What is the evidence that sound travelsebiic(i 4pl*/ as a wave?

What is the evidence that soun0wwn9y3 3mta id is a form of energy?

Children sometimes p+r.txc48xu gr m;)zyg s6 tv.wlay with a homemade “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. 12–29). Explain clearly how the sound wave travel4r .6.xt rc;wgz)y sgumv t+8xs from one cup to the other.

When a sound wave passes from air 1h /,t)mwsqfointo water, do you expect the frequency or wavelengt/hst mqow) 1,fh to change?

What evidence can you give that the speed of sound in air does not del bfr*f (bc-7eg3cf t)pend significant7ct le-b3*)f( cgffr bly on frequency?

The voice of a person who has inhaled helium sound yl* 8ejdi6 qd)zsrf19bv-ui /:-rhwes very high-pitched. Why?

How will the air tempeqvl+mp- ,1qhu31hiloyk w)* vrature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of1 :yi , 1ew-zqqpd. dsa3boh0a sounds in various frequency ranges. (An examz dwq3ihp qs ,o0-1b.ya ed:a1ple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together askinrxcx e o6 y-v5:mvj3j4w9) you move up the fii9 -rvm5nc :ej ok)v6w4x xj3yngerboard toward the bridge?

A noisy truck approaches you from behind a building. Initiall g5mk *-d5xaxgy you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Sectig 55-dmag*xxkon 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spacepn)ze 59khs a(p*qld5,” whereas beats can5)9nzapdl*5h(s pkqe be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequevs ;k* pcr3kr+ncy of the speakers were lowered, would the points D and C (where destv c kksp*+3rr;ructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearlsz5xxpel3)owj,yx i6d3 q (7ing 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, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noised (lpzxyqs73i) je o3 6,l5xxw reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. E svc)3hc0qwn0ach wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are0n3hw)vcq 0 cs the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in7ght+pxk ,a4 n the same direction, with th,hnkt7xp +ga4e same velocity? Explain.

If a wind is blowing, wi9m6iy,sv5ch ,wtavc( ll this alter the frequency of the sound heard by a person at rest with respect to the source? Is the shm(9v c 6ac5,t,vyw iwavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion ong1nf2 q1)aw ;ixmmdmw( tz s60 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 1wn t z2im1xdm(asgm 0)wq;6f of the whistle? Explain your reasoning.

  A hiker determines the lengh+egavqx ;g8ae(u:t )th 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 2.0 s after shouting. Estimate the length of the e8hq(ggaa:+) uev;xt lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of h5r ov 3iv-9icr5: smrbh3x 6cqis 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 spe:oscr69b3miq v vr3h55-xcr ied of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wahx b qk5cij+ i33,bc6xvelengths 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 just abovep+iz(*6:;y q tds x/gcec7tmd 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) by the fish,7sd/ y tcigq*m(xpct ;ze: d+6    s (b) by the fishermen?    s

  A stone is dropped from the top of a clifxqij2 a 05wz3go: 0llhf. The splash it makes when striking the watea lq3j:l0 2xhwg0z5oir below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the groun)swpe q8fvgrbxzzwa( *o)92,m cn x8 m -n)sh/d, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air ax )napfos8z*wh,2)v x r(ew8g)z9qmn/b mc -snd 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 n48ld2c waph. distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (8pcw4nh. ad2l a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 d; j9gxb w35w1w3cof ylgt6ez7i9v-reB?    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-czmb .tf k2fv (qzj+1d4xpo : whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lsgfger ,3o-*jx6ix , yevel of 95 dB when fired simultaneously at a certain place, what will be the sound level if oy ,f gg-ij x3x,*seo6rnly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equallnw*/r ;cgi)0ra nk z;iy noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience i ;c/z)rwk rn0ii;nga*f the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-tsnj;)txw ,s4w o-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intx)n, ws4st wj;ensities 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 5uw 0j1w g4c )unoho) *,uvbggin normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphe,4j0wh5c1 bu)gu wn) uv*gogore centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area is o g*98t)os:4 zpwf 9pp4gtfu cd* 4dgi$5 \times10^{ -5} m^2$ (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 At+d l2rey.oi8jx 0 ,fw is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeai+y0l8 j wf2eto.xr,d ker 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 front of u9j(ss uxc r64a loudspeakers (j4u uxc69rs on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in w+vbtkf 9-6q ssound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9sv q6-t9 wkf+b.]$\approx$   

  If the amplitude of a sound w/j1:qr k sa0trave is tripled, (a) by what factor will the intensity incr1 q0ra:trkj/ sease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal db,e )gpgo-7h risplacement amplitudes, but one has twice the frequency of the other. What is rhe,7o)-g bpgthe ratio of their intensities?   

  What would be the sound level (in dB) of a sound wavemhp0 ,(odc7j k in air that corresponds to a displacement amplitude of vibrating air molecules of 0 d (k,0pjmoc7h.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have w(4d wn; 7mxj/ts say7dhat sound level to seem as loud as a 100-Hz tone that has a 50-dB 7 4syj(/axsw; 7mdt dnsound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that 4 8 7,(vzirhiizvgf* uan ear can detect when the sound level is 30 dB? (See z78iri * (v,g4vf izhuFig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Wha /i3u-mwyx*sx qt.*sd t is the ratio of highest to lowest intensitsixx*y-w3t .m s*dqu/y at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has ay nym;d 6 -)0z,pucdiuwj0hw( fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass opi) zdy; ,c jwuy(-un6m h0w0df 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Wc.zk 41w 78 ..fqnwzsjdq(*ta f7sdmrhat are the fundamental and first three audible overtones if thzs f 1qn7s (wd.r.jfw.8k*m7q4ctdaz e 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 across the t 2-zqbd ffti5 :k1r*jtop of an empty soda bottle that is 18 cm dee1 5j q*fttb-f :id2kzrp, 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 or/1t uys/.xj8mx2zc i 2gfv7jngan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), w2 cj/zvfy2g 7mx81ti/ xns.ujhat would be the 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 Hmfluk1,nxh o93-d ujt 45i ej+z as its third harmonic. What will be its fundamental frequency if it is fimiu-ju e15 h o fd34,n9t+jlkxngered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m longqwq7 eare8z68mzx:7p and is tuned to play E above middle C (3:ramqp88 z7qz7w 6 exe30 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 3wcmqm/ fe))oemits middle C (262 Hz) when the temperature if) q )w3ecmm/os 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 e1b x;s+gnke)e// i pdat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpip 2thoq x*4x4gece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middlexp g2h4toqx4* 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 resonat8 z anvj 4k.;+pu7lp;i1zebwke at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequenckj4b1e p z +vkznulp;w7;i .8aies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two suwch/-;pw-:sz di hx7xccessive harx isc-/hw d;:ph7w- xzmonics 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 (gcb evf/0m 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 the audible range for a 2.14-m-lh y.:2 kz9hqgcong organ pipe at 2.g2hhkc qzy9: 0 $^{\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 ci23n kk4hccee. -fp4o/ v/yvoutside and is closed at the other end by the eardrumee2v ki .cc 4nf-3ov /cy4pkh/. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryn9nlmg hhj*++ql 0sa, ing to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? h +g9*lnmnj lh0+,saq ±    Hz

  What is the beat frequency if middle C (262 Hz t,he,/fatn2s oe+1i4 fj 6blu) 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 23.5y/tuxu)q6ajwdni*/ir0. .b r 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, estimate the operax0/ a iw iu)b* ny/.t6ruqr.djting frequency of brand X.    kHz

  A guitar string produce v* ks7su4tl7xyj0: tns 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational ftk7js0y47:lv nt u*xs requency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to t (l s2v ghmdd0xyv6px2ggcx:;vvkou 97m 7,f3he same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequevv ;3v od ,y (9cfp um 2gm:hxsxgglx60kd277vncy heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two idekk t/t0pg a:qh-j3k2pntical flutes each try to play middle C (262 Hz)k:/ak gk p2t-0 hqptj3, but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequencyitne * ux+cx ,.m*ba2j 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.2x+a u*e.t,n* mbcijx 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 hlsx -khv r48l6iu af7q-x6*q stands 3.00 m from one speaker and 3.50 m frah k-s* uq-ixllf 64q8v7rx6hom 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 tun :-h.acdx)ze7pey g )yer 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:eh.))x dp- cy7 ayzge 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 air4a73)zi3hhdgae5 faf3br, :b s+nrm n. How many beats per second will be h s 3rrbz+i:na7dgan3,ffb e 3ha)5 4mheard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren i38ps) jocsv.i5pd *)z ob)ye+er9ij dsd+wt*s 1550 Hz when at rest. What frequency do you detes+rod.b9z3 8cydps)oj e)5et+*w ) sjid vp*ict 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 whose sir 6:9wo dnnlvc.en emits at 1550 Hnc6vl. :no9dwz 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 toward you at+dor:( l :xco 0.ezuxjex,jvars+e 09 15 m/s versus you moving toward it at 15 m/s Areoo+exa r xd0e:ljjz xcv(s0e9u .,: r+ 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. Whqofak8j7hvu 5 kdlsxj;9. *jkpy*+b,en one is at rest anjbqp+jyxjs5l k;ovuh 7,9d.8ak*f*k d the other 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 kHz and ua+6bc.j zoz7receives them returned from an object moving directly aw c7.aj z6oubz+ay from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed ofn(6g6k 33asv9 s ym xh-laomm6 5 m/s As it flies, the bat emits an ultrasonic sound wav6 s valh6mmxkos(-g3y 9 n36ame with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler p+ p/z;vl99p:f gf4p*m mwy6gol(jl texperiments, 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 tg6gmfwt ;9o v9 yp:p+f /jm(*lppz4l lhe train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasou0pfkmyg o ; jgj-3*blod5 06lznd waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is t0;glpjf y o-obl *0z6m 3dj5gkhe 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 frequ7a6jmwg f m0wz09s*a9f9* jsf/g mviy6jyx v8 ency $2.25 \times10^{ 6}$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 sner:89 j2t2fzanobwp0 ; jq6hound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hea ht;9n0anwj6: fqrz8 2ojb pe2r 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 n1* qz:d +sygckl:6ld moving 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 pkt eub7rq1:8 the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airpl reubqp8 t:7k1ane’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 whesj2 *tiw(uaqw d+ cwp1. 7;feqdswh 9:re the speed of sound is only about 35 m/s 1;c .s 9(qtae wpihwsq7d w2udjw+*:f
(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. oq4*6g4x oewc ny5ys6 Determine the shock wave angle it producesyoq6gyes4oc46 n5 x*w
(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 gcj(b o8/ k+3bxyqdt -$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a +ql;; l 6 qgd+0i,i1q zlewqyxplane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you heaql+lyx0iqzwq;,d6l;qe i1g+ r the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downw o(j9(ww z8*16h ftlyazfgzs0ard from the bottom of the boat, and then detects echoes. If the maximum depth for whics90z8fg z*zl (f1t o6whajw( yh it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octav2:*s(1 d :rz*lvhc hcujk)qfc es are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calle3:gncd u7a )rvjanz5(d a sewer pipe symphony. It consists of many pla7 jvz5gcndna3a u:r()stic 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 from a person makes a sound close to the threshold of wha+ x: :j dqr)ibkj;;human hearing (0 dB). What will be the sound lj)bh:;d ra; +j:q wikxevel of 1000 such mosquitoes?    dB

  What is the resultant soundi g*( g :uzasrbhd5g90 level when an 82-dB sound and an 87-dB sound are heard simuad*ug5 sh g09(zi bg:rltaneously?    dB

  The sound level 12.0 m from a loudspeak7 jqpsyfx )ud aux 3emuep,:5fd1e;0-er, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in pexjpf)xa,:fs0q-m5 ue7duud3e1; yall directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. mx u51csxao)r2.v la. The power output drops by 10 dB at 15 s2x x1mvr 5c. a)lua.okHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear 4zop rqia2l59 protective devices over their ears. Assume 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 q lirapz24o59 distance of 30 m from a jet airplane engine?    W

  In audio and communications sfcg:+-: f egyuystems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a fex7ko:tr-io/ s lq1 3irequency 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 with5*8aypv ns+ )btmjsz/ a fundamental frequency of 440 Hz and a mass per unit le sj)z5 tab/vm *npys8+ngth 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 vizsdmk d)kid+ ( d0-- )tfu0cotbration above a vertical open tube filled with water (Fig. 12–35). The water level is allow stdd)fz0+udd)i0 (ktkco--med to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube ; 7z; *e lbta)mwkn+cfax7/nsthat is open at one end and also 75 cm long. How much tension should be in the string m/esnwa7tb;+k f*z7 ;cax)lnif 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 avp, / hmx6ej.vs 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 two de.ctytvo:1h-qx fm w- 6t32n sources. The sound is loudest at points equidistant from the two sources. To determined- c32wh .tn - xm6eq1yttv:of exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train 8nz27 vs9pdztju ,.opq v1x:t is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving jqd :.,2s tz9u7pt o1pxv8nz vtrain?   m/s

  The frequency of a steam train wh 8fbdx) 16fduary: x3uistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)rdb)xx 6y 3f8ud1fau: ?    m/s

  At a race track, you c 29ov21oh79 3bzpfeg brtu3qtan 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 atpef2 1g9vu93oto3 bz2q 7b rh 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, hgv4 mkm v)vkma* b1+-produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Ho vkh -ba+gm41m )vv*mkw long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a s 6qa5la 61mlzdtationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what iq1l 6ma6lza d5s the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normallyx2*o:o-7 uqdf ,lzxt l about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasoundx-xl,2do:*uoqlz 7t f 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 -pe+k6c8(v/nxk kujcv a,0wl the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat af-cj0/vk+(e pc,x8alw kkvun6 ter that wave reflects off the moth?    kHz

  A bat emits a series of high *a5c5mp9b2fv ylw e2*fkf6ur lkb.z-d+ z n3sfrequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. Ho-a5 scfb ywmnku62l29.lf bzpzr*3e+vfkd*5 w 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)4wt x8st: j.ph was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is 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 aj xpth8st :.w4s an open tube.

  Room acoustics for stereo listening can b-z/p.6u vl btlq vsn1-e compromised 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. Calculate1--lzqb.v tsp vlu6/n the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called.f 1a niz ughj 7gcf/vh0zm.77 “singing rods,” involves a long, slender 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 1/hnh7a. mgzgiv.c7 f0u7fjz 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 ea5xa i i 2e+o/jbb8se-pr at a frequency of about p5e b-oi j a8i2bse+/x1000 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. Anhkd ad jwi -9io+- zied53.ar2 observer on the ground hears the sonic boom 1.5 min after the planei ohr. 5-daek3+jawiz9d -i2d passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbqqd)wkwi(- j0h u-7 nr-wj/pjoat 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