What is the evidence that so c, 5osjfgkmd-rp4:q4 und travels as a wave?

What is the evidence tha7u6nv6 zn0mharw p4scw+x t; 3t sound is a form of energy?

Children sometimes play with a homemade “telephone” by attachinsp6fs-8d xa4v g a string to the bottoms of two paper cups. When the string is stretched and a child speaks intoxa-4fv 6 8spsd 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 fre.r2f m6 micg7kquency or wavelength toc6mi f r27gm.k change?

What evidence can you give that the speed of sound in air . mpi4so/w ntut8q; t*does not depend significantly on frim*o4./ ttns u ;qw8tpequency?

The voice of a person who has inhaled helium sog8u4ixt7g2;axzzl :io0 k2ltd6(dfu k rn+q )unds very high-pitched. Why?

How will the air temperaturej8 fb91rrnvy c + m3j. ulrk*:ench4q- in a room affect the pitch of organ pipes?

Explain how a tube mightva vsdt+v2 n)- be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler.+2at s-nvv) dv)

Why are the frets on a guitar (Fig. 12–30) spacznrojey m 1l1w n/t8;iz qxp3t.k91z:ed closer together as you move up the fingerzw 3.lnpe:ni1m9kzto ;q /jzr yx 1t81board toward the bridge?

A noisy truck approaches you from behind a a brvko ,g0 sn,2flb:0k9swz: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-frer:bzfanvsk 2w09k ,s:0l o,gb quency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “inpd*tme fp 0 7+-nvhq6cterference in space,” whereas beats can be said to bf0n7pmv pc-e+d 6*tqh e due to “interference in time.” Explain.

In Fig. 12–16, if the frtcw- - *nl0f9z. 4k;o +dkb roldalb9wequency of the speakers were lowered, would the points D and C (whelkf0 ; zkoc+*lww-o-d rdnb9.t bal9 4re destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people ,8:h3dxgwfdj w;e1r bwho work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise lfw xb,: eddh1j;wg8r3evels. 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 wavej/xczhsnc z ;3n;64ooezo3qy, g)u4fs shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly diff4j)/coxez;qouo;, g 3f hcn6sn4yzz 3erent frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the svbk4am88 ze7*w0di7 -qrxfttource and observer move in the same direction, with t8mtqi87e d4*rt 0k-x f7azvbwhe same velocity? Explain.

If a wind is blowing, will this 515c,psab w -g(s3 jincbnoc3alter the frequency of the sound heard by a person at rest s5s1bcba,w35p- n3 (co nijcg with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various p/p+i 2-kyyiwpositions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whis2/ ki yy-+pipwtle? Explain your reasoning.

  A hiker determines the length of a lake by k5+oza.n( za ;-yrw6hx+xdoalistening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 (rx -w hka+5ozx+n;.d6 yaoa zs after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side o:* *x, ucoz:v.ozlamwh;3 ozq ba 7ah2f 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 sound in seawater x, uh zc.za3o7* oma :bozl2qh*;av w:is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavele+qk 3dcxwfm ;/ngths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting jud +)q ;)m*x 2fekpwliost 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 much time elapses before the backfire is heard (a) k+fo w pl*d)2;e mx)qiby the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking ;p 7yh0avr7r uthe water below is heard 3.5 s later. How high ispva7yru;r 7 h0 the cliff?    m

  A person, with his ear to the ground, sees a huge stone strik oe*z0pg n v u,oty9t/5bma77re the concrete pavement. A moment later two sounds are heard fromno0pa 5o7 bt9zv7*/eu,r yg tm the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of disd,(6. z/ xij .l7:kqv zsojonltance by the “5-second rule” for estimati xn qjkzv:l .siod6/7.jo(z, lng the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level od,,r/ vymwz 8uxkg1 ua+nmv,(f 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 whoseij.s9nl j;o r( intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simult,z *a usq3dcab) 8ips1aneously at a certain place, what will be the sound level if only one is exploded? [Hi a ,ub 1qc)s*dazsi8p3nt: Add intensities, not dB’s.]    dB

  A person standing a certa5 ox.xx r/a5v b jo)6pqmfa h5sd.0l2din distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? /l 0 .5phqj mx6ox5a).5avddxo s2brf[Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, w6rt 0qj:xf *fhhereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dBq*6 fj0htxfr: =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person sh7nigo5f40,rht5 zh kv5 1fggpeaking in normal conversation. Use Table 12–2.5hvh 7t g0kf1g f, o5gni5rhz4 Assume 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 strikes an eardrum i y(s 68ujkr0cwhose 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 isi6dz,dpuu05 bk)(. +hqpwet end* cd6 rated at 40 W. (a) Estimate the sound level in decibels you would beq* k6)cu, ew 0.dzdd (6htpudi+p5nexpect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in fron0axv-,s/o )qnwf4 awu t of a loudsp),/ afaowxsw v04qun-eaker 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 difw0p-+mzbt +jx jh f;i:ference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9:; 0jij wmhbx-t+pzf +.]$\approx$   

  If the amplitude of a soun2 mf iyjv5i.n0d wave is tripled, (a) by what factor will the intensity increase? Increaseinj0y. fi52vm by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equ9ejkgmxw,l9 y7lyjkyatu :-y16 y* 3q al displacement amplitudes, but one has twice the frequency of the other. What i lakgy6 1 wtj79jqm9-u,y*3 k lx:eyyys the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that ; w -qv(8 cmxm2*gmddxcorresponds to a displacement amplituded*m2mq (;d vxcmwg- x8 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+bb(iguq)h3 1ep pfz :e that has a 50-dB sound level? (See Fig. 12–6.) 3 pb: +)uie( zqbhp1fg   dB

What are the lowest and highest frequ 7j6o ionyhu-a6j1a2y ,k uih;encies that an ear can detect when the sound level is 30 dB? (See Fig. 12jiuy2o6-,akhuj i176;yn h ao –6.)

  Your auditory system can accommodate a huge ,hpq6p 7d /j bm4bob3qj6)svp range of sound levels. What is the ratio of highest to lowest int obj7pd/3pqhbqbj)m6sp4v 6,ensity 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 frequency of 440 Hz. The lpl ,rxptw:-u-ength of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension mu-l,wp utx-:rpst the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threa6a2:sg lqpdbc;(o 4ze audible overtbo sa2( aqlp6 z;gc:d4ones if the 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 nt7yxt0se. t: would you expect from blowing across the top of an empty soda bottle that is 18 cm xs0.te nty :7tdeep, 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 spanning the range oo,5 ;yw/anmrk f human hearing (20 Hz to 20 kHz), what would be the ra / ok;rnwyam5,nge 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 Hz abc)ii12 qw0uv s its third harmonic. What will be its fundamental frequency if itw ibq 102)vicu is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long andgixdn.ws.) yvwnl/qz bu8,rgj7+7-g is tuned to play E above middle C (3w .nn) wi.,zvgjgsd/7+xb rg yq 7l8u-30 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 .id 9aa gx 1wdy;.bqi1that emits middle C (262 Hz) when the t.waq.aiyxb1d1gi9; d emperature 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 / 9io15dhxdh xs0 0p lnah +8l-fu-btkat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiec x4(0banzd(5. q rtoh(qp w/pve of the flute in Example 12–10 should the hole be that must zq ptqv0b o((p(5ha4./drx n wbe uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not a:nqehj b5gz*-;v fwt(t any other frequencies in between. (a) Show why this is an open or a closet;hbvw5je znf gq-:( *d 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-st c8pp,gj: k at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 33,- pg:cj tsp8k0 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 mk)s g6 y-4lmnpge+q;$^{\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 thr 2.,oad:j5vhda ck+s e audible range for a 2.14-m-long organ pipe at+dos5d c :.a,r2 avjkh 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 outsiudd41b: 4n5qatmpk+-o uk 1 (0jhrgk gde and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fab(m 4-nkgg1 jh:d0roupkd +tu 4q15kig. 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, bn,(c2j;ppfc dhm .x strings, one of which is sounding 440 Hz. How far off in frequency is the ot;cb m(n d,.hpxpc f2,jher string? ±    Hz

  What is the beat frequencs u*sz;rt*. fgoab q-.y if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operatb ;d;t)j kuo/s-mo/jyes at 23.5 kHz, while 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 j;sk) mo/-to b/djyu;, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when qqvb*f. ,h:ppm+,b9 ru1;uc wbqb xm6sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibratibq +xbb pq;.:p,cmh1uqu9vf ,mw b6r*onal frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension its658 /yt t8(x s5j .4pi qvhjttc-dkln one string is then decreased by 2.0%. What will be the beat frequency heard when the two string/ ck4iq56t8 vts( t8td -hylsj5jptx .s are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will 1 s6usqs (-vxbbe heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C anubsq (x vs6-s1d the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Forkr m2::tff 7 x:yulgk4y B has a frequency of 441 Hz; when A and B are sounde4:f:7ytgx:lrmy f2u kd 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 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 from one speaker xd6. fdywby7 n .*h3vyand 3.50 m d .76xb vyy*d.wf3ynhfrom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibratingx1 e vyb0zka+p. a820abe 35qsnpggd5 at 132 Hz, but a piano tuner hears three beats every 2.0 s d2s e0 pn5gq b.a135+ga x0keypz8bavwhen they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How 4b:v ; gsak;stmany beats per second will be heard? (Assume T = 20sks ag :;vt;4b $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s-m f) q,d rj3:luwn8cy siren is 1550 Hz when at rest. What dmu) cwylj-:fr38n q,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 fire engine w1j apal5 p 2ztjo((za/hose siren emits at 155l(/zzao5j1 2(ppa at j0 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 is moving towbw /nzyl1 /4xoard you at 15 m/s versus you moving toward it at 15 m/s Arbln1y 4z //xowe 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 hyjvx 7rvj aii81 w16x3orn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What xx1yravj v7136i ij w8is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves aaww;x;r9c4q tt 50.0 kHz and receives them returned 94;;wqxt w racfrom an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fxl+fmdqk,s3p7; o t 8.rwn f6r bk(2vjlies, the bat emits an ultrasonic sound wave with frequency 30.0kjvxpk;8 f+2.7m6 (,f wrr3qlsn dobt kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movinyw6 uwb(vo r4.g flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest inuv y6rw b4o.w( 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 measura.k;ne9zfji x1c; 5iie 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 th;9.ian;c1 5izfk xieje expected 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 ofn/izgvf mvn8:r)l. a * b5ps;l 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 f8)irn8 spx3b yrequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers heapn syxb8) 38irr 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 mooyed16 bsr8j0e a 9rw9keg4vs)6 y8dwving 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 where the speed okrmsv9wz j 8,ocrb( l,sb.8x/f sound is 310 m/s (a) What is the angle the shock wave mwosbcb s8v,/krzx(rj ,. 8l9makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the th t;qc1bv/8udfin atmosphere of a planet where the speed of sound is only aboutfb 8d/qu1tv;c 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 thmd, p4w0kof zjg ,w.i.e ocean. Determine the shock wave angle it produzo w m ki,.wdjg,p.f04ces
(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 tuq; d:2/bn bh$/theta$ 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.u4ifx gq6f d va8zs1. * 4+cfgen5a5wp5 km above the ground flying faster than the speed of sound. By the time you hear the sonidpsv w i gauxa8cef1 6zq5*f5n44+.fgc 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 downward f nar- m0 fp5i,s2vd)xfrom the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed-vip5sn20)x f fdr,ma to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are therjt ;0jvb nal bc/4;omii: -so*e in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It*d bl5lnx 9hw6 consists of many ld*nbwlh 695 xplastic pipes of various lengths, which 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 f 3b si- .76opzvuq.f duwr.5lxrom a person makes a sound close to the threshold of human hearingrsl3wpd-6.xv5.q z. 7 of buiu (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-*,o 6tst:,mfreoy5zv )7 ksm pdB sound and an 87-dB sound are heard simultanpstsz, t5r)6fvooy* m,:7mekeously?    dB

  The sound level 12.0 m from a loudspeaker gj*5k)pyes)0p;ec9vp fh: y d, placed in the open, is 105 dB. What is the acoustic p*ep hgc0vs yy);d9:ppe)5fkjower output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 10z x)r3(i6vjs.pqj qw-7hq b8d 00 Hz. The power output drops by 10 dB at 15 kHz. What is the power outpuxzirhvb.3s-q78( qjq w6pd )jt in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over thr-ivci+f :bw33e jhl6eir ears. Asfi brec:wl36jih3+ v-sume that the sound level of a jet airplane engine, at 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 gain, :pb+9:ryj kjx x5e +zc$\beta$ 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 t6: mqvsaar2g* o a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fi clt gm. mldx/+l:ov +d2y5+jwxed points with a fundamental frequency of 440 Hz ancm gdv ol+:l/5x2 lwd. +mytj+d 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 tubn rtak .*(ss*dhf).) 1puqds be filled with water (Fig. 12–35). The water led*sbd qka(h)*p ts )f1n. r.suvel 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 strine/s5dn itn g.(g of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the thii(sn gntd/5.erd harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatg p2*mdarzj ib2re vx1/tjt8lhl+ +x;oy3f-0e as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from gq9 g bf4j7 ynok0/ 0da*s/piktwo 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 poin4ia goy/7jg0d/bn *kqpf k0 9st 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 stationar1kabmuj.q a rmyg,+*m-z- 4muy. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train a- .a,ubma jum4qk1m-mgz*+ yrpproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appryzvcyb)4)e c .oaches you is 538 Hz. After it pas ybcv )c)ez.4yses you, its 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 olod7 tk;la4 m3f cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the soul3l4 kd;o7t mand 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,uio 15b:4 skeu produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How oki 4bu5:use1 long is the other?    m

Two loudspeakers are at opposite ends wg6uy-) rp* lu:f3 uphof 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 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 speaw6pyprfguh * -)3u:ul kers after they have passed him, at C?

  If the velocity of blood flow in the aorta*jra3*l;pr lv e6n j v1xud)o4kq6 dq; is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume thr6klr *x;) j3ul1 ve qddoanqp vj;*64at 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 the wjlie ( o.0vo; tl2+z.zix)dibat at speed 5 m/s The bat emits a sound waveto.jzl0liov2iz ;.) +dwe( ix of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mot4ae1p, ; fo:g n ue2(s/aex 2.ofpnxwth. The pulses a ( sp e:ou;afgaon,2 xp2ne1tw.4x ef/re approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vil)fokeznry3 (+ lage 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 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 en)(f +yo3 zkran open tube.

  Room acoustics for stereo listening can be comprob d/y-ukml 0wgv-1 1lcmised 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,k-10y1b/dv uwlcl gm- 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 ruys7pa+ rfz3 m2-0zgtods,” involves a long, slender aluminum rod held in the hand near+mpgrya37fs0u-zz2 t 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, 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 pv7kk* p9-8yiv h3(qlvu2w,cou b0 jgear at a frequency of about 1000 j po ipukv(l, gqcby32 9 v-w80vu7*khHz 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 grounqbb7tzlsom+ + wc ,x 7j7o7uz;d hears the sonic boom 1.5 min after the plane passes direbsjoclw7um;b z+77t7o x+z,q ctly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 wf:h m 5gsg-(m$^{\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