What is the evidence that sounino ty-6 qh-o7d travels as a wave?

What is the evidence that 4. 8i0l frtklzsound is a form of energy?

Children sometimes pl3 o:ram b)lqa)ay with a homemade “telephone” by attaching a string to the bottoms am3):ro la )qbof two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into cqm7*n6duv ulr) (4a6hb:7y neh4oay ,g 8an ywater, do you expect the frequency or waveleng(nyov6 e: ,)4uybq*ga ulrdhyma8 7n a74hc6n th to change?

What evidence can you give that the speed of s.fe8-hd s6z dwound in air does not depend significantly on frf8 e zd.hw-sd6equency?

The voice of a person who has inhaled helium sounds verq0mgw6l a6k6 py high-pitched. Why?

How will the air temperature in a room affect yxg.kqddtw): 86aw7ndz( gk(the pitch of organ pipes?

Explain how a tube might be used as a filter to reyey8 -pbkco6mb 5(3ctduce the amplitude of sounds in various frequency ranges. (An example is a -k6 e t(cbypm8cyo 53bcar muffler.)

Why are the frets on a guitar (Fig. 12–30) spa2xhgl to25d: dic;gz0vdv6x2n+nn - tced closer together as you move up ;dt2vo-xcnz+ dg 2ht:l d6gi2nx 0 5nvthe fingerboard toward the bridge?

A noisy truck approaches you from behind a b fp-9 bhly4pk-uilding. Initially you hear it but cannot see it. When it emerges and you do see it, its pb 9fhpk -l4y-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 “interferenceepav;t6ac 4jt ;37orl in space,” whereas beats can be sa4e cj 6v;;oal3p t7atrid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequxvj1-d; dxf8i ency of the speakers were lowered, would the points D and C (where destructive and con8 -xdxi;v d1fjstructive interference occur) move farther apart or closer together?

Traditional methods of protecting the heaj;47gr ubi;ak ring 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 uj4i;kag;b r7do 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 waves1van2 r pw:qj* shown in Fig. 12–31. Each wave can be thought of as a superposition of two soun nqwarvpj*:21d 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 source am *h +knyufs20skn)m2 nd observer move in the same direction, with the same velocs mfykmnks)+n0 u 22h*ity? Explain.

If a wind is blowing, will this alter the frequency of the bm- zi;5hzs ypm 8ki9vxw09n;sound heard by a person at rest with respect to the 5 vi-9nmkw;9mh0yzp si;8 zxbsource? Is the wavelength or velocity changed?

Figure 12–32 shows variou7ibs) tvardje.6 6e /hs positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which positio 7h. a6dbj) /6sveitern, 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 l 85ymb6mu++bx mvodt: ake by listening for the echo of her shout reflected by a clitd5m b+ub86 +mxy:movff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jla3 fzst)x4(2u,osnkch9 en d0s g8)just below the waterline. He hears the echo of the sound reflected from the ocean floor directly bel93sgxles2c,d8s )n n4ka0 ztj(f)uh oow 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 wavel4re+- x5/hv,ccc ad9ri b8fqhengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting jus8(4ldzdfj/0*kae:a1nh0a0x75uj nj fj cwhxt above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How m50z0jk /0xd jae1la(hhcn f*dx8nf 4wju:7ja uch time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped fr64iiw e;0)hfbwynq+p om the top of a cliff. The splash it makes when striking thnb04hif+w i;q)ey 6wpe water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the.vejvr1wc* 8tu7hd1i ih xpm . ar1b+/ concrete pavement. A81eduv m/.b rijachvr7 1*1wxtp+h. i 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 occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over ong9 alc i guuj0h8*3+ d7pacfls ste63/e mile of distance by the “5-second rule” for estimating the distance from a le/ ga9lh7l8c*3sj3 ucgdt0p s a ifu6+ightning 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 of 120 cxh4 bxe tf vjqm.78:*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 adyr+ (hfafiwlu5v4 ev8. 4zjz00x n m, sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousl53 nj/8 hh3:lawq3vyqd rmy8o y at a certain place, what will be the sound level if oqdhy jqr vaw/m8335y:3 oh8lnnly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wie oy/l p9 0o6q 4xj(w(xqvdjw(th four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the cay9 (wxoqp4((jvw0/ qdl ex6oj ptain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to v3dd/a;jjg7m5i+3 o1hcbja n have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the75njd1 3g o b+ ca/j3;javihmd 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 normg e s90vg(4 b6pckk;iral conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on4ivgbkesg6( cpk0r ;9 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 agqwgipy 6 c4r8 y8b,n8n eardrum 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 isgaj9ft n91 eq ,c/a,uu rated at ntq9aae9g, ,1fu/j cu40 W. (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 dv:uj( p j+n+4 hyis(pbB when placed 2.8 m in front of a loudspeaker o+(bnvsij4+p p (u y:hjn 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 differenc1 xbnrp./x3g/f2elv2wsd b )ce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this3l2bdesgc bn.f 2p xr vx/w)1/ amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wille 3yv v7j(:wvy the intensity increase? In7jv(yvvwe y 3:crease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eq9kekb7hr et drdwbz:5 /1 d3 2vd/5tobual displacement amplitudes, but one has twice the frequency of the other.e9b/rd/ b 32wkkzhd 5t5d1:dvo7tebr What is the ratio of their intensities?   

  What would be the sound level (in dB) of ,pa 55qj2drmytj)pcf4qb o;/a sound wave in air that corresponds to a displacement amplifpa4j) 2,yj5 ;rqbd/o cp5mqt tude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to sgkn8,u 1 phwn+eem as loud as a 100-Hz tone that has a 50-dB sound level? (See n+wp nhk8,1gu Fig. 12–6.)    dB

What are the lowest nmry6td y (d0pjzk:z80wh 96kand highest frequencies that an ear can detect when the sound level is 30 dB?d9 0zkhj d:m686ytp0kwnzr (y (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of ajb*(x2cs8 jsga(t s 1sound levels. What is the ratisj( g1aa8xjcs t*( bs2o 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 fundamen uo(i nk .a987uvsrfe,tal frequency of 440 Hz. The length of the vi, ev.i (87ao9usnkufr brating 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 fuy fuce2a:5fjq w6pr)vo;p1 o6ndamental and first three audible overtones if the pipeou ypj;e1 vf5:fqap 2c6rw)o6 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 frr/r nr*; lnc1wequency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed itc;nlr nw1rr*/ was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spad5r 3x* 69z-*a; hp ywt4(kxldcm0tlswz/y iw nning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes req-zzy* kwha3 l60li /*mtpt(wxy sd4xrd c;9 w5uired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz go42b4gx zjhhr u ;(grq4.x*zas its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its orix*4gb rg;u g2z4qrz4.jxhh(o ginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to pz8t9s h::qv (6 enlqielay E above middle C (ehe:6i q s(9tqnlv:8z330 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 that emits middle C (262 Hz) whwt/xmexg3 3 q05ytdl9 en tqg9ttmxx3/ l3wy d0e5he temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune al.uab:b h cv*/mu+mv8 t 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 E4.qd4g:d8z.ly59ogw6yu ks4fj a awn xample 12–10 should the hole be that must be uncovered to play D above mid9onfl d4a. wgg.wkauz:6j 48s4yy 5dqdle 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 pf wsrz8rzqbx513p k0qe( xt0, ipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other fr (qpw1 f x5kbxz0rse3q,t08z requencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long isnvah:nl2 1 9cl/bc n.s open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and2nl1 n/vc9h. n:saclb 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 2eokby 3bjh kuw 63,3m$^{\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 vac r 5c*jy5v 6wg:5exorgan 5:aj* 5we56v rcvgxyc pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsuy2z xr2djah ve(0l/ 1ide 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 ouravylz12(j/hex 02 df Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying2;uj:(h,9 o cl d vhwy,fjuv)q to adjust two strings, one of which is sounding 440 Hz)v,h l9cfuqjho d(yu ;,2jwv :. How far off in frequency is the other string? ±    Hz

  What is the beat frequenc6n+ kd;hpd;ha/ zyoh1y if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another a(ft vv1ice)5(brand X) operates at an unknown frequency. If neither whistle cave51fi a)vt c(n be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 35qcuy;cpr1-c8 t 7m)qz0-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the)zr1q8c ;cymt- pc7qu string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same freque h-.ioofn0xv y,:zg4b ncy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard whe h4fy0:n-.g,zo ibvx on the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identi a, p53m q8mi6nk(dnufcal flutes each try to play middle C (262 Hz), but one is at 5.0°C and the ot8p (ni,n6kduqafm3m5 her at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a f3(fu; xvf )gwo-wab* mrequency 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 when A and C are 3o ;vaw-m(*fu )fwbxg 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 p*)q93q-8q ;px ifm j-a5 ry;zog uj/xqe( rxmterson stands 3.00 m from one speaker and 3.50 m fr;rzf9*j)ypgj5m (qt mq r8qqi-/ ; -xx3auexoom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a pigpg lauhj 4d)qb 7x4/gf-niw2 j 5,m-jano 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 of tqh iwnjxm4 -7jalu/ ) 2-bd,g4ggfpj5he 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 oij9 ogjws23xnx9.d e4f wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Asseig2w d4x 93x.9jjno sume 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 r 7;aa0s2n (rpx mi9hgpest. What frequency do you detect if you move with a speed of 39s ( ; a0xmrp27npagih0 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect kh c k4z l0(yxe2l(i:qif a fire engine whose siren emits at 1550 Hzkl (zlq 2(i0k :c4eyxh 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 sourjhixgu9 - ae36ce is moving toward you at 15 m/s versus you moving ti6guh a 9-je3xoward 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 sxls/hmnfn( :tf9i- tm;xhi 4+poj2 :hingle 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. What is the frequency the horns4jln/hmiihtohftf;( x:n:p +2s x9-m emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves g+kurs2ie 28+hd8cdu at 50.0 kHz and receives them returned from an objedhu+ks2+u8g 2 eicrd8ct moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emit r,:bfu m;y*dbs an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat heab ;udfm :y*,brr in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was p f u- ee83rk*skdj7g:llayed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if t*du3 :ekreg -ls8kf 7jhe train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to meaxwu/ 50ffy h(sdtv .e4sure 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 expew d0th5fu x.( veyf4/scted beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using uk pj2( 0rmgof/9xkh.9for5 ktltrasonic 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 freque a9 fe rv (oi-ns+my-l)y9se5qncy 570 Hz. When the wind velocity is 12 m/s from the no)resyyf+9l a-q i (enmsv59o-rth, 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 mzqjo :kwtl-y1n-.a/i-j p* u qoving 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 Ma+c1x8 ev,3 tgofc suv.ch 2.3 where the speed of sound is 310 m/s (a) What is the c x13v 8+ c,gvof.etsuangle 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 atmosphez v l 7guh+(9w+dmozgrcvj 8-6re of a planet where the speed of sound is onr-79zvh vg (6cug jo+wmd+lz8ly 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 ofrn/ baxm.lim 02,s0g7g h:bwave angle it produsbag:xm0 h .lro0g7mi nb2f/, ces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle p22oi sp6;4m9g esup tm4 :,t jv)vter$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ov(fg4sgjt+s17qwt ;w klpn9 j6erhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34+4pj (1wkwq sjgg76t9ln;s tf. 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 .ox 3. 1aqcwcsipe9v9 sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh wateva ew.x 99q3p.c1 scior)?    s

  Approximately how many octaves are there in the human audible range? nljr yxeeb h01( 4 3eyrxegtzc,3:*t5$\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of ma 4f zx7)/vgyme :qpkn7ny plastic pipes of various lengths, which are open on bo7gnq:kzpv/fe) 4yx 7m th 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 threshold d9whj0 5qr b8fof human hearing (0 dB). What will be the sound lev0h9r qbf5w8d jel of 1000 such mosquitoes?    dB

  What is the resultant sound level wh8ww( 2ozwnk9 een an 82-dB sound and an 87-dB sound are heard sio9kwew (nwz8 2multaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in t/e (q; 0c:nq3q gyc0dew )dlhyhe open, is 105 dB. What is the acoc ;)qhn(: 0 3lwqyqgededc /y0ustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 Wmcy b-jl b,9x-2xe0ccfz r( c, output at 1000 Hz. The power output drops by 10 dB at 15 kHz. Whab-,cc92 x0(xez c,b-ry jlfmct is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protec ey :ysufj6gj83t- ,*c6ks/xxpe;un jtive devices over their ears. Assume that the sound level of a jet airplane engine, at a dis k/sjj-6c yfn,;6:t*sxxe jg 8ue3yputance 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 by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sys-wxgv e;gxa0 1:hu o,utems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned+7icp3cw qbbv70qi* w to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamental smqa5-* +s8f*zz. bnn* l.kv5iysksqfrequency of 440 Hz and a mass per unit lenns-s s*5kbi.yks*.n8+ z afqvlm z*q5gth 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 .j3jlf8h wu/e vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequen/fl8. whjj3eucy of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is 3enkwf) tfc5 : nsij3ei- 9fmz; iv9 w6g)qcn-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 in t9sqf3 3-nijft)wvm6:n 59)nw-kcei gzfi;c ehe tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fulm jp-sbbn)ev. z(w+: fl 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 i3la s 12+l kn )lwfrigitp,-m:n the 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 l-f,1r n)llipt:i2 s3amkgw+ 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 tra09bhjj y 1vtq;in is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the mo v0t1;hjb9qy jving train?   m/s

  The frequency of a steam train whistle as it approaches you is 5)0ug5d m:enrj 38 Hz. After it passes you, iger) ndj:mu5 0ts frequency 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 listening to r+ 0 juvr27xadthe 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 it goes by on the straightaway. How fast is it going? +uvar2 7rxdj0    m/s

  Two open organ pipes, sounding together, produ;rz y3m (k9sonce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the otmnr3 (y;9so zkher?    m

Two loudspeakers are at opposite ends of a railroadpvnnzzp 3ud7i0k dc+-x /t 7t2 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 from the position A, in front of the car, (b) he is between the speakers, at B, and (cc pp 2/n3 vu7tz -xi0+kdzn7dt) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta ieg pecj:pe6e28* vbp;s 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 travel with a speed; jppe6egv e2p8:*b ec 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 flying toww vjrw7:yxd2iw s6wen) asi8c8k4 b*7 ard the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave i8 wcb:d) 6rysa8*w7ew 7jv4k2wxis n reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses a/qwi,yyq b4s 6s 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 frw6i yq,qb4 ys/om one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sendyg58vxg - llm/ 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 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 v /-lyxgm 8gl53.4 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 listeni+ fr1 40g2pbd8vdlrl9sm tew x21v -ktng can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the prev t2 28r4+bplg0d1vm- ltfre9 d ksx1wssure 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, callec)el:mk( ws 0 sc;vzu(yo1( kx8x7pff d “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 practic zxk ecxv0kspy(wfuf)8c( o:m s(l7 1;e, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the thresho6pye8: ccvmarpl +.t c. )h0tjld of hearing for the human ear at a frequency of about clh+: e6amr py80t vcjt)p.c .1000 Hz 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 hear2/gxrd5c rl2ag8-o cznyq)4 ts the sonic boom dog5xn -yclqa gt/8rrc42 )z2 1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb1riu8cnd cq4mh25 p c3oat 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