What is the evidence that 3xp9.y4kl / lydvz8pdsound travels as a wave?

What is the evidence that sound1 o( t/bzabq4h is a form of energy?

Children sometimes play with a homemade “telephoneju . t)f*in ossg q +vpcw2g+ah052(fjhu0-rz” by attaching a string to the bottoms of two paper cups. When the string is stretched and t g2qhro0hs+-cp (+) 2gwf vz.auni*5sufj 0 ja child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the fre2aj 24/zjvjei 67wrk :uz x;doquency or wavelength to 4vxwoed jz i6au:2j;/ jrz7k2 change?

What evidence can you give that the speed of soundg7x8b 0 ur0p:o k+slqd in air does not depend significantly ons qbd klxgpu78r0+0: o frequency?

The voice of a person who has inhn 3t(s 3ip5d)y rx46q ew.xuta0tc+bc aled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch ozb fve9/n.1pe- y b:r1ev.zsl o8pe 7d0olb*s f organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sound7f3v0bxs x r1po(k;koshu yrc;k5;o7 s in various frequency ranges. (An example 713oso50x;k x kob(ryrkfsv7h;cp;u is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaynfa u;0ka dtnds 8+.p)e .a1jced closer together as you move up the fingerboard toward the byta s.kjfn018.;)dueda a+npridge?

A noisy truck approaches you from behiv;zn.)) vc5aer3v kzb7 oid)e nd a building. Initially you hear it but cannot see 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 ;k )nda )roze7b.z vv5iv)3ecdiffraction.]

Standing waves can be said to be due to “interfere :0yezpuajl.nnke+ 3 x2bj,z3nce in space,” whereas beats c pe,ke2au.ljbn+zj n 33zx:y0an be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woulm4re sg-i)5vq d the points D and4 viem)-g5srq C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods oxc+g4e*1xjc1 yw(m lff protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise+ g11cx y*xmwce j4lf(, 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 thought of as ahc0j0hv q6ttjuk-6o 7 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 far 0qh0k -6juo jvth67ctther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sameya izpg:rb6ij )(ryb , du):4b direction, with the same velocbb )zyr(pai,yjgi dr)b:6u4: ity? Explain.

If a wind is blowing, will thi15hzr i,rnx6w s alter the frequency of the sound heard by a person at rest with respect to the source? Is the waveri r6w5,1znxh length or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swingbai2d+)6swz:s9y vd f. A monitor is blowing a whistle in front of the child on the ground. At which +9d dbizw6syv: 2sfa)position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listenkl9bg a+wh:e)ing for the echo of her shout reflected e: lwak+)bh 9gby a cliff 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 sii)qjy 4 2j+()tbjhyhrde of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of soun) b4 yyh+jr) 2qt(ihjjd in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths i;cbak)szq 95j kuycf 0 p+7ld(n 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 ,k lv x*,)-o8 2hdo r.ucrzecujust above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km awalxeo ,)u kv r *2rz.-8d,chcuoy (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splan .6chg.r1ab,a 1 oefvsh it makes when striking the wate,1aevh1n 6cofr. b.ga r 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 t0 m((bqa02m/.lgu4.hfy2 vfr cj cihlhe concrete pavement. A moment later two sounds are heard from the impaiq 2 l/u vm.mbfl(.cah0y 0(hcr jf24gct: 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 one mile of distance by the “5-second fb o.pe.0jiyi )k; t)7lbytn -rule” for estimating the distance fr)-t;bl)iby.p0tio y f nj.7keom 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 leq(p2rzj3 u9txtq7 -rwvel of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity ztjd6 +phl7)e1t1tjn is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously atcq 2qc2i a3liq9- xlr, a certaicill23acqrq 2i-x 9 q,n place, what 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 airplabgcj+ ,aazc1;/dj4d ine with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this pers j+dz; 4,gcaa bd1cji/on experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dBdo)v qilve e r u)8k(4+ec7iz5, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signalzk o7v r)udvqi +ec4l e)8(i5e and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound nia;6whf4i 00 x oxnfl2nk6ums ch8tzb,*5j .from a person speaking in normal conversation. Use Table 12–2. h0tb4i* oac lk8 wxj s.nn0zxu566nff ;,2ihmAssume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strik/9zft2xp s,6/h3d5a u 0c9jt7belzjxub mtq + es an 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 ratemwzd5o *8d gs/d 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 point 3.5 m dwdmz* og/85s 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 dBzu7 3tbpbp.1-h7g f:z-kk qwu when placed 2.8 m in front of a louds-k 3 h7t1f7kb- ubpg:up .qwzzpeaker on 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 difference in sound level of 2.0 dB. What i/o6m:t1 1y yvslk, 2jha l+yxys the ratio of the amplitudes of xt yy1,/6lh1 mk+j:yl vosa2ytwo 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 factor will the in )ct+23gi+j:x ewmwe3t;r zuvz56dj itensity increase? Increase by a factor of2riz3wv5ed3jg iz;tx+m+ jt) w c:u6e    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudesj(+bgc6o 3r rx, but one has twice the frequency of the other. What is the ratio of their intensit+rgxbr6c3( ojies?   

  What would be the sound level (in dB) of ad12v: efk jre, sound wave in air that corresponds to a displacement amplitude frd:v,kj2ee1 of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz ton+o t+o47 hnlynbv 6qjz5+:iam e that has a 50-dB so+7iba hotmqoyn vj 5n :6zl4++und level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when tyfi7*bu4d* fr/a0fwvyx m0r 9he sound level is 30 dB? (See Fig. 1w9u xrr*i/0 f ay 47dm*vb0yff2–6.)

  Your auditory system can accommodate a huge range of sounw v 09hj)ekz30dyhxc6d levels. What is the ratio of highest to lowed h 0j 9hzw)0y6k3xevcst 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 fsvvt91z5 w9sf+ss * thundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the strinst5 +9*f stsv wvh9z1sg be placed?    N

  An organ pipe is 112 cm long. What are the fundameya8c1y w74 hmr cr/o i,dwy8d-ntal and first three audible overtones if the pipe ,w1iw-ryc8c/4 oa ddy8m yr7h 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 fromq1b*yrn kvh ;;6m skz4 blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a yrs;;n6 hqvkzm*1k4b closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the r0se/j - bfqtg. ekyz**ange of human hearing (20 Hz to 20 kHz), what would be the range of the l*j*bqkg/tefye z .0-sengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency be6ay2h4dv 2qw: wn8sof 540 Hz as its third harmonic. What will b 2 haqdnyewv628b 4:swe its fundamental frequency 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 ithslgqwq9d/5y-5x 9i s tuned to play E above middle C (330 Hz).l-99dt x5qyq5/ sghw i
(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 pyye/2*bcnqu3 xddcl 4 kr 4xq6bs1-.emits middle C (262 Hz) when the tembn* lc cdxxpb.kdy s3-u/q2qe 644ry1perature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 u.sb( zg oga*lv :17sk$^{\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 12fgi 6xqa+ka 8)g2tfa9–10 should the hole be that must be uncovered to play D above miai 8gf6kaa+9q 2t )gfxddle 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 resonatez2zr9 bjgr +3pu k+a,u at 264 Hz, 440 Hz, and 616 Hz, but not at any other freq2pr,3rz bgakuj+ +zu9uencies 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+:d.l +oyxuo v7 a1crh open at both ends. It resonates at two successive harm7 .:1h ydrcx l+o+uvaoonics 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 9d:pj9i 2ou oq$^{\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 audibl17mdt o .ybtgcoes-pyhd*)9 / e range for a 2.14-m-long organ pipe atg1. otymbt)e/d 9ycs*d7 -pho 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 26 yzzrh+rd:y 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the r ry +h:zrzdy62elationship 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 - cxz /bdbi6e-s when trying to adjust two strings, one of which is sounding 440 Hz. b /zb6 d-ixec-How far off in frequency is the other string? ±    Hz

  What is the beat frequency n 2qd0vc b7/szy-ipt qck; v.4j88qkxif 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 anot*f, q7 mkbm brxhj/*7qher (brand X) operates at an unknown frequency. If neither whistle can be heard by humans rjkfq7* hbmmb*q,7/ x 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 sounjk8m- ;kjv ,ps ;ve(xmded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is ;pk -j emkv;,(mxsvj8the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Thenj-stmri ux* hub93,5ubsm( 9 *bb :au tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are pbb-bms :jm*, 99ur3x* 5a(uutusi hbn layed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes fwg:z v2ue9r1djo1jvqf7 -m 3oz5 xf8 each try to play middle C (262 Hz), but one is at 5.0°C and the:j17xr 2- 5qz f3 djwz8ff9voogu1mev other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tunind;*7ne iun4pa,mnvn (g forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded togetnnm( *e u7p4vnin;da,her?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A sa/eh s.59ydkmjp,i5 person stands 3.00 m from one speaker and 3.50 m from the oa5,sm5j e.is hkp/dy9ther.
(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 pianc6ohuzoe(m1 9 ( n:muso tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating (uhco(m1zo 9 u6: esnmat 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 waveleq7cep cg6vqz8lk;1 v1ngths 2.64 m and 2.76 m in air. How many beats per second will be heard?c pq v7v;cke61zq l81g (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenc*vv:i7sldy3rkrq(8uspx l3mp4 / 8 ng y of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do lp x3/qv vpdryng8 ru l47:k3s8i*sm(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 ahxg7yzda )a.xt0 ua8e t5;k6t fire engine whose siren emits at 1550 Hz moves at a s 7xt zxa)85t0y h.6dgatk ;uaepeed 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 tn tfz3wnx y. j:;lah2,oward you at 15 nlwt23h ,fy.z; xn:j am/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one iz +tm0tloszf7vfc 47*:ehql 94 t z6,xtbz1qms at rest and the other is movzov stlc 4q mt74 hxzzfe1:9t70 lb6ftmq+z*,ing toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonb:+x0 vuho 0qnic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it b0qoxv:0unh+ at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a s 8lggsv1 nt:4fpeed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 3gl4v:fn8 tg 1s0.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playelaj cdrh-;(h 8d on a moving flat train car at a frequency of 75 c-hd(h lj;r8a Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppos qlt1 ( m)n0zb/d.go x)fmhtim66yq.se the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 c.1(xf b).ttm/si0loq6gnzyh 6d)mq mm/s directly away from the sound source?   Hz

  The Doppler effect us6rj37wps8j rx 1ta crv1:. sfwing ultrasonic 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 fjpew) 8v4),,lvfu d o-gxfd;f requency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will obser- jev,o fwpx)ulg8;) df4f, dvvers 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 f74ns4j) y ig fk(*dp8nq n1/wvz4ucb on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 wheradjzh5u *ct*)bd 44kue the speed of sound is 310 m/s (a) What is the angle th ct4 uu)b **khzajd4d5e 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 w;f vim6ek ,5qthe thin atmosphere of a planet where the speed of sound is only eik,w 6vfq5;m 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 waver;sc lc,(q s-bxv,lb2dhc( * t angle it produvr(( ,scl-q* lhbbxt;2cc , dsces
(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 )nn6g s-pm)dphm .u q)7 pg;ri$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plbyu979lyr* s 2asge+ 6a5w0bby q 7dwoane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom,ed9 a7yb0*w bg75r2bl ou9ys6way+sq 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 d7ftn em, ywx**evice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detectsf*e 7nxtw,y* m 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 octave4g3wias f 0b fe .o4q6gzhhoz)*.nk,ls are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Itcj*o6hid+ cm.w4xjp/ m88kvv consists of many plastic pipes of various lengths, which are ope6mc8ic v.kj+ xw/8oj*vdphm4 n 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 c uv :*9mu;(jbhm6wh szlose to the threshold of human hearing (0 dB). What will be zwuu(v m 6j9;b:* shmhthe sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-da kub k (2j/vd64-f1ni bg1+5mxc znamB sound and an 87-dB sound are heard si6-51 abk/mv4x amzkni ncgu+21j f(dbmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed bd d:4flu5*; e/spqfuin the open, is 105 dB. What is the acoustic power output (W) of the speakb sfu pl45;d qe:*/fduer, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output a+x9wfw 30zsr8iwvtm 1t 1000 Hz. The power output drops by 10 dB at 15 kHz. What is thewr0z w9tv1+ fwis38mx power output in watts at 15 kHz?    dB

  Workers around jet aircraft2 l-5hzyw k.z(3ggsbz typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a dishs g-l 5 z2(.gzkz3ybwtance 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 communicatiok4w(qe8o b9;*bil1:2mupb iql yx 2zsns systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to acgia8. dv- -0j.y v79 uku9o wwv5hxja 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 betweai-dj o + s ;8.(gamhlouks3r8en fixed points with a fundamental frequency sar;m o.soal+-kigdu 3h(88j of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled wbu. 35:sgczrf 2kt+y iwd7c- ddjt: k6ith 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. Whkib7d.:c+6dj3 u t25- y zskgf:rcwdt at is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at o,z+:t-qxy) .*bfx;znf wso nane end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental s+z ;q:-.bz)no*ft,f nxx ayw mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass way+ yi at0*nfy;s observed 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 hpxaw:4o 4m /fc7x,rj*j,ol trange coming from two sources. The sound is loudest at points equidistant oajo,x m :w h*44xl7 r/pc,tfjfrom 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. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. T;).4 +tfpoheszxw.mu o8jb 4whe conductor on the stationary train hears a 3.0-Hz beat frequency su4wo zb xet)w 4;.f+ojm8 ph.when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a sfnijxfc;*/:8 lh bu7 pteam train whistle as it approaches you is 538 Hz. After it passes you, itsxl;/hjn7bfpi :u 8 *cf 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 to2w4 w b:wakh vop,o*8o the difference in pitch of the engine nwk po,hv :4o aw2wo*b8oise 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?    m/s

  Two open organ pipes, sounding together, produce a beat frequency5*t+ fcqyc/q2ctu ra( of 11 Hz. The shorter *qc(q+a5fur c2/t ctyone is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a95 r.q.jxmppq 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 fre 9r5mx .qp.qjpquency 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 is normally about 0.32 m/s what beat v.a/ z0n2 zthgby0 tk5 8+lssrfrequency would you expect if 5.50-MHz ultra8y/5 n grs0z0+h ttl vbazk2.ssound waves were directed along the flow and reflected from the red blood cells? 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 while the moth is fly :-kc8dep7,+r pkzsb ving toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What c87ksbepk,dz:v pr-+is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series ofub- gq n+s-lle:54lmh high frequency sound pulses as 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 n5: lub4l +mlh eq--sgthat the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once us ib7gj3u; 1tt)r.2o 1i vhldwoed 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 musoj)l;3dutwb o h1i2tr1 vgi.7ical 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 th;w1wm77lct;sis8k,w,wnts/nbcw p + e presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the/;+i c w;,nsc8,s 7mb1tpwl7twks wnw standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lt cmfe 0x;fc , h(jo(+dp9/xtgong, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little pracfot((0md thj;9fc/ +g, cexxp tice, 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 threshold of hearing for the human ear at a frequencc5*r mhg,w oo/ w9rwqa4nsqw24e-)b m y of about 1r2w/5 ohmbe 9c ans*4om)gwww qqr,4-000 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 hears tfqun 1ain60m s. g8vjh-p1i a,gz1*ht he sonic boomf111, qgah0s 8i.m6- ngvtuz*hnaijp 1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo gzc8n+,8m5nu) uvxrn at 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