depend significmx4ya v lfq;4.1esn8 aantly on frequency?

The voice of a person who has inhaled helium sounr3 tuhjdg(8-l szs9yq4t54 dnds very high-pitched. Why?

How will the air temperature in a roo 0;c :kfbkm//z8nmcl ym affect the pitch of organ pipes?

Explain how a tube might be usedxb.*e9bwwu c(rcw 7:y z-5 cgcbzez,kr:v7c5 as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car mubc7cw97-u .crzb55ew:, b wzg*rvkec x(cyz:ffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as z6n-wd89:jz7v hwk z.iggw- f you move up the fingerboariww7z w8g9:6-jf - hvzn.kgzdd toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it )km2c tgg(ylurcc, l*6r lt)jj6d04w but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the ) 6g6lw m (ykc4,urc)dg0ll2jtj cr*t high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wherkfr0- -hb s w baha9(6n(vo .zyylg)9veas beats chwhr kv(9f. 9a -v) 6gsoyzn(labyb-0an be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woulaotaow3lx wk/pm-pb , gs:*78d the points D and C (where destructive and constructive interference occur) move farther apart or closer togpp :wsxmkt3l a7 ow8-/b*a,ogether?

Traditional methods of protecting the hearing of people who work in areas with iatlj07b q4h wa4,;cywmm h// very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are /;w7y4ljbq i0mmac , whht4/aworn 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 Figwlwb; tm0q g8q )lx 7nqkh.:*dcpo ;c8. 12–31. Each wave can be thought of as a supd.8:7hck8 qpn*wcbgl m )o0qt ;q lx;werposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if oumn j5h6:n f3x)l0+xxeqqy0 the source and observer move in the same direction, with the samonyx6 + 03q0u)5nhmflj: xx qee velocity? Explain.

If a wind is blowing, wu -+exan3md+m ill this alter the frequency of the sound heard by a person at rest with respec3-++dxuna mmet to the source? Is the wavelength or velocity changed?

Figure 12–32 shows variou,c/on9mo6 cl rs positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child heal/mrno, 6cc 9or the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the 4-dvaua+ylnq omc . 00echo of her shout reflected by a cliff at the far am v- 4qau0.+oynld0cend of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the e;qkx 3/zr( p3x9ovjjpcho 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 sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depthx k prxp(vj/ 39zq3;oj.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a rg;nnc/m4tu76im; x lr/bq3rt 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 l,by gzv u2e4-a foggy day. Without warning, an engine backfire occurs on 2yb-v4uez,lg 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 top of a cliff. The splash itl/xr812og1h r vw;xll ofdevj ,vj62+ makes when striking the water 2+1xo 6of21elrjjhrw,v/ d g;xl lvv8below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concr++lqxs 7lgb .3,/ 3e qzlobfaqete pavement. A moment later two sounds are heard from the impact: one travels in the air and t ,q+bz/33gsq+lxab qf .o l7lehe 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 “ary 7uj0 sl1fo*: xr1h5-second rule” for estimating the distance from a lightning strike i1 jfl01yro7 xsa*rhu:f the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thqdkf:y(tla*ac z *pa5b+zv)-e 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 intensifg*rg0:2l0-q6m baavl68 h mu9 tidlgty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fk oq51q by3 9njcw7umi81 zzk+ired simultaneously at a certain place, what will be the sound level if only one is exploded? koj3 9qyc718qu izwm+1z5bn k[Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with*d0 9lx qpxt,5)av;tgac-m be four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not d9geva bt0px ,l);* tx -amdqc5B’s.]    dB

  A cassette player is said to have a 7u(+icr5f )jgqe 4as wsignal-to-noise ratio of 58 dB, whereas for a CD player it5 +u fijwsea7gcq(4 r) 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 s79xhokn jtz. 2/jzbn 24c,7igk jiy) upeaking in normal conversation. Use Table 12–2. Assume the sound z,. uhig7b 2kk4xjtc ij9)n nyj/oz27spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eard 48w4*shstfq rrum 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, whic -xl 39w4hkdole the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker conne3dlh w oxk9c-4cted in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB whenxz7ou edu67:a-z l(kz placed 2.8 m in front of a loudspeaker on dal67:zxu( e -zuz7k othe 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 diafw:nt n)( ; 5p*qvnfqfference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]v*5n nf qaw)n(q:t;f p$\approx$   

  If the amplitude of a sound wave is tj+i-, a)s ya3vghicbx.f;g;do( fl( b ripled, (a) by what factor will the intensi-j;is f;adoy.bli hgf()v gc+ bx(3 a,ty increase? Increase 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 twd tw*cmc xxidgv-pda0 pe9jpr0 ;83f*f6r) 2dice the frequency of the othew*;mfc r9 a6ded*idtxr820f0pv-c3pdpx jg ) r. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave inwr yi a6kw4lz7u (nd,wzg1*yik;8twav: /x )z air that corresponds to a displacement a ti71 /dr:l*uvnzgx k w4y6wwy8i,zkaw)a;(zmplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level p:/worg kls 0pxp tuf4j14a *1to seem as loud as a 100-Hz tone that has a 50-dB souk 4ptp*rs140waxu/pl1f go j:nd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies t* c cn9zu*p/myhat an ear can detect when the sound levu c/z *ymc*np9el is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound lev1z sffh 9pa u+dx8l-1bels. What is the ratio of highest to lowest indx+hfaps1f lzb 9u81- tensity 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 odwrr nkuefq;:v-3n q h -8k*v4f the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must t ndq3k-kwvehn ;* 8uvr-qf4r: he string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audihucx 90 r-k: hvvps8q)hk4 a*gble overtones if the pipe i s4hv 0h-uh)kpgcq rk :*8xv9as
(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 facg6 4:;h 5c,t h9vo3pinyimjrom blowing across the top of an empty soda bottle that is 18 cv 9 ntmc ;yhj,3i6o:4pcah ig5m 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-t i/f j2av*1c gnpjl0y * +ce+r)l:abfmube pipes spanning the range of hum +20c*feyafgjjabvrc:) i+*/n1l lpman hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a m:zgogt ob(02qsx7j:duz j65frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its:o bdut(x z: 6 jgsm5o702qjzg original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middjmq b6n60b8c0 yd*h5ad na*de60u qztle C (330 Hz)c6a q 50 nmz*jhe*q 6 bt6u0ybn8dd0ad.
(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 otf8z7e.f l0e.ru7 w hlg)owd 8rgan pipe that emits middle C (262 Hz) when the tempe.wh8u7lfe w7t)0ro 8 zgfdl. erature 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 2yvmbtnj2e,j :)9lhs( 0 $^{\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 holeftyvc4 sjap.lw1 gc(,0k z8/z be that must be uncozw8 sc(gc. 0/4vjfy a1, ptkzlvered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, buhxj k /0n jux0h7e,x:lt not at any other frequencies in between. (a) Show why this is an open h j7 hex lk/nu0j0:xx,or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonatel;y8 w ytrki+,s at two successwiyytl;r+8 k,ive 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 h yw3q k*;:dl /lv0irk$^{\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 2.7s)uk2fn5*v n9urfbqd0u 2 cu14-m-long organ pipe at 20c usnuv7uqfb2dn)0*2fk5ru9 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lognw*3o8y2pa 8rqzmop // gb y)ng. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the sta2)ba g* y /yworgzpop/883qnmnding waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tr+kh e7-xc;yryl2:) ,miww o qcying to adjust two strings, one of which is sounding 440 Hz. How far ofw ,2i);kh- x+q cewcyo y:r7mlf in frequency is the other string? ±    Hz

  What is the beat frequ03s 3smsk,ntf ency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (bi76rcld:r 6re h fx)egj+r)m,rand X) operates at an unknown frequency. If neither whistle can be heard by humans when playederg,e frcd)x7 hr+ r6:m6 lij) 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-Hz tuk rffj .1nk3-wning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Expla.1 rn3fk -fjwkin your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in mx f(w ggezz f1 o7 s,v4dfgm, mz:2g+8wx0k:done string is then decreased by 2.0%. What will be the beat frequency heard when the dwmm:(odg08,g k m:,w1 2ffsfg+xx4zzez g7 vtwo strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middica6p57i+pyc le C (262 Hz), but one is at 5.0°C an7ia cp6ipcy +5d the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fz 1wt0vpu ky2)ork B has a frequency 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 a2uy1k 0vp )tzwre 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 personlvy )rodfh3h1 py:9) .( xoxkz stands 3.00 m from one speaker and 3.50 m from the o)hyh z pokl o(1xd9y):3.rfvxther.
(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 vidqid2q;7:l g tbrating at 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 Hz, what must be the fr;7 qlt2:qdgidequency 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.vriuxdq/h: q,xzo7)2 64 m and 2.76 m in air. How many beats per second wi)x27u dr:oi,/xq vz qhll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 155q76 jng,byn1 ojnr3(b0 Hz when at rest. What frequency do you detect 7n n3,ybq(j n6jr1gboif you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stilkxhxk5h37 sm((te9 ryl. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s 9 hxym35s(e(h xr7ktk
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shif+g d2gzf bq9n;t in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you movf n;q2+9 dzggbing 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 freqx)ei /o hp:pa;uency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 /haepopx ):;iHz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasu;ypr xsq,bb2k2 gd.9 onic sound waves at 50.0 kHz and receives them returned from xbpk2gqb2u ;dy.r9, san 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 sp66lsjubja17.bri t b ,eed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency jsr. bulbij,6bt 167a30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doek6dri u)qo)6(.y d(hp alt*cppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identiceh) o.a)(uid6 tdl(6rq k*pycal tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spen nnyu+-/0ds p2q/omieds. 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 arteries at 2 cmq/n p ond-2yn/0s+miu/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencyc m3o z2gtdn(: $2.25 \times10^{ 6}$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 1k(g4ou *nmiq frequency 570 Hz. When the wind velocity is 12 moi 4 q1*g(umnk/s from the 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 on land if its speed atmo vbd6i*b*zi y:yft gw.0w;1 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 o ioh;64y lz -btp6t30axdw-ksound is 310 m/s (a) What is the angle the shock wave mak htdyo z4 6xw b3p-0;6-kotiales 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 sounmzg.8v*uw/ntume.1zcse 3d /d is only about 3w.3ezgn zucd./s1m u 8*emt v/5 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 85b.1.,58 2vv mbhfj- dgwbsjop 00 m/s strikes the ocean. Determine the shock wave angle it produob. sbf21j8pdvbhmg j. w,v5 -ces
(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 ) u: yj dmmuzee60ty 8rgk5/phl9.r d2$/theta$ 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 1.5x xjewr:/7,h t km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled hx 7:rj,e txw/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-Hmdoglyk. 23+ q4gtf92gt 4 pqpz sound pulses downward from the bolf4qgt+.qo3td2y9g4gp2kmp ttom 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 t)7c)z6kp6q pwwt- o(zgmmy 5lhe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists ofecl3 iczc78ix8 smb9 , many plastic pipes of various lengths, wh89,c7 lbicxiz3es8mcich are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the tas ji(tgxkb2*9 j1p7b twld(;hreshold of human hearing (0 dB). What will be the soun(ax1jd*k bljstib tg;(p927wd level of 1000 such mosquitoes?    dB

  What is the resultant sound levelk9xsoen51-8n58u7 tf m aeghim+i8 yr when an 82-dB sound and an 87-dB sound are heard simult8nt75mr9f8go i hasxu e85+keimn- 1yaneously?    dB

  The sound level 12.0 m from a loudspeaker,b cx8kt2 p vqde/p56govoho+)3nbo :3 placed in the open, is 105 dB. What is the acoustic power output (W) of tvoeg5+2 :hnko 6 )q/d co3pxb8b 3tvpohe speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The-mbf n)k0j 7gfe+2*(as rpgb s power output drops by 10 dB at 15 kHz. What is the power output in wattae)*0g + fsgfrms -(kbj7 2bpns at 15 kHz?    dB

  Workers around jet aircraft typic g 5iuc23lpmle -jsnwc 9pr12+ally wear 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 radius of 2.0 cm. What would be tn- rgmeu+p3 2c9p2 1ij cl5swlhe power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicaf us4z fpb75ud;i1b2ations 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 vio jxt4eon1iab/801g eelin 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 violin is 32 cm long between fixed points with a fund / g8joof;4gpiamental frequency of 440 Hz and a4 pg8ogf i/o;j 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 int6 m2(ewo+ djtro vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the 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 tw26ome( dt+j rhe frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one+v d) wd(3uavr.;kytq end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic . y( v;)vktqw udd+r3ain the tube?    $ \times10^{ 2}$ N

A highway overpass waslek : t)9itc+z observed 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 50k9l,;py40 rf8 lw dgdy0–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequen04wf yy ,rd plg89d;lkcy 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. Onex 4 eikg 426n6lhpx9xj train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed o6 knx4x xjpli 964h2egf the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is xop i),u81(ywr rd1 fz, rq4ru538 Hz. After it passes you, its frequency is measure1(qyzp8,ri1rrd )xw uoufr , 4d as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just t72fddltp+ f;hwv a*9by listening to the difp ;httfflw* +av972d dference 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 frequenc5ao8 6k0xsp ily of 11 Hz. The shorter one is 2.40 m long. How lonk0pos6a x8li5 g is the other?    m

Two loudspeakers are at opposite ends of a railroad car aso, r u3)p l5l7w)eyq,6vpctlt it moves past a stationary observer at 10 m/s as shown op53cwe7ur)qt,tl ),llpy6v 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 p b ud.i;gu8a.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 reflected from the red bl8.u idabpu;.g ood 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 flyi h,8vzf(aop: y4oxjh3cfa24 ing toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequencya8vfjfi zhoyo3,( h 2pa 44:cx of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a k8kt.zrm7a s.moth. The m z a8.s.kt7krpulses 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 emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alb jtt)/g1d8o mpine village to another. Since lower frequency sounds are less susceptible to intensityjm dgb/t 1t8o) loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stere)agv 8iieml 4/o listening can be 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 i4glem/a 8v)im 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 demonstrae- ocrp 5ld2-ction, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod ispe- c5lc2- ord stroked with the other 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 frequepj/jkjob 0 o1j8 r0u-wncy of about 1000 Hzjo 1prw-oj/0kub8 j0j is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground h6-ibq4 mr a+x;jzsoo 3ears the sonic boom 1.5 min after thjba ;z+rm4 36qooi-sxe plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1g 367 gieg8kfe5 $^{\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