What is the evidence that sound travels kzo+mpcks 6 2do4a;o3as a wave?

What is the evidence that sound is a form of energy ik 6kehjycw64wq;f; 1?

Children sometimes play with a hom8q9 7nay ydh.mn;j q5nemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig.h75 andqmn.8y j;qny9 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from ai6 h0ca-t.oi dj)ep9l5b4 vx ogr into water, do you expect the frequency or wavelength to c4b)6co-gd. 5 jtahi epvx9lo0hange?

What evidence can you give that the speed of sounx9nzcq k2h d03cxdv3:d in air does not depend significantlxkcvqdhzn c3 :32 d0x9y on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why?.-cumlj+ a /f)mu t;ic

How will the air temperature in a room affecx as28/7et.m 3njffeot the pitch of organ pipes?

Explain how a tube might be used as a fwbdx(h .7 ;7ura rl.ktilter to reduce the amplitude of sounds in various frequency r7xua(t7kd ; .rbrwl.hanges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer 2*:ckwh9d4*g *tgiio sibr)vc c;u ),pg1oca together as you move up the1 )acpcdi,s;*:woogi*bt krc ) 4cv ghgi2*9u fingerboard toward the bridge?

A noisy truck approa(;i alofb0/fl ches you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddf (al 0li;b/ofenly “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 rj./; 0sd0r6k sfefee *y6lbbto “interference in space,” whereas beats can be said to be due to “interference in*ed; jb0 y.0 fr6 seeklr/bs6f time.” Explain.

In Fig. 12–16, if the frequency of the spcy 4 51v2lpjwzeakers were lowered, would the points D and C (whezw 4 vc2ljp15yre destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who woj zvu27 7oi(bcrk 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, in(uvb7z i 2j7coverts 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 u+ 4ziw8g0rch 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 c g0 cu8+wh4rizomponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shi9w)qs5lo:q1h7izozb ft if the source and observer move in the same direction, wit: 7o5ibq9 shlw1qozz) h the same velocity? Explain.

If a wind is blowing, will this ahwc7+anzpnq+ct:8 +alter the frequency of the sound heard by a person at rest with resqna+zanwc+:7+ c tp8 hpect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a ce 8pvte+6v7: q f0pdy * wkz+cdc1d9bjhild in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for cpv c67 1tf+0 pvy*+ezkdedd9 8:bj wqthe sound of the whistle? Explain your reasoning.

  A hiker determines the l9*je7f o 3anzwength of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.ez3*woa7 9jnf0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just bei e ,-si7d5pu6-v debvlow 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 sound in sie -5-, d7s6uvb ipedveawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in af8e )1zi;6q2 9 mo zbz6vxahcwir at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a schj5 t +zo*:yii, wuvc;kool of tuna on a foggy day. Without warning, an*,ct: yu vk i5jz;+owi engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from tk 2f: mj5heq7 vacn/u7he top of a cliff. The splash it makes when striking the water belm :7jqvck2ha/ e7n5fuow 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 concrete pve u6mfcf* dx,7ro (i*avement. A moment later two sounds are heard from the impaf7 *ovuf e(c6xi *mrd,ct: 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 errofi;h8h.fk4sk p5ed2it :8twj3ij u-yr made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike j 4w:kds3 ih.-uhf tipj5t828;fy ike 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 dB?bf-gfl rt)4;e    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 inteyqd55c l s,0 5sv7upiznsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levelv94z mwj qtu2/ of 95 dB when fired simultaneously at a certain place, what will be the sound l m2/zwj4tuv q9evel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certaina4w6ebq cm .x0 distance from an airplane with four equally noisy jet engines is experiencing a sounb6qma0cw4. ex d level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is saidxs(uu 6pgnes 8cds: y7; ;n)au to have a signal-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 background noise for each device?s :;cnxsdeuag(uys;8 )76 nup 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powef v* popqw39 dy/./sblc05im ir output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreadsfi/bvci3q.*s po05p d9lmy/ w 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 strif(k i)fb :k4eekes 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 rated at 250 W, while the more modest amplifier B is j izw 6xv.k.g0mewfq 63m/ .84uay mhirated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker con6. 8u6h .imw0 mzke3iyxqfjw.g4/av mnected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when plal1x k2/-qk 1bho r,/:qetu fxpced 2.8 m in front of a loudspeaker on the stagrk2olk xb1q ,p/ :/exqf1u t-he.
(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 i6gnc74s uupbwuz 2 v3 g2n;*;q, alvben sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by bvplbe,nq6* 2nsz 2 473uau cv;w;gu gthis amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of aq vhad:,2eiz+ sound wave is tripled, (a) by what factor will the intensity incrz+evah i2,q: dease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice u9ex(s oxc -.65nqnfnthe frequency of the other. What is the ratio of their inten( .nec6f-s x5xnoq 9nusities?   

  What would be the sound level (in dB) of a sound waqs4:3k9blb,l 2pfu dive in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 f2bbk,qpil s :d93u4lmm at 300 Hz?    dB

  A 6000-Hz tone must have what sound mhil5l.rjo7w75s, af level to seem as loud as a 100-Hz tone that has 5siro l7f. m ,a5w7lhja 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencj j2u0qux5y2ccos( b9 ies that an ear can detect when the sound level is 30 dB? (See Fig. cs2 ( q0o9uy ju52bxcj12–6.)

  Your auditory system can qtr+a7u2v *nl accommodate a huge range of sound levels. What is the ratio of highest to lowevna2l*+t7q ru st intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequjy z f2zyka9byh(qn* hgle1.+2+u+bdency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what t1k92y u*b+y2+ nfzgbdq a(y+zl.hehj ension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundw.ch a8uq u8n,rl rj) r2dp59damental and first three audible overtones if the pipe is d8r dl w285cu auhr) .9jnp,qr
(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 freq a2sbtegrgz0* 5*p;ev uency would you expect from blowing across the top of an empty soda bottle that is 18 c**g2p eab5v;s0zgt rem deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes tmnx+:.jm 8 hpspanning the range of human hearing (20 Hz to 20 kHz), what would be the+xn mp8. jth:m range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hzr9zou brmqz9bno )n(9h;-rf ) as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% ofo(n;u9) zh)o- bm9zrn9fqrrb its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mizh , wxw2ff j+5 v5;dj:tn,jrfddle C (;5jd fn :hx jw5zwfjtrv +,2,f330 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) w:4 s4yq7igm rthen gq4st:7 i ym4rthe 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 a8t 6(ty5fqg xm(s ayx;*6uwiot 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12yp3fxhzfw*k1 ;3go5 l –10 should the hole be that must be uncovered to play D above middle C atx 31w ozp*; l53fyfhkg 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, by s;33ig tgam)qt/ g pw 5:g70znjte4sut not at any other frequencies in between. (a) Show why this is an open ors am3 )p g/gw:4gt0tst5ez7inq3g yj; a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 ,1i*/ ls2ra kp/qxppu m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Wha*sur 1 xl/ pp2pa,kiq/t 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 8 qiw0.l,rf;q 4 r:7qyovr a;suxh)xy$^{\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 pruy+) rm,qk0nly:wl z15* p3f(bzugx lesent within the audible range for a 2.14-m-long organ pipe a gl1 xp:()ql fyrulzm5bu0n+w,zk *3yt 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 outs *a,4lcfhx mmmzmls6* ,7or; ride 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 an*z, xm,c*sol;r 4fa mr67hmlmswer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears ozhkq: sr5 pf;o-t.yk0 w3t o+lne beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ;fzkro0 3:.q+lyt- p koths5w ±    Hz

  What is the beat frequency if m9d;u cq zw3k/eiddle 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 anothe / tlh0iw*pg0(go(oux r (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 operating frequency of brandgoi*(ptw0 glo (0x/hu X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tux4q3d m5h ag(rning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the sth xm3qr(4gd5 aring? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension xq8 b4a u,vrq o(mfrn1:f+h+yin one string is then decreased by 2.0%. What will be the beat frequency heard w 1 rr: 4ynavm+h,fu+qo8 qx(bfhen the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two :hwx ) 1:iclo+mygt*;1 0er yblwyi *nidentical flutes each try to play middle C (262 Hz), but one is at 5.0mo*g ty)rh xb1yiy;0w1c +winl:el*: °C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, Alqc vfpw lg+c+93* do0, 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 Aflo+gcwp* vl93 q+c 0d 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. .g x8xw 81rt7fuw+j zzA person stands 3.00 m from one speaker and 3.50 m from the other+1fuwx8z8 rz7x gjwt..
(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 1ch :iqz3ta d1- v0c-ok32 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be zht0-i1o-a vd3ck : cqthe 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 wavelength u hxnc.xo* dsws9),m9s 2.64 m and 2.76 m in air. How many beats per second will be s,.cnxh 9 )wusmdx*o9 heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cee/ ,utb5gb1w vrtain fire engine’s siren is 1550 Hz when at rest. Wha/eb g,5 tbuv1wt frequency 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(ogvq+g:q rz.ssxkza6 - :2yd fire engine whose siren emits at 1550 Hz moves at a speed of .:r+yssd : zg2oaq 6zxkq- v(g32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you 5sek sd7.vhr7 at 15 m/s versus you moving toward it at 15 m/s Are the two frequen.s7 rh 7v5dksecies 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. gj ,odtacoz,s 4/r d*3ms9 f,y.ozab1mq 42fxWhen one is at rest and the other is moving toward the first at 15 m/s the driver at rest hea, mdtxs /a4far49c,yof.z 1qj,z*o dsmg ob32rs 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 oi vmg n4far * *-73ep5iyrzr.vut ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is pm-r nv*45ei ry7zrgi3v *f .athe received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s Aib:5)kute8h+d3 h biks it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflhe i)t:i3 hu+ 5bk8dbkected wave?    $ \times10^{4}$ Hz

  In one of the originalfxbd:xqso,r+1 gyj :9 Doppler experiments, a tuba was played 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 the try,g:o9 fxq: jx+bd1srain car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speedsa2d1x+ 2hxg,h9 jpu my. 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 expected9+hxpyuhagjm1,d2 x2 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 ultrasonic waves of4gv(.kkxnb) 4 u itqv h07zz2 ue:tdx/ frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity s/a ,bxh+sdr/deskjkk.9 v 8)is 12 m/s from the north, what frequency willkb9 /,.rks)xsde+kdjha8v/ s observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if 0zedl:mtj pge7/;6 ooits 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 ny5esz7/ 4jfbc*yy)d 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction n/csyy)fe4 yd*7j 5zbof 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 at/+:foha nxui7hoe(f 5 mosphere of a planet where the speed of sound is only about 35 m/a:nf u5e+oi fhho/ x(7s
(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 s)vjag *tq-wrn9g :j3m +g9 utatrikes the ocean. Determine the shock wave angle it produces *9qv aj:)nuwg- a+g jrmtt9g3
(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 , x5)wqbec.yv$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grow4e7) x mcuq-s8s(obb und 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 kbe b8 cuqwss-74x)o( mm. 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 device2z,l fpdcf-4 x that sends 20,000-Hz sound pulses downward from t,fdc2x-lz f4 phe 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 water)?    s

  Approximately how many ocgox(5d.o iko( taves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consbx 2.txgsu+0; woe)jvists of many plastic pipes of various lengths, which are open onu;t g0w.bsvo+2jx)e x 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* ycg wo8a(hrwmq41s 8 makes a sound close to the threshold of human hearing (0 dB). What will beg (ha8w 8r1*oyw4scm q the sound level of 1000 such mosquitoes?    dB

  What is the resultant sxiw * i)+iip)eb7c1a found level when an 82-dB sound and an 87-dB sound are heard simultaaxe i)bi1*pf wc+7ii )neously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opeg bbv7u5ug5uz. :0vp jc3dn/rn, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates e. ngcvuvj:/bubgr57 3 udz05pqually in all directions?    W

  A stereo amplifier is rated atdkfo7nf2ji3-dtx rn ,o;x2 g+ 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? d rf j2d2i7gx;on 3otf,-k x+n   dB

  Workers around jet aircraft typically wesqtj hy v ,k:,hv)4ir--m(a ipx1)ugqar protective devices over their ears. Assume that the sound level of a jet airplane engine, a, uh kvj:m-gi4 )aqx1hq)(,s p vriy-tt a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the g 8e8uy5mg1zsulxbk l+,,qgw3j mf)u(0 mtxd )ain, $\beta$ 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 odw s:ayb1 yz+ f9un69a 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 fu+hh)lcrt4glu+ ,r * bx m::gaindamental frequency of 440 Hz:u 4l:r +c mrbxhiag)t+h,g*l 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 vtl61x 5y: xf .,zbixlxibration above a 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 rexfl6l.i xt5y:x,xz b1sonate 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 tube that is open at one endk)iabmhv;)ep))( x vm 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 harmo)ahkiv))evm (mbxp) ;nic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate a t(ljjz vil*/)s 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(.o ; ,bdjqyc0rq lt0 cb2kq9k tone in 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 thac(r2bjq9k .0bk l; oqy0q,cdtt 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 424-67toioqu*kka -0ti.mg4lya6 Hz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approache 0-g4*76 kmiqoa6ik.taoutly s. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 H-ixd7r,lg d-z im+uv* z. After it passes you, its frequency is measured as 4+-,*z-xi m vrdu7 igdl86 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you y1n/7ld r6-oa .mqaz os5nnz h28uy9c3y bzd. can estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it g8mu9zl.a2n -do bay /dy6.oq7s1 rzc zhn5yn3oes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soun1gwvlc p5l4/t ding together, produce a beat frequency of 11 Hz. The 4v/g1lc5wp t lshorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at od5))gny+sxos+j (1p inne6 z fpposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency he)i1neo6 dfjsn+) 5zg yx( ps+nard 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+ tuswxyz,pup2 7 x6a, normally about 0.32 m/s what beat frequency would you expect if,ztu uax7+w x,s pyp62 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 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 toward tj c4p. +h arpb bcy*ki/cp94*nh)sk2che bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency oyc p 449bhk2p iccn*kch+*rs/ jpa ).bf the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pul3ke m5z, oxs jvjxw20/1ubpt-ses 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 that the echo frow/xu,-2 k1vtspj eoj xzb5m30m one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from oa46ao, p yzdgn wq):y:ne 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 3.4 m long, and it p,dzay:64yqa: ognw) 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 compromp.gg.l2+9yvpkxxi 1 wxg 12 euised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundameng1xg1e2x . 9y pw.vgp+ul2ixktal 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, 8w*j.ply bz5ab ;d2egslender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringi8b2dz 5gleay.w; bpj*ng 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 wk/9vv*s2g(hnc si f3hearing for the human ear at a frequency of abo9 vn(sgs32 vchw fi*/kut 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 ,tz.qbgj(k-46iyb eeobserver on the ground hears the sonic boom 1.5byke ztq g,(4b6i-je . min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 13gyw3tb;1j ,m p2ve a,tnxrc95 $^{\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