What is the evidence th vkdzy7a a/v1,9ww: geat sound travels as a wave?

What is the evidence that sound is i o i0 x35,xjv:8o.kmzmnon1ra form of energy?

Children sometimes play with a homemade “telephone” by atto+w7nl7xtlu o-yn -w 3aching a string to the bottoms of two paper cups. When the string is stretched anwnxwul-l7-noy 3 +7ot d a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, d/( ;jb9oa se3p ,benhjo you expect the frequency or wavelength to cj ne ba/;( epj9shbo,3hange?

What evidence can you give -u7pm6 zz r8ljthat the speed of sound in air does not depend significaz6jp m-u8z7l rntly on frequency?

The voice of a person who has inh u,khktv :lqv5 0s6f-la):v vhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch 1+g g8phz xw)rof organ pipes?

Explain how a tube might be used as a filter to reduce the ampu,-s x;sk d/;kiiu3 wsez x.d4e)prw:litude of sounds in various frequency ranges. (An example is a car mufflexi.4 s:p;sxk usee 3)dwrzwkdi/ ,;-ur.)

Why are the frets on a guitar (Fqztn 2r6 ;(d2 p6cxtknig. 12–30) spaced closer together as you move up the fingerbozrnn6 p ;tq2k 6(tdxc2ard toward the bridge?

A noisy truck approaches you from behind a building. Initial.n kgxx j/uoo )zlq ov7.jt2kpq wxx,4i1o2+2ly you hear it but cannot see it. When it emerges and you do see it, its sound is sudd.ln z 2qoo.4 gqwpuvk koo,7 tx2x)ix2j/+x1j enly “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,” whereaso3yq,j+(k.v k vnegc10a+cot beats can be saidc0ja(.qt v, v3 n1ok+ek+ygco to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakerf6/ u6qzggu /bju*iw5-yd;a rs were lowered, would the points D and C (where destructive and constructive interferenceu/*qb -u6df;/a y5 g6ijwurzg occur) move farther apart or closer together?

Traditional methods of vg;4) qk1f;8v(esxgsw2vjs+ a5vdqi 8 yt/mnprotecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, tsfkjs8vqva+xnm4vt v8qw5)/eg ; ;2 y1sidg(hen 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 tho64cg6v73:bbfygzmj l ught of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. 6yb7bzfl6:jgm v 3g4cIn which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same dir2cdt q ebh,i kttp5qm5zb.(0:ection, with the same velocity? Expl tp0 t:qq ,m5ekbdc2.i( b5zthain.

If a wind is blowing, will this alter the frequency o-su5c4+:i wjb czc( b/dx; atof the sound heard by a person at rest with respect to the source? Is the wav tw+(;sbubzd c/xc4aic-5:joelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A j2sk: 8jf yl7uyh7o u0monitor is bljyj7:y8o0 7uk2flhusowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her sn3dul )swq nao6r) ,y9hout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s aw 36nq ynrsu),oa dl9)fter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the watev,dz8 ;f6jiv hrline. He hears the echo of the sound reflected from zd;v i68hv,f jthe ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wav;ne,k)uxb.ik2 cjp9eelengths 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 boa 0 ynl f(bjy;p.*vpcnkin+ 55nt is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat y *;inn.jy5pb ( fcknlp0 +v5n1.0 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 makes when striking t3kdda/x7j 0z+yd5aq w he water below is heard 3.5 s later. How high is xj + ya0q3a5dd7/wkzd the cliff?    m

  A person, with his ear to the ground,i7f8w g,t e2fd/ajw s6 sees a huge stone strike 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 the da2ij/ftsf8ew7 ,wg 6y 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 distanc xy/vca +8vb(zx1:lsne by the “5-second rule”s+lvy( nc :b vxx1z/8a for estimating 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 at the pain lg0xi+o+ e5 qkkao*d i8qhk92kevel 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 l0( wyjn60grm 4 k7o8yal+v atr2ke3c whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound )ucgpl 2uns 7is/-a9nlevel of 95 dB when fired simultaneously at a certain placuu9s /la7g2cn)n ip- se, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a ce/1akc elwj e,hn2de* *rtain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound l,ek /n*dc*jeea 1hwl 2evel 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 ratioyz,ud kj3g*dnq. qt77 of 58 dB, whereas for a CD playerq*.jdy ,7ugn tdk37 zq it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in :dbc(f9 +dyqynormal conversation. Use Table 12–2.(bddyy q:fc9+ Assume the sound spreads 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 earghqny, n:i,8rhi(+jg drum 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, whill (c j.m6jfjj*3zzd u*e the more modest amplifier B is rated at 40 W. 6(f juj jlz3mjc z**.d(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 registered 130 dB when placed 2.8 m i)vfd4ipi 7 ;bhn front of a loudspeaker ;ibdpf 4v)hi7on 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 differeuy*gn9jwl+ 7 g6adh6 eho8ffodq;k 3;nce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whg 39kdufya+8q6go nl ;ohe;fjd*w76hose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wa:f gz8 pn xu::3cz,pga()5+t9h hk gliskswl -ve is tripled, (a) by what factor will the intensitl, cu8pw3a:g(iss l):zg-z:+gxhh nt f5 k9kpy 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 twice the f6j3*rewnb i(,xm; ;;c i:wydojo7 t i*wawu3erequencyrw wcm,u *xi 6(d7tyo:a3b; ejwiowj;*;3nei of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that cor 1mbr; jf-qp)oresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz? b1)or fmp -jq;   dB

  A 6000-Hz tone must have wha : )+akeyc)jnrt sound level to seem as loud as a 100-Hz tone that has a 50-dB sound lev+cn)ry :a e)kjel? (See Fig. 12–6.)    dB

What are the lowest an ezopc axbq2z ,vvwdsz7; i 34:mmv(w/ c10yb8d highest frequencies that an ear can detect when the sound levezve1vwbzi o43za c :8xvw0dc7 ybpqmm/s;(2,l is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. W 5bq1ly1 e .rl*yxr+hb0 8nutfhat is the ratio of highest to lowest inte brlqh1 yx8n. *0fu5etr1y+l bnsity 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. 1m(mj8cm8u2u znc:c wThe length of the vibrating portiowm1c cc:(2u 8ummnj z8n 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 tdl(r)m-mr,ej5ac cye md5s gsk.ep/gp32+ 3fundamental and first three audible overtones if the pipe is ecap 3emrpm55)dgr de tkm ,/.3-j(cyls+sg2
(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 blea l,85vcea 1sowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wa,vl 5cee asa18s a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of hu i)f bg9ddo xdlk,-n.aai7 2x k-(ck3hman hearing (20 Hz to 20 kHz), .g3(2k7a-9iknxfcid d-db, axhlo) k 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 of 540 Hz as its third harmonic. Whatchgicf)s+y0cbm3ig b),+ e* w will be its fundamental frequency if it is fingered at cs ,+m)+b 0giewhfyigc c3*b)a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is o)iar qfl2(*2 / p8wsz-d ziyrtuned to play E above middle C (330 s 2zwi/pr(y *z)8r 2qifadl-oHz).
(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 organ pipe that emits middle C (262 Hz) whene4i5 m 08fdvvi v.s+cg the temperaturdgf4+ve vs0v8 i5.mice 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 *rgw 0xzpgx 7s1.ft d*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 thyu+q/ vwfi2eznp1+ nbymf ;82at must be uncovered to play D abovefbim1p/ 2e8n +uzn;yv wyf2+ q 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 vhegt a0 ;hve3g*stp:4 +fa;gHz, but not at any other frequencies in between. (a) Show why this is an open oaee g:va ;g0;t*h4pt3shg+ fvr 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 endshyrt2 a/pa n(;mh3 yn0. It resonates at two successive harmonics of frequencies 275 Hz and0a2r(y / aph yn;nt3mh 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 mnyhfyg 3 75k6;yn wgc6wr4nt/z/ 3qrjz.a-t$^{\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 pwu / lx43 1;ku,v3blg qc7qkwxresent within the audible range for a 2.14-m-long organ pipe at 2xvx7qwb 4;1k3/c3,u wl gqku l0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is .zaf/qd /h1;cnkyt2zop e*b4approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequenci;fp/ze . 4dcb/qtanhz* o k21yes (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryiq js:6awybzlkv z(,c4/1hqk: ng to adjust two strings, one of which is sounding 440 Hz. How far off in frequency iszb:k ,1/ lj 4( ywzs6avcq:qkh the other string? ±    Hz

  What is the beat frequency if middlelkvou8cahvqm w ,90 cr, *nx74 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 au dy7jdhri 4c5 8rn4n/nother (brand X) operates at an unknown frequency. If 4r u745ryi cnd8h/jn dneither 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 wq5a;js6tiv e0j1 p o*phen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the stri1v*asp; op6it50ejqj ng? Explain your reasoning.    Hz

  Two violin strings are tuned to the samizz n*3y5ht8drg x*/ l:u+q; 3nb wdgje frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat dx* + lgh*tq3w;jg35di zun8 nyb:rz/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 play middle kb0a q vfr s*r41u/ m: g)s*cn;qchm1aC (262 Hz), but one is at 5.0°C and the other k ubfrsrm a n0:;4mc)s avh/g*c1* 1qqat 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 uxvy :n6g. 6fjd/4zgtHz; 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. Wha gtn6f4j : xzg6./udyvt 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 percv.qvp5cu +tuek2i8u9l 79 agson stands 3.00 m from one speaker and 3.50 m from the otheraqup79v 92gl+5t 8.u ive uckc.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a pian,slk0.wem/p eo 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 frequency/0e,k s we.mpl 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 beats 6fgud+2m/u ic per second ugdfc/2mu 6i +will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’po 4jdnv34 m6gs siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/sm3gdo4 n 4vpj6
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you d,zqrv)- x t7ee(x(l fxetect if a fire engine whose siren emits at 1550 Hz moves at7ftxz,((x)l r-evqex a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freques +r2 yqfj-g/, zfe/gency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencis+/ -e ,fegj2qfz y/rges 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 frequencyyv*lz vp /fi29 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/pflv9v y* 2zi.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultra3 dn2vr:k c) ugof,5x+yhr+,j7nfvdh sonic sound waves at 50.0 kHz and receives them returned from an object movijy:3rd x rfkh7, )2g+,d5vohf nvu+ cnng 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 of 5 m/s As it flies, the bat emits an (f h;m6fkc) meultrasonic f;f e6m c)(hmksound 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 played on a movi5;dt 3oydauq:ng 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 s; 3:yo5datuqd tation at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultraqy mdb)ph yq:+,/xy/ )fp m6gtsound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s dir tp ydx mf/qy)m:) b,g6/pq+yhectly away from the sound source?   Hz

  The Doppler effect using ultra);lg oi:km fs (*c9iy) kw5/mlyjyd u07x7azcsonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequdl2 jmh ekr;;p (l3bm+ency 570 Hz. When the wind velocity is 12 m/s from m;2h+3;p e l mdkjr(lbthe 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 iag d- 5pq3xj t4:jlit67o0oelv z x/s;f 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 310 m/s8b6ho z,zuox: (a) What is the angle the shock wave makes with the d bh,zu zo:o8x6irection 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 plan npdu0g9y .fq2et where the speed of sound is 2qn9.0 dfu gpyonly about 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 wavx ;k)dq 5utohaq89mlu( ekj 15e angle it9o5 mx5; )18(ljukaeqhtkud q 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 mq2owumx3 (3$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a (bl:t-oin k)izn 5 6oqplane exactly 1.5 km above the ground flying faster than the speed of sound. By the time (kn o)6:z n5tl bqioi-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 sound +s3u +j rt+shn/x vns1u8k;dfpulses downward from the bottom of/nks++fs rj1;s8vun x t+ h3du 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 octavesdv 8d688ltk4mrh dz0qynx mzm2dq 98* are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has l++3 ,ikutaeya display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open+kae+yul,3 ti 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 closi 8-m-z2mhuyj,c7q i akpy-m/ z0pw y1e to the threshold of humaq7/y- p 0zmamzcypu8y-ji1,2i h km w-n hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB q */8;sp0p f7zqve yo -dlb-sosound and an 87-dB sound are heard simultaneous-s/odbqp-* vsf7 z lq;o8y0pe ly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the 5dw2ay9oz4x6po(q ooxz1-pc y6 fu )lopen, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it razo9xy5aq)f2(p 1xo- pz od wu6loyc64diates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output detly dhe1j g. k,awng629)5x*aowzf 1rops by 10 dB at 15 kHz. What is the power output in watts at 15 kHatje faeghz 1,21n)5d o6*lw.wg9 k xyz?    dB

  Workers around jet airkxut kd-.+lsc5r:7w1n 9eu4 kulmdgfn ez- ) 1craft typically 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 7 xtfud9zrl.)-k41sn kk1w5cel- ue ngu md:+ the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicationkf4xqy 8t(ly; s 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 tunem6*8freiuc )+ejt c ,wd 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 violio sa2.,bl qpwmz:rh6, n is 32 cm long between fixed points with a fundamental frequency ofp2orl.,q6: s ,hbzwma 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set intorr7b2 i6kw5cy 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 ik27w 5i6 crrybs 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 that is open at onew+kx**3 ki cn2iob zzdb0:)3 fg+wich end and also 75 cm long. How much tension should be in the striz3cdz0:gfc wi)+ 2kon+b*kh3i*bwx ing if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was olow0f) 2 80izslg w)xpu6rq b8bserved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sourw7( 1(z pkndz-/jk idu* b,1tp9jlyumces. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves abo-1d((nm kp7zuy9 li pd1 u z,/b*wtjkjut and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on thehdddv-p )d-f/x1u6p.j+t wmx stationary train hearpd )wt.h+x6-jv -d1/ ufp dmdxs 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 it approac6:rtlwu9fuca+l2yfj b3:t5z hes you is 538 Hz. After it passes you, its frequency wa+u:3lr 6ty5:c2t flzf9bju is measured 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 by listeningmhb aqc7* ianr9pk4ib)4mk3/ to the difference in pitch of the engine noise between a)*bk7rp/q i4m ni 4kcah39ma bpproaching 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 frej hhp+),24ek;wcd mj nquency of 11 Hz. The shorter one is 2.40 m long. How long is the o ;2dk, )hmcp+jhw4enjther?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stztc3cibuwg-o5n6m0 brb5ot4 ; us 7.k -k7xfkationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is bet .inc547w k0ofg b5tou73cs tb6-k;zmxrku-bween the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood yac.qf 0aadc t9*p s7/flow in the aorta 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 blood cells? Assume that the waves tac*a9 pdt7qf acy. 0s/ravel 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 flyingbkqd5h8 g mgs(o6 *:gg toward the bat at speed 5 m/s The bat emits a sound wave ogo :gh*qg 8gkmd (65bsf 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 frequr (i*/no1eqxm z 1:kysyg0 x+fency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 m1n0zk xegxys fr y1* :oq/(mi+s 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 Alpinembix02x py-tdpcfc0n 2( af/i8a;d*j 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 fundamentafj ym8fbx* a;0dc2tic/2p0 pda(n xi -l frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of s wt/wt b0bcs ug/q((x8tanding waves, which can cause acoustic “dead8bt 0/ cwsugxq(bt/ w( 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 demonstratirs;2ioj t00 id y tq*felsa4c;y8 ts10on, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “singleosa4y 0 q*0cf0ds1s8 2t;jti ;riy t,” 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 heariga5z-lm 8ljl1ng for the human ear at a frequency of about 1000 Hl-5l 1zjma g8lz 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)hds isvzdli h*-76m+x v2aw) hears the sonic boom 1.5 min after the plane passes directly overhead. Whathdh mi 6*7+v zwids) alxs-)2v is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat uoi ;c3d3l :7ilaid(u 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