What is the evidence that sou0 zpogxqzj ev-7p 678 fvy-.uund travels as a wave?

What is the evidence that sound isnb0m6p+.mp 3py:yd hz a form of energy?

Children sometimes play with a homemade “telephone” by attach/3gmbtlgi j4j4lgc d-y02z 6l ing a string to the 3g46bt gymclg/0dli z jj4l2-bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave pazsz;qh:si8p) at+ k4wsses from air into water, do you expect the frequency or wavelength 4t sa s)i+h8zzpq; k:wto change?

What evidence can you give that the speed of sound in air does not depend 7 12e kuk,ezfgn0kmg *significantlygm7 nzug01ke f*kke,2 on frequency?

The voice of a person who has inhaled helium -fhi 6heixn7t*/kuismbd:;8 sounds very high-pitched. Why?

How will the air temperature in a room affecf19d)vkfq0 uhsdob+ , t the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the avff5yymcm jr*,-h3w :mplitude of sounds in various f:h,j* 5cymrfvyw-3 f mrequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced cig1hdy 3wa;d y.1zu zmq7 9d 25jh7y ;n)urpefloser together as you move up the fingerboard toward the bridge?hgdf; .y19 1n3pu h7deyz 5uwm )d 2yj;iqzar7

A noisy truck approaches you from bsxox he)/kn 1 ne+ (gl6ynwjot:g 24mn,7)aqzehind a building. Initially you hear it but cannot see it. When it emerges and yo )g qel)w4g sj y1(2me7okh/:,xn 6a xnont+znu 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 “in166ymx3o n txgterference in space,” whereas beats can be said to be due to “igx 1oxn3m6t6ynterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lower fnnp4 f,clp:;2l;cized, would the points D and C (where destructive n;4pif;c:n ,c l2fz lpand constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who 3jgj.c; kua z8work in areas with very high noise levels have consisted mainly of efforts to block or reduce no;c zj3 .kg8juaise 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–- sy 2be upgvhuk)hn*:3oykov:2xi n y+y207 w31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart)yo22e w ygnyxh:b psviok2vy -n7 :u3* hu+0k? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer;fowo,*gr:v5 *vgt zh3kdo n4 move in the same direction, with the same vel3 v*;h*o4ntf o:gwv,d5 okzrgocity? Explain.

If a wind is blowing, will ,sick94 ofx+x this alter the frequency of the sound heard by a person at rest with respes4 c9o,fxxik+ct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in mo(-dh g0avpt5 ttion 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? Explain your rd50h( ptgat v-easoning.

  A hiker determines the length of a lake by listelt/ gv5penby, 3y0x* ining for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2lpt5vgn*e/y0,bi xy 3.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the e9z/scqiffhl +g s5tk:z 9 qx-2cho of the sound i5fz9 zksq2+:- ltgc9 qfsx/ hreflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at ildo 5urwe9/4 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 jj8 z)zr6h,xi xust 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 m zzjhi,6 r)xx8uch 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 wfw e 60 w7wg kul6gvrx/ o);1qgws5;cohen striking the water below is hea qu6vsr 0; wgkwx7 cfg5goe ow1w)/l6;rd 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stw go9es cxu65ek*v8 ,srike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and theswe o89s,u k*xg6 cve5 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 hhjkswqh)+s80cb v0o 7g*z; u w+pt,pone mile of distance by the “5-second rule” for estimating the distance from a lightniuhzw;0ov8hc , php)s+k+qsw g70jbt * ng 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 vqn-o*yvy2*-s+ly um6hte.rsi( fz 6 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 shu:vyd8 8qou((kr* sf ound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce v.u bkhcua :y 8 0mwjo/d*/s-.fwg5p ya sound level of 95 dB when fired simultaneously at a certain place, whathfg k 5p/u /sac*o jy.u.0:-ymb 8dwvw will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four8notn;yzr y19 equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would thin y 9;zyt1o8rns 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 signa-ca;ka1wvkb5 b 3xv1t l-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the back1;kx1wva53btb v ak c-ground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output fpg z+jl7hlp2 5v k;s3k4m3 uhof sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly ospz;gp7 3f 4+ uvhllh j2km53kver 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 eardrum whose*.kln u um.6ym8tgl i( 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 mo7ha5pm+a t7l xdest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you woulthx7am 5al+ 7pd 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 me7ibrth2 v8gn/ ter registered 130 dB when placed 2.8 m in front of a loudspeaker on tt28bgrvn/h 7i he 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 diff g f-dr1wm(xet* a+:lwerence in sound level of 2.0 dB. What is the ratioawt d *g:(l1xm-f ewr+ of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factob1erv+y) /bx lr will the intensity invxyb ) 1/r+lbecrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but k6t -6eiy odvtf/qq 1o/j:bz+ one has twice the frequency6od- tq+v1yoz:jbetk / 6/qfi of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresys 2ctg v(zf.ho0*2 nxponds to a displacement amplitude of vibrating air molecules of (sfn 2*c o02tzgxvyh.0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-7fab uf 0o0v+gHz tone that has a 50-dB sound level? (See Fig. 12–gvfa0f0 +u 7bo6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sovp, cb a7 n0la+fji)m+rjk*;bund level is 30 dB? (See Fig. 12–6.) nc0i+bv ;kaprm+*7 ) ba,fjj l

  Your auditory system can accommodate a huge range of sound levels. What is the r-g udlmbjh+w4d9 -4qcr1kg jtim3o8 (atio of hd4cougq gb jilr 8-djmtwk-9+3h( 1 4mighest 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 u;c ;nmlnjs0.a fundamental frequency of 440 Hz. The length of the vibnsu.njml;c;0 rating 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 firs fo(sgz fhdk6.;dnd40t three audible overtones if the ofdhfdd zn gsk06.( 4;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 acroq)ex4p dj24 vh8ilnc 92chr z-ss the top of an empty soda bottle that is 18 cm deep, if you assumedl h9v8h) -4z4 cenix q2dp2jcr 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 ( eus2n8notd tb 2/k4xorgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pips2etbo dt(2n/xu 4k n8es required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third har m,p4pxd5fm4p monic. What will be its fundamepxm45pmp d4f, ntal frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7t0j;b9z,0mvr sav *f*goy*vx3 m long and is tuned to play E above middle C (330 Hz). yrzsat0g m*bo* v0 *v;f ,vjx9
(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 orgar3 b8-z oq qr6uz*er2en pipe that emits middle C (262 Hz) when the temperature is 21 eo 2rez3q6-zb*qrur8$^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 63bj .oug5udv 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece o3r 79tso5bhveem( jt3f the flute in Example 12–10 should the hole be that must be uncovered to play D above mt5 9(e3j3hrb7vos temiddle 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 pcpc2kqo/ 1 *7t;k dthat 264 Hz, 440 Hz, and 616 Hz, but not at any other 2;kpctko1 dq*/7hc tpfrequencies 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 is open at both ends. It resonates a0foqt-o v;l a3t two successive harmonic3ov-; floa0 tqs 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 4 k-c du0gu+xk re-4 r9knd/sd$^{\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, oma 8jgwx ux : u8a912jfptek+ambr7:b(4ex an pipexarake(4ap2b+t,u uwf879 jmxjox:1 be:8m g at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm a.em9 kalrm/3long. It is open to the outside and is closed at the other end by 3ae /rkl9am.m 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. 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, o70c 1u8qhpw nmne of which is sounding 440 Hz. How far off in frequency is the other string? wmhn 10q upc78±    Hz

  What is the beat frequency if middle C (262 Hr t f:h )xt7(iq(4cfpsz) 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, whiluw 85c,zd8yo ve another (brand 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 operati v8uzcwyo5d8 ,ng frequency of brand X.    kHz

  A guitar string produces 4 beats/s wt g5vvlni.85 ohen sounded with a 350-Hz tuning fork and 9 beao 5vlvgnt5i 8.ts/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same jw-of:+gv;uf58 w ay1xh hw rsk/0q j7frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat a j0y -7xh/hkr:ofg8fw5; j+1sw quvwfrequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eaei:.i: p1 c/ca jvud,xch try to play middle C (262 Hz), but one is at 5.0°C and the other atdipu,/ 1.x vcic :jae: 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, an;vntzf88yu vo.j/w ny/,u z4xd 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 t.zvywfv/j8n ;ot y u,x48 znu/he possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m p( an2or84u jqwpes xzje0)9;from one speaker and 3.50 m from the othz9ern j)40xep(ws8jq o; pa2uer.
(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 iikk 9e-bxi/;k /4bcqed 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 4-b/i x;qb/eii k9kckat 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 wavelengths 2.64 m and 2.76 m in air. How many be7kydj ) q8w*z1krle9 lats per second will be heard? y1 lr9w lqzjed8*7)kk (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a nuvh;00y,y 32dxapddpeb-3k mkd k1 3 certain fire engine’s siren is 1550 Hz when at rest. What frequen33udbea3xmhv0-dy;np1 dpk y0 k,2dk cy do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whrohcxh8j(3r*48ossgu5 x: w1ywux j )ose siren emit hw) 1 x*r4shoycw5x s8juoxj:u8rg3(s at 1550 Hz 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 i/ +s eb e qksu/g3u6u6a90gefy8kg4cm s moving toward you at 15 m/s versus you moving towardf+q9 ckg gesb3eu uu0 /8s 6/y4akmeg6 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 equ)t/mnbec25lw, fy;v m ipped with the same single frequency horn. When one is at rest and the other is moving tow/)25efl tnwmv, ;cb myard 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 ultrasonic sound waves;74ziszg1qxvt svvm x-e) 7c8 at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the rec)tcsx ;eg s4 zqiv71v7-mx 8zveived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat eew( diiu*us8kf0s8s) mits an ultrasonic sound wave with frequency 30.0 kHz. What frequenc0s*i ewus8fd8uik) (s y 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 fla. zez oydj+m65kkghs; (rb /w9t train car at a frequency of 75 Hz, and a secyskzhm9db (;6 w .kz o5+jge/rond identical 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 drvf si0av.24;) scmeultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arterisrd; fsv24. e0vc)mi aes at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency k kx -4p/ zy*igdf 8)mqm)yg8o $2.25 \times10^{ 6}$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 wind velocity ipb*kiue4 , bg.s 12 m/s from the north, what frequency will observers hea,p bik4ebu.g *r who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its j/g(wpvmeu. eh. jt(8 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 rwm)lpvn0 4fnt26. u3i awy* kthe speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’)l tp 04nkyni2wv*ur63 mf wa.s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet wheouw8c wvvjcf6. d-- 4cre the speed of sound is only about 35 jvd4c- .o c6vwu-f8 cwm/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 m5; mn aupl1pa5(zgx e*/s strikes the ocean. Determine the shock wave angle it produces ;* 5um axlegp5p1n za(
(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 1jkd 6 prhb;g($/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead0.n wuuhn40 g9wu ff5e and see a plane exactly 1.5 km above the ground flying faster than thu gu0wh9ef.40 unwfn 5e 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. 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 pulses dowtj6,6y;yf k4yn0bvsqu-*tztpby7w y5g3 )aynward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designewf;yjqkztt ya*0 6b yn yt g yy54v)6,-37usbpd to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audibl 9vywjg*xr1dy jh;6j/e range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe spdzb 9f0 z,)vkd9xsjf p 0s-+jymphony. It consists of many plastic pipes of various lengths, which df-,p0zj skd90 f9spz) vj+xb are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the4 l 99upum37 1w5jwwruuh+whyv3m3th threshold of human hearing (0 dB). What will be the sound yl5 h33u4rht9ww9w1jw hupuuvm 37+m level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soundrsu ;i)p*a/)kq,y pp ou5; eoe are heaa/ u *e)e 5yuo)pk i;popq;,rsrd simultaneously?    dB

  The sound level 12.0 bq5 7ngt)7 a--jowr3 aakml+rm from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directi+ q lar7tb-awjo-agk73 5m)r nons?    W

  A stereo amplifier is rated at 150 W output at ef20tdg; a6kc*cbktn tf7*8 k1000 Hz. The power output drops by 10 dB 0 kettg; 78bcncdaft**6f kk2 at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their e+ ljcuq1 h1kxk;43xa goxtu-xo s e+.;ars. Assume that the sound level of a jet airplane engine, at a distance of 30 mt-oxkhxuqck+eaj+s x 1. lg;;o 143xu, 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 systems, the z ho kzr+-(7y; vgugua iq-;,igain, $\beta$ 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 nnob dg7 n df8wzw,378a 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.n9+ eci+a mia cm long between fixed points with a fundamental frequency of 4 aan9+ ei.icm+40 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set :bi(ph3eir q i,a98nhinto vibration above a vertical open tube filled with water (ebhia38r:,inhp9i(q 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 frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tub/)z( sk l(t6a c5wtipsh( g caz1lo35ce 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 fundamenkzl 6w3/ (tl caocg1)(ts5caph5izs (tal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to res *uh: p x,1rz2rkk7nrconate 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 kmh+yzojy 5do0(4f( ve7ojh;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 than the other. Wha(7+mk0o5eojhz4ohy;jdf(v y t is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor oslq (nh9:i; dde,y+m i0pvw-osg,ob 5n the stationaryhpo;n0vm,- os:+dyg qs, lw 5i(9bied train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam lmcr 0ms+l2d/53vtut train whistle 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 vetlrm mv/cu23t 5ls0d+ locity)?    m/s

  At a race track, you can estimate the speed of cart/ue. :rzqa fn9q q:u+s just by listening to the difference in pitch of the engine noise between approaching and receding cars9a.u/ernqt z quf:q+:. 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 frequency of 11 Hz.vd8nd, d(s tu(c0w (xa The shorter one is 2.40 m long. How long isd xdt(8sduwc( av (n,0 the other?    m

Two loudspeakers are at oppositpqwvfl au3/ 3,e ends of a railroad car as it moves past a stationary oba fvpw33l, q/userver 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 (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is2ui2xa c -v g,d4k umjw21;jfg 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 cel j;k1av dcg4u mwgij2x2 ,-fu2ls? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s ydgii)o les(6 6kl7 p6while 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 afte7i6edsiko(y gl6p l 6)r that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as ityz8nb6z4 c;vh approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far ;hzn6 bvcy4z8 away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wah3nal w :a7l6gs 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 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 l 3 :waghal6n7about 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 b9t uzq::4rx4sveld 2of standing waves, which can cause acoustic “dead q2 e9ulb v4dr4txz::sspots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumdtn ;7i4g 2aininum 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 clear, lou72a4ingtnd ;i d, 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 po1mq 1eh qw2uu9j 3r.at a frequency of about 1000 Hz is 31pqr19. e quj2muow h$I_0$ = $1 \times10^{12 } W / m^2$ 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 Macha1x le t7jjo(+ 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passl a1+xo(tjej 7es directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15zyn:vaew n/+9 re, rr5 $^{\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