What is the evidence that sound trafju((a 7+qt ritbvx: 8vels as a wave?

What is the evidence that sound 7kn ggm. u08rr1,h djkis a form of energy?

Children sometimes play with a homemade “telemjs z /:q:4xbemjv/hqegp s-/7z1 9 evphone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into/x qh gmvs1s/:ev7zmb/ej 4ej9:q -pz 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 frequenm1bmj+ubkq +y x(: zt17q0bk w9v hhj:cy or wavelem yq: vj b(h +1+txk0wbqz97hj1:mukbngth to change?

What evidence can yoy5.6tb0 tvcmju give that the speed of sound in air does not depend significa0v5ctyjtb6 m.ntly on frequency?

The voice of a person who has inhaled helium sounds very -uj0 ,e,flsky9p 6fhe +ymh s8high-pitched. Why?

How will the air temperature in a room affect the w1 3o uxurp*j7r3vhaotj1( /vpitch of organ pipes?

Explain how a tube might be use lma:n-jw,+rud as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffle+u mrja-nw,: lr.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togetheahlvh,qalw)/6k7 s, gr as you move up the finge )hasq7kl/la,v hg,w6rboard toward the bridge?

A noisy truck approaches you from behind a building. Initiabr * *jt7zo 0q/dfr2killy you hear it but cannot see it. When it emt*q7*2 /fo rd rj0bzkierges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said m,ye6. txytg*.9q p c ftc:7eriyd9 o3to be due to “interference in space,” whereas beats cand ,yer ctfm7yx*tt9.oe6 p:q.3yi9 cg be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,l ;sv e;t d -8/(ihbokwwg3:pu would the points D and C ( lv3dhk:gwp w/i;e(tbs- ou ;8where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectwwdr i9 44 (esl2tdndu8,bb l5ing the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in 58l,l d i ws92e(dwubtb4 dr4naddition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as bp5lf y+4 lsw,a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component freque,4p yfbl5lw+ sncies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in kna-dj*q+9o m71ny (9b40attpn r witthe same direction, with the same velocity? Ex+ ta94-bn91my7wod qkp (jn0i*tran tplain.

If a wind is blowing, will th/za uv(6sbkg (8zd5e1,w uytuis alter the frequency of the sound heard by a person au8wtvz de( 5/1bk,u( 6uasgy zt rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positiondm mcnan4 i rz;-ga)(4s of a child in motion on a swing. A monitor is blowing a whistle in front of the child 4)cgin d -a4m(;aznr mon the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening yv93kou k0:yp.o0by x.e2lgw 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 s uwpgv03 :yybl x9o20oke.y.k houting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the ech.;v 9l 01 emvjl/tgbjpo 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 significantlytl;bj 0e.g/vml9vp j 1 with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in g3j+*6 h askuac t6f9 c2.-derkiogd9air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school oo oo9scc3 hd/o4ha3o 5ef l,;mf tuna on a foggy day. Without warning, an engine 3mcaseo;/ c4h9f3dolho 5oo, backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of azk z6f)yt,;b h cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the clky,z;zhb6f) tiff?    m

  A person, with his ear to the ground, sees a hugi7m7vy jqc*(yc tu( 1ne stone strike the concrete pavement. A moment later two sounds are heard from the immy vct1 i7nqyj (7(*ucpact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second ruls u;f1,eko3jupwb4r ) w99ufoe” for estimating the distance from a ligp r,1;9js9o 3uw u)okf4feuwbhtning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at iuqj.gd7860w xf q19 48p+ytnmspy6 vs)zpgm the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity istaohe14w 3 td( $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leve 3(fet*xbbhfn5)m)w yl of 95 dB when fired simultaneously at a certain place, w 5 y)f)(3bxhm*fwtnebhat will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance fv; n/oy1l le9irom an airplane with four equally noisy jet engines is experl1i;ye9n vo l/iencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to67 ate m 6 )vcec;8zlgd7)zcky-noise ratio of 58 dB, whereas for a CD pzl c;y tgez)m7d 6 vec)c68a7klayer it 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 kjdg5- m :m.xaoutput of sound from a person speaking in normal conversationmm .ag-jx: dk5. Use Table 12–2. 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 w6to)zrpuhol+3jo8 fnr2 -zb1x qu28 jhose 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 t 8g:ju fkl/h4 cdmlj6km48;fe he more modest amplifier B is rated /lckjfkg le6dm 84j:;8uf4 hmat 40 W. (a) Estimate the sound level in decibels you would expect 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 whe y5g0lx1,l a1ax 4s80xdlnvhwn placed 2.8 m in front of a loudspeaker on tx0 0xwa8llsy1d gvx,a 415h nlhe 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 differei yst5u 68rm m55oo7bxv9 m2itnce in sound level of 2.0 dB. What is the ratio of the a ubyii 9mmvm5658 sx5 rt7to2omplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whatl)rceq4oi6,x yf *8d.-d kvth factor will the intensity increasec 4) *vfx .-yt,kqheldio8r6d? 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 -a/les0y9 wd- lc+iwk 3exa6o has twice the frequency of theixsl 3l/k9awo-0+w -dcea 6e y other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sou/fg .zzaqld2. nd wave in air that corresponds to a displacement amplit fql.d2zz.a /gude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound le0ncv0s vknq6 6z l9ch,vel to seem as loud as a 100-Hz tone that has a 5,cs6n9 vq0 zvkl6hcn 00-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an b 0h5igy.aexw;r1t: n ear can detect when the sound level is 30 dB? (See Fig. 12–rt5n.heb1ga y:; 0wx i6.)

  Your auditory system can accommodate a5w9lb- eoij)y huge range of sound levels. What is the ratio of highest to lowest intej wl)9oei -5ybnsity 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 fu+jfajo 6cg3d6e 76ciendamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, a6ac e3ei6co dg7jfj 6+nd it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are thy0w0./elgt yd*zbdp2n epx2 )e fundamental and first three audible overtones ytnpl2)*e ewz.2d00xypdb/gif 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 across thn2,yu:v ;nfqte top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube? u,t2fnynqv: ;    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-t6s1fs5ws*h lp ube pipes spanning the range of human hearing sswls1*p6f h5 (20 Hz to 20 kHz), what 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 Hz as itu g mz.7v98t 4+7b wsmgqh ucy.qwl+/ls third harmonic. What will be its fundamental frequency if it is fingered at a w8wm++z .ucsg94/g l.qlh7 t yvqmu7blength of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mj rii ff2+ c,jzuh1+n,iddle C (33 iznijcrfh,f++ u21 j,0 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 ort5ggod:buq;yi i,6* pen organ pipe that emits middle C (262 Hz) when the temperai5,uq* 6yo;rt:gdibg ture is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at l2yb,p g+7php ;e5f ui20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thxoca.w3: p)nd* er +ude flute in Example 12–10 should the hole be that must be uncovered to play D : dcnwa*)o +e .pdrxu3above 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, butq hx7 14(ym aymt;8 v (dllwzqzxho32. not at any other frequencies in between. (a) Show why this is an open l8tdx z aq yh;ow7zx(24(1qm3. hymvlor 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 opupp.1 yd3 4d.+wol vod8l ,ecwen at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Wlo, 4p8.pd1.lvo dy wud c3ew+hat 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 ti+gvfwcfqf. 72/*7 yo v2odpa6hfv8 $^{\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 6s1 *- 4a;xvgpspqihlf ry,m- within the audible range for a 2.14-m-long organ pipe;,m-gs*vs6 qfrpylpi ha41 x- at 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 outside ha5t0 n1n+dsnand is closed at the other end by the eardrum. Estimate the frequencies (in tn ntahd sn+105he 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 beatg5f w-uw dah70 every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other5u- h0wdf7aw g string? ±    Hz

  What is the beat frequency if middlsnc3 lbyw2 ez8n y:-z s2en6f0e C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (bra y iowvj9,86cind 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 simultaneou i,9c6jo iv8ywsly, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 35;b cw:(ng2obi 0-Hz tuning fork and 9 beats(n2b:;g oc bwi/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 same frequency, 294 Hzn ed 2m usf9f8g6j4.ad99tscf . The tension in one string is then decreased by 2.0%. What will be the beat frequency h8t9f9d 9a6scsue mng2jff.d4 eard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eac52dio)dmw5 1ui+sj u th try to play middle C (262 Hjd 5s+)1om5u2uwiti d z), 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 frequency of 441fr*q 3f4 y9m :igaw+i sg4yt-i Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A andyg+mfa4 4i9tyrw- q if3g*i:s 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 vg:4 (mhidk) vone speaker and 3.50 m fr:hg kvv d(4mi)om 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 tur +v5a 9q 8cpay syq55ig0kz1o be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If on pq 9yu+caa k8iz01gvy5 rs55qe 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 many beats pui*:4z)utejpfe6;7 hy ownv.er secondtuhfoeiv.z:yw7e*4up 6j ;) n will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 3s8i 2bi.ssc* /felt r7jkmp( Hz when at rest. What f s f87*ec2ssbr3li/i( kmj.pt requency 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.ez(c6 sg)+gd hq y 6qkoa6+k;a What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of +6qk eagq(y ;ko6sga)+zdh c 632 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz souryu13iet( mc y)ce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies cy)emiu3 1ty (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 eqw*xd . :jib4btuipped with the same single frequency horn. When one is at rest and the wbid: .t4x*b jother 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 receives themb)m fjzw.lf,c+1i/ syb/5yki8ug,a u returned from an object movin5j, 81/ca i)byuzslgfwmfb i .uyk +,/g 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 flies, the bat emit lv*j(p ,mfupd-l:g0ts an ultrasonic sound wave with frequency 30d mt-l: *pl (ufpv,g0j.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 09wfgn:04 k psfbc5 2h8q1y lb cl6udpplayed 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 hear0ny9bh 0gl:p pdlq4suw 1kcfcb26f 58d if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Su9itbcg 0rsio*: ls.-ze. v o1cppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected bzbi*9r. g ccsv:el0ts-io1.o eat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrwm3n uqeq zkb5bkj: 3k 6(q8k-asonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570.y:g9 xv2 oowm*ty dw) Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located,2x )gv*d9yoytm. ww:o at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed 38q eh(s9bssp.uetlll5i i( 4 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 sou dt8ny g7dl++t.yb-ls nd is 310 m/s (a) What is the angle the shock wave7lt+dl gt8d ny ys.+-b makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a ppbd z g-m9)ff g6wg91planet where the speed of sound is only abopmwg bf9p1 fd-g)9zg6ut 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 8y4cnfp4qlhl71 f s s,1500 m/s strikes the ocean. Determine the shock wave angle it prodqslhyn 4lf1p74s 1fc,uces
(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 9a+z/f6c 0re: ,z;;mf yg otnt6ob qhd$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a m6h:f b7 +1hsil *(itgiamf8xhxe1+*nf( vr pplane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has travelaffpvitm1 7g + s86hb((e1xnhxfrhi* l* :+i med 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 sonarhozb oz:linvdl +;1bji3- n.- device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is desigbjl zzboho+.3v-ln -;n:idi1 ned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves areg: p,-n3 pu0 mdgv2edp there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of 0g -faei etb--many plastic pipes of various lengths, w ebgi -tf-ae-0hich 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 fr l5,*h ryutri1om a person makes a sound close to the threshold of human hearing (0 dB). What will be ur,5 trh1y l*ithe sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are hej6 y ;leqt; s3wdz03f3zbrib9 re l)9uard simultanlfjsr03d b)6t93 9l;brqwuiz3yz;e eeously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 106-wx8oatrbgg:sw ) g5 5 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally ib6-xwt5: grw8 gag)os n all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outp4qy9n9n 2 jl:qbu9fjjut drops by 10 dB at fj99 :jynlubq42j9nq 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicallyf q5z pm+p4(mv wear 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 pow(54fv pzpq+m mer intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatio4wx5ycur0 r *1 ww.tzkns systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violi bbp hld2:f ,cr(n:/ydn is tuned to 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 fixed points with a funq 2xup zf.4xbd (/ws*cdamental frequency of 4. (/p4dbw *scx2qu fzx40 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fillej bv.pes7+e(alv 3w2e *2m hjdd with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the2+s e(pbj 23e.vwh7ev lad*mj 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 that is open ;ff)u7pmvrdy( m0i p7 at one end and also 75 cm long. How much tevy fi;dru7mp) f0 mp(7nsion 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 one fuj /k6oo(s 3k3l4lrqwfll 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 sources. m0 n6u)cnvn/e 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 level0c/v n num)ne6 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 if p vs0 8zf4tef)x4/hks stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Whavp hf4f)kx0 eft4s z/8t is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afb2.)r6u u8pvsvvx;o*mwr .ni ter it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume co pwv n6u; bs8voxi.v*.r)rm2unstant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to 2c5noodipx 3lzol.+5 the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a oo5.2n 5olclp +di3zxfull octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a,g eqq 3xsqrk)e0,r2i beat frequency of 11 Hz. The shorter one is 2.40 ieqr qk0,x,2g) qsr e3m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves m x60svx+efsbg .k(z6past 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 theseksf +(vg6z xx m0.b6 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 dc, .wk** c-8ovwc vrq3rl yk:the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrq*lrw,r .c:d 3koyccv-8 v*kw asound 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 speeg7s(4xw a. zeepx3 cx,d 6.5 m/s while the moth is flying toward 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 aftx(e4x,3.e 7ax sgcwpz er that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it apx ei4*tff(e4cproaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How(x4*e c 4fifte 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 sel3 l;sx1bsgbdph d.-go4i(/ac6/ ip hnd 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 s i.ihs c a6lx dgl/d-phb1;g4/( bop3one 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 comzof pvu mhwh c/.w(21,promised 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 standing waves icm1,z2./ upwhf o hvw(n this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lon ac 3e., b cfmvbr*m*xpp(2;vtg, 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,a( 3*,m efr btpcpv*x2m.cv;b” 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 fxxz 1 -qdp4v+csj: :xhuman ear at a frequency of aboutz:v- 1c+fx x:xqj 4dps 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An obser81 bv/opbf4oover on the ground hears the sonic boom 1.5 min after the plane passes directly overheo4ov fpo18b/ bad. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb2-rpq 1w5gx s8wckbecc i ;8e+qg6fd8oat 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