What is the evidence q 1; v1tgtffh-that sound travels as a wave?

What is the evidence that sound is a form of eneez dlk*b:pt l)2 wku.7rgy?

Children sometimes play with a homemade “mj4s je;x: *fitelephone” 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 :fi;jj4e*smx 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 frequenc /ppw*mxkzu4)y or wavelenw/p*4ux k)pz mgth to change?

What evidence can you give that the speed of hn.,jy+hkdp7 ka. x9ysound in air does not depend signific khn.h y+xyj, 7pad9k.antly on frequency?

The voice of a person wh/s2uvl/x xxcf 4y 4xu1o has inhaled helium sounds very high-pitched. Why?

How will the air temp 16h(um+jz/lxo2gbjn38jp. b11 eqhc,rf lbterature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds 0/c m);wpzu1 m/n ysisin various frequenp1 /m) ;z0ywcs minsu/cy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as youoh h1ag+p3g aj.i)fc 7 move up the fingerboard toward the bridge?oagj i)g1pfa hch .+73

A noisy truck approaches you from behind a building. Initially5u ,1fs pejc/sbug9-t 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-frequenc9/c j5sb1fgsu,tupe- y noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” ,fjp 0 1lggch,whereas beats can be said to be due to “interference in time.” Expjh, lp0,1cfg glain.

In Fig. 12–16, if the frequency of the speakelb gwk 81z hv44ox:at8rs were lowered, would the points D and C (where destructive and constructiv:olt k84hxw g4a 18vbze interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing.pa+. grwz )e g7vkd8e 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, inverwg+v r8 ze p)d.7ka.egts 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 thouxwef/et-t8h -ght 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)t -fe/x t-wh8e, are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move:2/ji,fz,.w jl.vbz7n ;yg izdi oy1c in the same direction, with the same velocity? w.d :y; 1/ibyzg.i2njvji7 ,zl,ofzcExplain.

If a wind is blowing, will this alter the frequency of the soub q,1i /ibrbx6nd heard by a person at rest with respect to the source? Is the wavelength or vel qb/xrb,i 16biocity changed?

Figure 12–32 shows various positions of a child/ocne;.hs k7a w 1lq0b 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 fr1ha ;qe bc 0l7nso/wk.equency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening f(s t )vl:bn3uxor the echo of her shout reflected by a cliff at the far end of s(btxv3 u n):lthe lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ,4ntkz xxklovo,* i 2+a6l.wa 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 is 1560 m/s (Table 12–1) and does not vary significantly with de.l4l*k x ,2 xitak6onzv,oa+wpth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths inwj6g)i+ wje1q)q7jyqxp1 a 7c 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 xn1 6zda a;*fais drifting just 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 beforea f d1az6;a*xn the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes wdiybv;5 w*as 0+vf*c jhen striking the water below is heard 3.5 s later. Hoya0b w+s i* fjc*d5;vvw high is the cliff?    m

  A person, with his ear to the ground, sovlsdf- )d*3 qn ys,dhbhr.( 3ees a huge stone strike the concrete pavement. A moment later two sounds are hearqh ndy3v( dfs-odl*.rsb 3h,)d from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the b-77lp lueu o9: ho9susa )r,h“5-second rule” for estimating th 79sp)lu: -, ha7e9 bslruohuoe 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 of 120 dB:+pj zz(oy-fo 1 jyfn,?    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 si-ba 7n(;z byis $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB wvg.n (-7kq rkr89 :7x hf s9mdzjhkzh+hen fired simultaneously at a certaisk79 j(r+xg- q9kmfvrk h zh z:d7.8nhn 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 airplantbh)s:d lk lk/bc- h+ sy 5l7qon-8p7ne 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 o hdcs bn8k-t:nll-7q/+p)bk sy7o5hlne engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have am 3bi+zs7cno+z e-xb( signal-to-noise ratio of 58 dB, whereas for a CD player it 37bib eczs-nzom++x (is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal convecf7 pjrd4s*0) - nwcjgssw9r8rsation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered4d7pscfg 8s*0jj) r9rc w -nsw on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area is q0f80zc:rhy l$5 \times10^{ -5} m^2$ (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 modesh:fm pi 3g39ruw+ ul2;h wqlz3t amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 mzh+mp qwu:fg; w3u2lr3 3 9ilh 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 z 9j8tadr2a,fq-mmb 5i.s r;efront of a loudspeaker on tbt8m,;-raq2az9ji fmr.s5d ehe 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 soj6;)e; jgpmt xund level of 2.0 dB. What is the rxe)j6;; tjpm gatio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (wtz8fdk1fani- /ux( 6j.n2jh a) by what factor will the intensityufj- z6wa2nf kxj(/.1dtih8 n increase? 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 the fcqv2pzj t)6c1 requency of the other. What is the ratio of their ij)2ctv1 6czq pntensities?   

  What would be the sound level (in dB) of a sound wave in air that corresprknx-rjc7ba8s y4 (n9ie/3 xronds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 8nnrrjy79xc(ea-/4 s3rb x k iHz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tdzq, ty8 ao 65:zkz2mbone that has a 50-dB sound level? (See Fig.m2zt zq58za kbd y6o,: 12–6.)    dB

What are the lowest and highest frequencie9( wevhq1uhl 9a l4-ggs that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.) ae9wvlghlu(q 4 gh1- 9

  Your auditory system can accommodate a huge range of sou: ax -epugqfl-15kn o-nd levels. What is the ratio of highest to lowest intensity at xak: -u-f5 lg1on-qep
(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.s p381n/f fpkc The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tecf31 pnfpk8/snsion must the string be placed?    N

  An organ pipe is 112 cm lonxs4xc aw2t 3uq: m5f*jdxs (6q r3(cdig. What are the fundamental and first three audible o(t assiuj3:d 56mxr2*qcfxwc ( 3qd x4vertones 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 would you expect from blowing acrn l+; 5hohqk3gm6iq(ross the top of an empty soda bottle that q lk+nh5q6hi(3o;mr g is 18 cm 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 p2e8,z7n u fxphf5wkg +ipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of 5kxf+ h7n2eu8, wp fzgpipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. l*7zxdpi* - db( 5tiviWhat will be its fundamental frequency if it is fingered at a length of only 60% odi( lt-* i7dv5x*bip zf its original length?   Hz

  An unfingered guitar string is 0.73 in;t 7o ztcm8s)o i4zoov2z 97m long and is tuned to play E above middle C (330 Hz8t479ivono)om sicz 72z;zt o).
(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 mgr1.6blopb z6iddle C (262 Hz) when the tempe .6 pol1zrgbb6rature 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 aqkp7g(fl-p80a:s si st 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mout(i6ofwbpm-yb7b jon9, ).(qri)w ygyhpiece of the flute in Example 12–10 should the hole be that must be uncovered to play D abo )pgo( y qbynmo)-wj7(b6ywrb 9i,i.fve 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 kcv7o fu8 a.4rHz, and 616 Hz, but not at any other frequencies in betwuak. 7fo8r4cv een. (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 ix cr5nz (adc j+*p1lm1ju/1tt s open at both ends. It resonates at two successive harm 51czxd j*jl(tr+ n1mp/tcau1onics 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 j-(v2 .srgvneq* j*ja $^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for qvp 9pbgo9e9xaws;8( a 2.14-m-long organ pixab8; e9 9pwpogv s9(qpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appr bc 1j n*(ynm j(6scy7ije,e0hoximately 2.5 cm long. It is open to the outside and is closed at the other end by tj1j67e bicn(s ,ynhcme jy*(0he eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 gvf;,edmta f.c)7g *gs when trying to adjust two strings, one of which is so7mv eg *),dt.fga gf;cunding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat freqrb. lttzn,9w w :63s,+oausi fuency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5dom1o m*zqy3)y)(ccut 5j6/ jyyod-n kHz, while another (brand X) operates at an unknown frequency. If neither whistle 61o3/*)yz-yydtjcomndm qj ouc5) ( y 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 brand X.    kHz

  A guitar string produces 4 + bys)t0m00dbyupz 21omea(v beats/s when sounded with a 350-Hz tuning fork and 9 bevsmu aytb20y)b(pz0+em1o0 dats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the samks ex*r1ksd .w-85is1qqtdi *e frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.] qdd.8-ie 5sti*w1q r 1xsksk*    Hz

  How many beats will be heard iu. - 4lrzstq3bl9wpy:f two identical flutes each try to play middle C (262 Hz), but one is at 5.0°ly9 :p sql.4 tzwb-ru3C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequenrnuflb)z08 y wo978 pqcy of 441 Hz; when A and B fl z09q)8op8w 7b runyare 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 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 standsczove m1d40ai*/pby , 3.00 m from one speaker and 3.50 ce/, mzpib0v4yad*1 o m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tunf .)sb/ aoq+ do9nnoox 8:3hbw(v iwo;er hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the othe:w;wn )fbo( soo nihqxdo9b8 ao+3 v/.r ?   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 f qd2rx *xyw9iwwt fu:)5l 2-eair. How many beats per second will be heard? (qu 2y2 w5rf* wedwxfxit):l9-Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fir 3/;a3fmzs lsu8k14f +sc-cno+e niege engine’s siren is 1550 Hz when at rest. What frequency do you dete+8guo+s1f eci4kml;/z33 s esn-fnc a ct 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 detnk;w 4zz8/0jdip. l4 dcn7yyrect if a fire engine whose siren emits at 1550 Hz moves 4dzk/4 j70y;z p8nr lcw dn.yiat a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freqf4b)*fkp zlv1y* xq )nea1vg0uency if a 2000-Hz source is moving toward you at 15 m/s versus you movkf)e 4xbv) zay* *01p nvfl1gqing 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. Whdo g-*sj4xr 6pen one is at rest and the oth jsg46dor -x*per is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHgglc44o j:lf:,u lm5yz and receives them returned from an object moving 5lfom:4 gcjl ,4 y:guldirectly 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 tt * uriq/s9y6As it flies, the bat emits an ultrasonic sound wave with fre9*/ u6tytqsir quency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fl8mgr0 7itz 19pag(cbn0gsws4at 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 7a gb0s9m8rw1 ntsc04 zg (pgitrain car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppoaivxifq n;d38ch0 *w,zc29m.moid j3se the device emits sound at 3.5 MHz, and the speed of sound in human tissue3*f3mq2v 0j9;i xnc,hci. im o dz8dwa is taken to be 1540 m/s What is the 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 of frequency jmbo 0 ij;q) ,u(gcxlq0sw:f+ $2.25 \times10^{ 6}$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 f /z8vebpm6 *1w1 m*7iscfko uof frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers he 1 b/z7ocm msv**wf618kufi epar 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 l (eny/ +syk-rdand 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 of sound is 310 m/s5*cy ilg7t6 dp (a) What is the angle the shock wave make7dpl5 g c*yi6ts with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet wh zrxoa0 57h2p regqsko td,v7e54u0-h ,g2 pgcere the speed of sound is only abov 5e7,5h 0cd7 oq2pt pekr2,rogxg uzg h4as0-ut 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 wa,of;o3sf6y mbsd3a1 (u(speufp * cj4 ve angle it produce4 6fs udj3m(*fy(sfb 13sec p,;paoou s
(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 yk++nj7ka j*m $/theta$ 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 : (+jc qukdzm2ocph,2ground 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 zkcm2u ,(p+j:co2hq dkm. 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 4-hslkej+p4 1c , -+t yucplvnfrom the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in -4np yc, kusvht1lle+p j+c- 4fresh water)?    s

  Approximately how many octaves are there in the human audib(s fg26um8l)f0e;hzjb 8 ilp kle range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphk,suf i ym;m.lw8h:x 3br50 fsony. It consists of many plastic pipes of various lengths, which are op0wmy xkfh5,siufmsl.; br3:8 en 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 sounx n 0*b;ipdivgpg*4/sd close to the threshold of human hearing (0 dB).bn*;pp4i x *vgd/is0g What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB a-rx :i3t9 er ae0f;lh60kunosound and an 87-dB sound are heard sialateox3ir:ef r09;h 60n u k-multaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB2lip rr- ft5y5. What is the acoustic power output (W) of the speaker,i2 f-y rl5p5tr assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outputs1oe0: h,;+9fw ypp m*ntmemk drops by 10 dB at 15 kHz. What is the0mf +meomh 9 p*pe1sk:, wn;yt power output in watts at 15 kHz?    dB

  Workers around jet airc)g gx-m)d 56v xfue3riraft typically wear protective devices over their ears. Assume that the sound level of a jet airp uv3 gi)mexrf6g- d5x)lane 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, oq,hy. b.rft3the 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 a freque j/3ypej5jmu(o 0 x-q r/yfp1ougs, k.ncy 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 point 1axixanp,f /.s with a fundamental frequencyn/ax i,ax1p. f 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 vib7cg juf oq(c*v6t 9w(0kpu8sb ration 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 resonate wikc (svqwu6j0 8po 7tgb(f cu*9th 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 near3we cz s(hmks63(x-q ertnx)8 a tube that is open at one end and also( t)sn(qc6hmxrzw e-8e 33xs k 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as ow5o 6x d,0ettune 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 rq7n.va) u9iin ange coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly whauinvq.na97i ) t 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. The conductor onui( 7 yvr5a1pw the stationvp 1iu(y5aw 7rary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you iybf jqd*gb2lfi j* /c6) xdk59s 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocitxfd6qb*g9jk/f*c yjb5 d li2 )y)?    m/s

  At a race track, you can estimate the speed of cars just by listening irq xh9msmalh94-9u ,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 goes by on the straightaway. How fast is ihm9xi9 - u,ml hqsra94t going?    m/s

  Two open organ pipes, sounding togetherwx1gysj0v w7+, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Howvw0+y7g wj 1xs long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a sji2yt;- rah /atationaythj2r/ i; aa-ry 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 speakers after they have passed him, at C?

  If the velocity of blood flowqw5 h2k j/i4av/jwa2h in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wavevkjw2 ha5j h2q/ia4w /s 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/f p3 ukst10f2h5qrv ,gs while the moth is flying toward the bat at speed 5 m/s The bat emits a sound waqtrk5 hf gvf,3 10pus2ve 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 c13x1hv8 z cioa moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. H1 hix1coczv83 ow 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 viev lazh aky:o a;:0ic,w*s- (bllage 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 o0yoa a-wh,a(: blckvz ;is:e*ne 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 cbtwqfem 556)s5n slc5ompromised 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 fundamental frequencies for the stab qc5 n5s5)tle m65wfsnding waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” t rzk;h.rtnuv3/ *icl c ff7yn)l74-dinvolves a long, slender aluminum rod heldy7 lf tc lt;)in*dhkrn4f.-r7 cuv/3z 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, 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 7z6*6bs)ma n.a2t/r dsbb eofear at a frequency of about 10s2.r*6edabam6tbo szn/b f7)00 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 tas6b* 8b2sq ahhe sonic boom 1.5 min after the p2aas *qb 86hbslane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboahn-;ii2 e:tuc t 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