What is the evidence that sound travels aso98 -s7f0vz3useljgn(k; nd q a wave?

What is the evidence that sound is a form ofo ;1 vtkfvn:+fn cp2e;/wdzd6lo0x) f energy?

Children sometimes play with a homemade “telephone” by attaching a string to tni) fw ,d67xfihg 83g7j2xuilhe bottoms of two paper cups. When the string is stretched and a child speaks into one cug7 li3di)g8 fjwhux f6i7 nx2,p, 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, do you expect the frequency or wav)tm3w3 c c8g po(o)t x8jruo1loto(lpom 1r3 cjwtu)3x gc8 8)elength to change?

What evidence can you give that the speed of sound in air does/c5q:l7n o86q kcnct(bf fv* k not depend significantly tf 6nc5 qk c:7cfl8(vno*bq/kon frequency?

The voice of a person who has ix7l2 uzbcml 2n05zqq,nhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch o- t uj v.imgg/c2s3k4jf organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of souhbx52euh9 .wef7nxv m) oq g**nds in various frequency ranges. (An example is a car muffler.m e)h wf2e*g*5b.x9o7uvq n hx)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move ur we4ypamtf(.a6y ( fqndr+/( p the fingerboar ( r6rtmqny((afadfw4.y/e +pd toward the bridge?

A noisy truck approaches you from behind a building. Initially youwkg 6j ,2)flqi hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you heafg 2iq), wk6ljr more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be+ ahc8e(dkk5 n said to be due to “interference in space,” whereas beats can be said to be due to “interference in tihdkck58n e+a (me.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered1b wwjw6h(i1bgx* kb/- wj)*4k l q-lx qzq1sq, would the points D and C (where destructive and constructive interferew/q*xkbgh-*bjllk4j1s1wb)q 1w ( x6 w q -zqince occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areck.gm+ :7)hno(n uir uas 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, thennruni( +g :)uc.hok m7 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. Eay54q ezk6plr 0ch wave can be thought of as a superposition of two soundlqy 0e4pk6 r5z 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 the sourcei*e 12ynj9 0bd ),u h7c4gac c;roiamfr;fz1e and observer move in the same direction, with th91uai1 fmfzco;24ac*r,)cjy;egr7 eb h 0 idne same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound he pp;)7lhlg*xcs(f(s,e w:d zfard by a person at rest with respect to the source? Is the wavelength or velocity chfws(,zh lx7 ;efc( :pgd ls*)panged?

Figure 12–32 shows various position w, *dtf+4+rmraf s-cis of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which positionri sdcfwr,+-f am*+t4, 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 jh, wbzunn cb+l;m7.- 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 lu+lbcj;7w b mn ,hn-z.ength of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hearsyeb31ce*7 aah the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and d1ca*37hyae eb oes not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a3w, wbsvf i+i8nph 1-blx52lst 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 a foggy dak6in1lgijhf,nv- u* fn :j0, ny. Without warning, an engine backfire occurs on aj l*-:g6iik n1,jnn fv,nfh0 unother 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 it makes wh s+-zbsid6wjo/t: h 0den striking the water belo od:dssw6+hibzt/ j0- w is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the g8k- 1btc d:qvlround, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the ai:bkqcd8 vl t-1r and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over /k1im0gfm d* aone mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperdmg*/ f0a1 imkature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of )xh7c:1igx cfdt+0tn a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sounzr:dn8 9tse l-ij lj)/d whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sil,7t2 qhb/h ubnxkm5 6multaneously at a certain place, what will be the sound level/76lh bmn ,2xqbk5t hu if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally r/)b3yac bpn q ykw:47noisy jet engines is experiea/) npyb3 :b7 w4crkqyncing 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 dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratai7myf8,*,e ,ivc5vc rscb9 v io of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background ncfce a7v5*birv,9,i y8vm, c soise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sounq. 8euc6rh:/ad 5bk rl6vdh8di t d.6.dp/zmod from a person speaking in normal conversation. Use Table 1 dr/dc..z 8lp idh.h :666t mq/8u b5daevodkr2–2. 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 eeci h+ ya(ur,8ardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B is sxf )o -rm9gg)8tj0-n2ev fkv rated at 40 W. (a) Est- n-fgox8 j)v9g)v02 kefstrmimate 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 in frf9p*hvomm5)iz/ 1tbrp ez*j.ont of a loudspeaker on the st)peibmv jf1*/zmr9z o * pt.h5age.
(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 d8 ,xkm)ks ;abqqd0x q*etect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of tws;xqqb0) , ad8m*xq kko sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by9ozek *i/1kimaeb *z/ what factor will the intensity increase?o*ib9zzam eke* i /1k/ Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal ek/6bvk:e 4sudisplacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitb vu:4s/e6kke ies?   

  What would be the sound le .o a:y8,bqfxuqjqx-5vel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibratiox,fy -aq.jb5qux8 q :ng air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have kud,l f0 pep(+q jbh9+what sound level to seem as loud as a 100-Hz tone that has a e9+p(q kb ph0+fujd,l 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highe y5;0jyny )buaikz* 0,/ h+ mw2ppcwyzst frequencies that an ear can detect when the sound le/ 0i2 ah;bpuj5c*m ,wnzyzpkw)+y 0y yvel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Wad iq:5ntw ;6vhat is the ratwi6d5a; :qtnvio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 4iepwzf2m7 gu0)/r tn+40 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must th fp2 +7mti)u rzw/e0gne string be placed?    N

  An organ pipe is 112 cm long. What are th*s6l n(aeopkcy+ t 52we fundamental and first three audible overtonesksn +o2 awye pc(*65tl 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 top of,c1ni wt3 k(5m us/hvc an esn 3t5cv m/uhk wi,(c1mpty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipez+f odf (8zix6 organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be ixfzzo+ 68 f(dthe range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency o(zg7w5.dz-c i mjkux4f 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at m.wzu( gx-7 5j4dkczia length of only 60% of its original length?   Hz

  An unfingered guitar string is 0mb 1o3x9aom (ez h90z*czdd3c.73 m long and is tuned to play E above middle C (330 Hz). c09 b 3em1o(h3d xzamoz9cdz*
(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 thay9w46yrip *l3-r -qrqga2po jt emits middle C (262 Hz) when the temperatly q -yariq-9p2*rw p jro4g36ure 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 ml y 5,/roz at2mqwd *3uu..cjat 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 rz+br xhj d z(p98stw/4dv6-gthat must be uncovered to play ( r/t+9hg 4jvrwpsdb d8 -x6zzD 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, az xtxbnk*6nvz+g n29,nd 616 Hz, but not at any other frequencies in between. (a) Show why this i2+* nxxgnbn ktzv,9z6 s an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tubet ;xpc ui0ec1f:- 53 7ckzbesk 1.80 m long is open at both ends. It resonates at two succ1c;-ps70 kzce k ec5:fu ix3tbessive 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 ;lx;xz8rol 5;cdf; py$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-leagv*6s ( w4uic;3)r3 f5jrqbf- ndgb ong organ pipe aqfeb-36nacu f*r5j vg(4s)3; wibgd rt 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 oywijtfbd z *s2,/4fk 7pen to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig.7ff2z k* i/ds,w4b ytj 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, oj5vp d8jko+7 vc8 dk)vne of which is sounding 440 Hz. 57ojdvj8pvc8 d )k +kvHow far off in frequency is the other string? ±    Hz

  What is the beat frequency if mid0n ;arrq ,mna6dle 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 (braun2)hv xfmmsuqh(wz:fnm ax/6/sjg3j *-4j/ nd X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately,jxu 4h-sa3/nmwq (ff )/h2m6u /:zj xgnvs*mj 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-Hoiuj :k1dps6r 1wd i16z tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.w1 ur:16ji ddk1psio6    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tenjvaqvq.q5 3(6 j6n hb*ibyj 7ssion in one strhvb jbq7vy6 nj5 3.ijq6 a(*qsing is 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 play middle l+lf f 6kse qidw4:f--C (262 Hz) s4e6f lfdw-k il:f-+q, but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tunin mlcc( a erx)oqt142e1g forks, A, B, and C. Fork 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 are the possible frequencies of A and C? What beat frequencies are possible whecemtaq1 )2r e41o( xcln 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 from one speam(oy.fzrm+5,hjj p 0 gker and 3.50 m from tjrj (y fzg0, pm5moh+.he 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 sup 9crgxcn4x 1peb4wl 70posed to be vibrating 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 4 cx0le9gxn crb714wp 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 d +g8*yjrydp3vc vr /-beats per second will be heard?3g* c8ryyr+d-jpvv d / (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at b d7kdvy- x(v8rest. What frequency do you detect if you move with a speed of yxkbdv(-v 87 d30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequ*4-xa6y4daosesasjz+d1 o:n 5 y c4orency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32rsdca+:y*1djsa4 -o sy 56xzn4 eoa 4o m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movi d.j) j ss;mk6/*jrzves/in1yng toward you at 15 m/s in s.sjj1y*svrj) /d 6z;/e mkversus 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 frequency horn. When zf cz4uz v.ke:3;py7q one is at rest and tvy7 3 zqpfz4.u:c;ke zhe other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultravrcq-)ph a)a9xn001 )zw3bdkj ) avqlsonic sound waves at 50.0 kHz and receives them retuh)9rpa0 3naz1qvvw a)kl)) cb- qd0xjrned 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 spee5f0ew k;klzz*d of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hzzke;*l 5w0kf ear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat .9 gm(vxj, daiytn :1ftrain car at a frequency of 75 Hz, and a second identicatnmgxdaj:v y 91(i ,f.l 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 spygn3cbj4 ( -hreeds. 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 directly away from the h gjcb3y-(nr4 sound source?   Hz

  The Doppler effect using ultrasonic waves of frefp 79 hnrm24ijquency $2.25 \times10^{ 6}$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 of8-khky e 7kud:6k3tis frequency 570 Hz. When the wind velocity is 12 m/s from tk8k-ky36i7hdk e ut:she 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 movingz)7 szbzs skk;1kg m00 on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Wh(loefd sg352 zat is the angle the shock wave makes with the direction of de( o5sfglz32 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 atmospherz y3xj h6a0f.ae of a planet where the speed of sound is only about 35 m/s 6z.xh3 y j0afa
(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. Determi3ou 6r( xhj* : dps-;mpmx7hztne the shock wave angle it p7ht6-sz u;p djxm xroh(*3:pmroduces
(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 0q r ,abj(8 iau.j1jyl$/theta$ 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 ef4 tvw4 t 7 wv98wiwb(wqz*0glxactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear tbwv(ww z* fg709t4 4vwtiwlq8he 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 pulro+/qk tmr o .j79cs4hses downward from the bottom of the boat,kt.9o7 j mr c+qosrh4/ 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 o7 vyhe;0dc 8s xl5(ppyctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It zv:uv( ta md33consists of manyv m(uaz3:3tdv plastic pipes of various lengths, 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 person makes a sound close73r/ m jlpkn,l to the threshold of human hearing (0 dB). What will ,lm pnj/7lk3r be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level whxf1zcg)kl8 9gh h8y7* ppi3t wen an 82-dB sound and an 87-dB sound are hear ty)p g8zkpi g37f8x1*hcl9hwd simultaneously?    dB

  The sound level 12.0 m fromg a lhr),xzkl q0)*e4dy9 s4jln-e7 uv a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, *s4ua9) 0hke j dr-,zny7vl4gl )xeql assuming it radiates equally in all directions?    W

  A stereo amplifier is rated atnyn b6h 5*t)i82 ldndnti f,k5 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What isi dlkht*b fnn265d n,85it yn) the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear prot5opl* gd 6pj7t-5ybyf ective 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 the power intercepted byy-dtyb g55 7pj lpo6*f an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications syste)oi34uh68rnbil5 noo8g , wptms, 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 ih0+dzf *ovj3w;r m9bgs 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 violingx; 8oc1 ubr nvf530k5res-yr is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per un0cg 5;sn efko3u8ybxv5r-1 rrit 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 x;4li 2svvrg e4x)vf*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 s fxr*44v)l; 2vxegvito resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is+o 4ix) q;y:d28nj4gv tlivvg near a tube that is open at one end and also 75 cm long. How much tension should 4)ldxvo4jt2ivn+ v :ggyq 8;ibe in the string 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 on gty0d8s7lc 1ne 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 )op5pwvh hhyp/b;2j) 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source twy)h5hv);2 / j hpbopphan the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One trait4n*k 3u.-d mfol +prcn is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train aocnm 3 + lp.t*frd-uk4pproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistl2d5 drs 7oj wrjw-2vm,e as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant ve-m, 7 jvo2dwsjr25wdrlocity)?    m/s

  At a race track, you can estimate the speed of cx/ly. v045eui 4ds ulqars just by listening to the difference in pitch of the engine noise between approachingxql0 y dui4s5ue4 l/v. 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 frequencyf.qzc wsjy k - )m,+ucq9b5b4r of 11 Hz. The shorter one is-.j9m+wbs fyu)q 4qckzb cr,5 2.40 m long. How long is the other?    m

Two loudspeakers are at hgxio4;g)b*k opposite ends of a railroad car as it 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 frequency heard by the observer when (a) he listens f)k;oi4 *gbhg xrom 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 ar lm9xa/wnq-h0qtka;i(4 w s5pgo ,w1orta 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 wip5hwrnt 1 k94mg0(/ ;sqw q-ow,alxaaves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a mot zkd;em/ye:5 lh at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 5z: ke ldy;m/5e1.35 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 frequency sound pulses c d.a 6jj7kd l(tmd:.fas it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is ecjka(.jm:.f 6td7 dldmitted?    m

The “alpenhorn” (Fig. 12ktrc 94wrqsb1 t0jsb;2lazlk851ci3kb52nv –38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When ptjc52n qsb89lk 3s1t0 vw4ab1 r 5kkc2;bir zllayed as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromisedcpgqnag2s h l3/gf,3 5i mxvy 5.9/umq 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, u/p255ag hxs3v/i n mym9flq,q g3 cg.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,” involves a longlnni2-*lq)m (g6 icl mon.f6b, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a cleiog-fln)b mnn l 2ml. (q*i6c6ar, 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 frequency of mbp v jns42m5 u12cleri:xf:*about 1000 Hz is4vfe:p bmmc x1 li*u22 rj:n5s $I_0$ = $1 \times10^{12 } W / m^2$ 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 ac 4ydasa;x77 6e ar7irt Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly ovea7i;76 7rr acyxed4asrhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15f36nf ,qux(xdz4 btz rb*;u7v b5 x2ll2/nbnz $^{\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