What is the evidence that sound tr4e x6k b3pd:yyavels as a wave?

What is the evidence that sound is a form o f/ko* ,n(umicf energy?

Children sometimes play with a homemade “telephone” by attachzjpj5*x8e8c:blal ,k ing 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). Expl: ll5ec88,* kj apjzbxain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from 11 vp2rnf ;b9ohc6gyqair into water, do you expect the frequency or wavelength2r1 bcqh9pnvy6o ; 1gf to change?

What evidence can you give that th o/ads,db 393luns hm*e speed of sound in air does not depend signif 3n9h/, sadob3ds*l umicantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitche3bk n71 swu)a1 u )zxm)yimiu.d. Why?

How will the air temperature in a room affect the pitch of organ5x) djff t 4p : zswra*z46(8s*pxsahk pipes?

Explain how a tube migh +r dey*+s-,4cfc(nhs4qd5i3mkhq oj t be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An examplee3 h4 rj ksq m(osy+5ihnqc+df,-d*4c is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you tqa/y 9; kz *lomh22sgmove up the fingerboar92z/tgam ;h*oyl qks2d toward the bridge?

A noisy truck approaches you f9j.gvhhi- es lc:vo6(3khs46ym. k nlrom behind a building. Initially you hear it but cannot sjim-:lskvsvehh 6cny.k( o94 l gh.63ee it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference / e8q7id0kwat c(zxq1 in space,” whereas beats can be said to be due to “interference in time.” E8qkdzeq(/xc 1 w0ita7 xplain.

In Fig. 12–16, if the frequency of the speakerssscp v o6-(h4w were lowered, would the points D and s v- 6pco4s(whC (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of lc im3k,,5yktprotecting the hearing of people who work in areas with very high noisekciy, 35lt, mk 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, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be r ;jb) kigz0 p.5svbso9b j5/gthought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In whic0igrpvbjbs/ ;59b). kgo5 szjh 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 s:nag6up+s;)t q. bsbiource and observer move in the same direction, with the same velocitu+n. ;pb)gs:aqi b6 sty? Explain.

If a wind is blowing, will this alter the vd1h8k *w2vx f vopt* b0**kyzfrequency of the sound heard by a person at rest with respect to the source? Is thev1ob*xkft *hv0 yz**p2kdv8 w wavelength or velocity changed?

Figure 12–32 shows various positions og /: 2mnw1o fgm8plrln 9+pk1kf 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 hear the highest frequency for the sound of the whistle? Explainko21r8 fl plg9k+: nn/ pm1wgm your reasoning.

  A hiker determines the length of a lake by 7v b: 8q3wzjaslmls8/ listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s mblz3qvjs7s8 a8w l:/after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship+o+6 8 alp uwsf6b.xpf just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below6ff. +lo8apx puw6b+ s 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 wavelengths in airh)q1et/l*n efg go +:gk86 cly at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tunas7ihjov0ld. )+ y npgz;o- u3r on a foggy day. Without warning, an engine backfire occurs on anothu.ohp jgsrd )y z-;3i+7 nlv0oer 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 s mkb9g2m4+cr cl;/rha cliff. The splash it makes when striking the water below is heard 3.5 s 2klc9r cb4 +;s rm/hmglater. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge st;qcpul fb(c r 1bx4g)5one 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 they are 1.1 s apart. How far away did the impact oc1qr 45cbp l (;xfgcb)ucur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance y h8x0v/ki y(cby the “5-second rule” for estimating the dist 8(ykivy0/h cxance 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 level bzz-ojpln ay3ha5,+.m9 b 3 ulof 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 lgj2we ,3xp2ysound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB mcsn.4)j )yyx when fired simultaneously at a certain place, what will be the sound level))4sycm n .jxy if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an c:)p2:qxvbws0e+m s lairplane with 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 sh+elsc0 psb2qw : )v:mxut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratd.v/uvmr- trzb/b- b,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 noise for each,.m- d-bvbz/tu rrv/b device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person ntddr0de s;5: :c8ouyjj8 r7espeaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere t r8o r;j:0ydesn j8d:c5 de7ucentered 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 ear:;dkv/zq )razkiog5sjpf) :wfu3 c9( 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 rate tgg62;dxxc fiu(6f4 cd at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a pointgi (x6fx4gu6c2cdt;f 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 whefe 4o- *ov0skmgk ouf96hh- rde(e6b*n placed 2.8 m in front of a loudspeaker on *(khd f6me9se*0oovr- 4f-bu go he6 kthe stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound leveav.7tj g1gw1 cl of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diffe1wv .17t agjcgr by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is trlgrt66t(b0i c ipled, (a) by what factor will the intensitt0r c(6l it6bgy increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, aief95*h,/fl3l-mjrla 6ex5 z vvcp9 but one has twice the frequency of the other. What is the ratio ofv/ljv3cae5pa9 *r 9l6hf-emz,lxi 5f their intensities?   

  What would be the sound level (in dB)q,:08p ol5gi(u bvofb of a sound wave in air that corresponds to a displb8uifol,: (bp5 0 vqogacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have w(ng( fvgt-f. 1i3 z csro.dh uw2))vquhat sound level to seem as loud as a 100-Hz tone that has a 52)(wv(ru-stfn1i3. g c)dz. u hfqgvo0-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the u5: npwuai3p7fld,jyx8le30rn 2 8 pmsound level is 30 dB? (See Fil p ,:fujap p82undi83elm7 3r0nyxw5g. 12–6.)

  Your auditory system can accommodate a huge range of sound level2obi, .df yvd k;g/6)/zxxfshs. What is the ratiof;vz/hk/ oi g2bx6df,s. x y)d 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 ai lmkg2tlv:nk rb. 2-. y/ub0p fundamental frequency of 440 Hz. The length of the vpb.l:gbn 2 .vk0lir 2yu-k/tm ibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threeci8-)hj* n+m *s) d 2 apk6iqcvsezi1m audible overtones if th 6+csh 8pm z**cn vei21si))- adjqmkie 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 wouy;-).-p9ad yu +9 cdkmdlhbtvld you expect from blowing across the top of an empty soda bottle that is 18 cm deep, y+p9-9.-) lc ;kud t vambydhdif 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 q h-8j jay3ubsy 80es-with open-tube pipes spanning the range of human hearin3 yeusj-yqjah -88b0sg (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 frequb ;/;vonqd2c dency of 540 Hz as its third harmonic. What will be its fundamental frequod d2b;qv n;c/ency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play Ex2 3ow3m+21bulbeh 8x j07fqw czvk( bl,any; above middle C (vc1b mlbfww,o;au3z8x73(yexkl2 j+ n0h q 2 b330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe thygck amj;x8d /*)+m3r wvmk :vat emits middle C (262 Hz) when the tew x3 8v:m y dka*g;j/vkmrm)c+mperature 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 af8hg/nbssl vt//.cg(.l u c* pa+ep-pt 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 aa-y82 tfnqz/ the hole be that m2afna8 t-q /yzust be uncovered 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, an,zsw*le9 / b 7vacuiks284oq+q uu5d yd 616 Hz, but not at any other frequencies in between. (a) Show why this is an o 5y9ub/*+4qo8k7eucavds,q wsu z li2 pen 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 lobt m(/.fg,j2l1ik qdtng is open at both ends. It resonates at two successive harmonics of frequencies 275 /l2,.jtif1db (gm qtk 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 -vss akk.s5vl:q; 0 /+ wfipps$^{\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-long org fxuf:.,81iur( e)e;8mcbypqn m8 nt van pyu )u q8ffni p:1 mr8 (mbexce.v,;8tnipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open tof+1 j.vha-,g8dsug jp the outside and is closed at the other end by the eardrum. Estimate the frequencies p18djgg -uvaf,+s.hj (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 trying to adjust two strings,a)c.f ec4x yh91 evr8j one of which is sounding 440 Hz. How far off in frequency is the other strineyfe. 49acr )1v8hxcjg? ±    Hz

  What is the beat frequency if middle C (262 Hz) and y1o7cw(mn1fp $C^＃$ (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 (bra tmx- l krvzzy5p3oqf .bi )xu*++0hf+nd X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequqv*fi flby uxzm3+z.-t xp)k5oh r 0++ency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-H xgossbdd; :ty q 88;rfz vf*3alv)(3bz tuning fork and 9 beats/s when sounded with a 3stq 38vd; y(dv )br3f; lx :z8a*ogbsf55-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in on9 avh5g2 mwr5h+ .vw5tn0ujkge string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. ug+g9r5wt5h. nw mhvj25 a v0k11–13.]    Hz

  How many beats will be heard if two identical flutes each try to playew7qwg;rw sb3/6+kbtrs a q 37 middle C (aqwkbs wr7g /b6 3+3se7qt; wr262 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and ; :ze( yuyfk/gC. Fork B has a frequency of 441 Hz; when A and B are sounded toget/gf (:zu;yekyher, 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 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 rc7h06ephj2 d 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m fror jechh26 dp70m the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are suppos v g,sqqc;jy.-ed to be vibrating at 132 Hz, but a piano tuner hears three beats eve.qqv , sg-;cyjry 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavel sfcs(qm 1v8rp-:71o soal)rg*j2 6cq6jagnj engths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20 o pv*nqsja-jr 1sm7agj16sf) r8gc(c62q: lo $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency r,/dehb(- wm :u* 0mdgjsjau1of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/s/ahj( g s r:-ub *wud0,mm1dje
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequf8z7/d ol v:bpbk+ a/jency do you detect if a fire engine whose siren emits at 1550 pado/8 k b jv7bf/z:+lHz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toxw) 1r:dscc/xward you at 15 m/s versus you moving toward it at 15 m/s Are the two f /r)cw:1cdx sxrequencies 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 sa*d ru p0c bx.qiaxuv)-,c v6a4me single frequency 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 Hz. ccbxd6 p.v-,u)v0axa*rq 4u iWhat is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receive-oo(pek(af .oyw mk3 ,s them returned from an object moving directly away from it at 25 m/s What is the received soundp y.ofkk3 m(woo-e ,(a frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies kpe*,ig8j )up, the bat emits an ultrasonic sound wave with frequency 3p*,p8uk e igj)0.0 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 moving flat tv)ba5cs,a3d u4 uo mg-u0l3vdrain car at a frequency of 75 Hz, and a second identical tuba played the ua-d 3ov g3m0u54a,dcbu)slv 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 -4 fpoo xomci1*o/my4 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 freq mcpm /ox-4o1ofiyo4*uency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using uy mt6pmfn/g du -26a,e-:lgam ltrasonic 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 frequency 570 Hz. When the win ike1fe(p*b m6d velocity is 12 m/s from the north, what freque*b k 6e1pmef(incy 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 lan8pub0 kvh3v deh77zb,d 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 s2z3ugs3 *n 00g3xz.dgcr dbq apeed of sound is 310 m/s (a) What is zsgra g3du.b 03g q02cnx*d3zthe angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin at79 ra6 ;c39mmobmfsnqg-nkdm3 t9z :umosphere of a planet where the speed of sound is t c97:3muz qn9 d g3or6s9abmmkfnm-;only 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 strikeg wo 4 (0+rbdu,zwfbfkada-/5s the ocean. Determine the shock wave angle it produces - 4du(b+ad/ az0 bkofgwf5wr,
(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 z j2ive ,*h)e )*zq mim:r*n 4oytvbk/$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground fly hbw c8fp ne:6alw:0e,ing faster than the speed of sound. By the time you hear the sonic bowe 0:6lpn af:h8ec,bw om, 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-w2aecp wngz x -c99v2e9n7nu 3Hz sound pulses downward from the bottom of the boat, and then wnvx9 -9ewgc cnnpe 22ua z973detects 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 thec/e 46s8z,gut*epydgi*djhp 9gyv 19re in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called aa 5 *rpz40 iygx4dw*sc sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on bo4c piyasr 0 54dw*xg*zth 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 thtsj0v g)bsoo5epvs c -:6gpc*;nl-k +reshold of human hearing (0 dB). What will be the sok;o5v)g0s*tnjpls6s ebvgc op+c - -:und level of 1000 such mosquitoes?    dB

  What is the resultant sound level p ;;9 rd5afn2 vofrl7 bcgq::kyqf42ewhen an 82-dB sound and an 87-dB sound are heard simultaneouf;l: 5ga47qfyn; er:dk2 fqcrv2bop9 sly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the op 9kn2*ofboi lq)ji9g) en, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equal9qk ib)n)9gj2 ooif*lly in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power our oxxxpo7 yf+hp 069k1tput drops by 10 dB at 15 kHz. What is the power outputhof0x kxp19rp6x+ y7 o in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices overp66eqbo2gb/oax4ph6lhnmvi z:) 8 3i 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 e avq3x6ibb) ohn62 / 8h:i6egmzolp4par 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 communications systems, the gai+ 2qw ,yoh*yniky.7po+nyt, vn, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to 0sgo1uw4 ;a(9+r5uo2+qy(jx r e 2 lqjngwhmx 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 323jsr m2 m e*rcjm3 siz)0pz41t cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit lengtepm) zjmc3z4 j s*3r2mrst0i1h 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 a+h.k+afqsr *es z sbido* +l/7bove a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it doef*+o.sqdr s+lk*hbs 7/ia+ zes so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of m(evbscfv h/pa-* 4q.xow )d3z th -x6bass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic oh c - zd-3 vfpax)6xvtb(*/swhq4be .in the tube?    $ \times10^{ 2}$ N

A highway overpass was observej6il1(swicj q vr,-4pd 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 6cpoiz u po.b 35setfdu*),m+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 than the other. Whb+u d5o. ,sfpo3e uci*)mzt6p at is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on th xgyyh2 tj/xj.(3qyx56f7v0y pbnb4t e stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of y tvyxj(70 ntj3g qh65b 2x/bxy.fy 4pthe moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aft 5r dmrbgvj y853(zah:er it passes you, its frequency is measured as 486 Hz. How fast was5 8r 5b j3hdzmg(:yarv the train moving (assume constant velocity)?    m/s

  At a race track, you can esti/dh-hgwrv*24l ge9z /gpkt t3n3m0srmate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as itzt 4e29r3ld/ k3s 0grgh g*wvpmn h/-t goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, prz i ywer5q95;qoduce a beat frequency of 11 Hz. The shorter oe9iq y;qr 5z5wne is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as 07ite xr1z whgzx* .7iit 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 from the position A, in front of the car, (b) he is betweenh x .*egzir7iz10t w7x the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flowfz kou9ig9d64, ;ihn e 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 ioi96fn gh,k ;9z4udethe 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 c,i.e jddt l+. nrrfq r)/ifd9i9-)as the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat aft/n+.dr)ii cdjr-sfl d9q, .eif) 9rater that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a motii5 n3e,ny yl0cgbja8, ./oskh. 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 chi5k 0l negijny8 .oc 3b,y/is,arp is emitted?    m

The “alpenhorn” (Fig. ot1ab b7:(ima 12–38) 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 deepaiobb at(m 71: sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of standvuil2dcrh/8wvmd6 qx piqvx3b bi8o35: /5q9ing waves, which can cause acoustic “dead spots” at the locatrpdl c 6: 8do55v/ibxbiqv3q3xu8v wh/ m9iq2ions of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing y( oxqz)9c yhnrlu9il 1(;mx) 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 l)x)1z 9oh;(q9rn iyc(ylmux 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 theaavhxw+l- 0 z 1j*6xsl human ear at a frequency of about 1000 Hzl1-*+ vxal0ha6jsxz w 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 gr y,ht9.s 8v5zn,c(7r mijrnp wp:bh 8dound hears the sonic boom 1.5 min after the p(.h89s7,8c pj mdirvzpnt b,rny5h:w lane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ism4:i4jnh8ak,b rjfw5 mw.) od 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