What is the evidence that skd-e :*r5fe j 0rnn7doound travels as a wave?

What is the evidence that sound is a form of enerxwq9pe.t,8/hj. in;chfj b0 iuy5u+xgy?

Children sometimes play with a homema0r h ls ;cpd9zml00o.lde “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).m00 rd; lo0 pc9llhz.s Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expe1ob5 +myh.mkqt50/6 hlbsbee ct the frequency or wavelength to chan6 bqtb.e1/ems k50myob lh5+ hge?

What evidence can you give that the speed of sound ini()le mw8 wxb*3is(h9hfipx8 air does not depend significantly on frequency8 w3 lxb89fs(ixh(wmpi ieh *)?

The voice of a person who 0: rgtfl5. tttjqg)nn2a0ov 3 has inhaled helium sounds very high-pitched. Why?

How will the air temperature 22jok7afa6,qge3dq xd3u3j i in a room affect the pitch of organ pipes?

Explain how a tube might i6b l hu/xg q5;6wipj 13/zxzpbe used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a iz/ b5gh 1q /w6 6xui3jppxl;zcar muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer :smm3wk2xsp8 together as you move up the fingerm2w:3 pxmk8s sboard toward the bridge?

A noisy truck approaches you from behind agmt538eowc8 x building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-freq8mcot35xw 8g euency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “inte+aaz0j,3h8 +uf blwkl rference in space,” whereas beats can be said to be due to “interference in time.”,b jl8a+f +ahul0kzw 3 Explain.

In Fig. 12–16, if the frequency of the jmq,2 8ii5fcsb *(lzc speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farthjiclfsi ,5*zmb28q c (er apart or closer together?

Traditional methods of protecting the hearing of people who work in areasi5 tw ijag/ )kuol61x(+k 1iwa with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headp/+ (xojiaw)6kk1ita5iuw g1 lhones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as *twm:ci s9*en,ygkiwarf(.i, c /9 in 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 frequencies farther apart? Ecisik(ic,y* m rwg.f99*a :n,/wi tn explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directio 51-mm ,uotvu rx8kx5hn, with the same velocitv 5ru 81o-mhkx m,5xuty? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a 4k68na2m )1dcjeg8hmh5 7km c h(rxbx person at re( ck7c8 r4 xmnb2ajh md1egx)5k86hmhst with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A in+.zhfbz3 l4 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 freq4 zbl+ zhn3.ifuency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of h-zus bpne5xu(b,w +z9/x4 zwier 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 th, z(-w+ezpbuwu /xb4 59inxzse lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belo2b3wm p*q *nbtw the waterline. He hears the echo of the sound reflected from the ocean floor d mtbb2*wqn3p *irectly 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 depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in8 sq3z w-oqy:c 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 above a school of tuna on a foggy pxw :9 bzm8hbu2 7una5day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time e7b8ah p5m2nuw9x: zb ulapses before 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 splg,mha5e5sttu/5rv*i ash it makes when striking the water below is,shr 5vgim / 5a*tteu5 heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone str3*8x .td dvx;cv d-iweike the concrete pavement. A moment - dcxv3 w;ddxiv te.8*later two sounds are heard 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 “5-secon d zmgks6 v5830dsvjb-d rule” for estimating the distance from a lightning strike if the tgdsv j d5m-vb0zs368k emperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound atufdaar dm( h 88,+rwg+ 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 ijy.eabq3: 6qqz :gl8u /4f fjts $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simu0 g7ydquv. md-xg:2 ( 8vauaafltaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add int aqvy gv(a2dfdu:7 .-0 axgmu8ensities, not dB’s.]    dB

  A person standing a certain distance from anz nj b2-nqc:( 8ukxmaimhgjg 9z;r947 airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intn(899nmj g;7u c xq2izrhbj-4gm:zkaensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-no8q(zntjr5xb8 es88x21zw arpwtb . x7ise ratio of 58 dB, whereas for a CD player it is 95 dB.2rj8rz aex b8.xx t5snp8tb8(w1zwq7 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 cot4bu 3 rjrd2 (eyq+3im bp-diuda9y06nversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mout6yu 2rydi3damb0 uir43 ptj+e(9q bd-h. $\approx$    $ \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 eardr uoo w*lodi,7k s:s3l/um whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated h1icaj v8/:noat 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 loujvc/n io1 8a:hdspeaker 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:2w fr-xi2ja k meter registered 130 dB when placed 2.8 m in front of a loudspeake ja22w-ikrfx: r 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 dis9vi-;x /hcgf-v x o6ffference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint:vhfxgov s --i;/9c6 fx See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fa4 k -/8lh/h7urleinhs b(a ka81+ggw rctor will the intensity increase? Increase by a sirgb8 e g4l1(r/kl/7hw auah+h8-kn factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one ha.eddi7g(f0jn s twice the frequency of the other. What is the ratioj(dniegf 70d. of their intensities?   

  What would be the sound level (in dB) of a souncaw/7y,l:gdq; pljqlrah// 6 d wave in air that corresponds to a displacement amplitude of vibrating air moleculad7,; lqwl/q/ayp r: hjclg /6es of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-H(uf p2jt drv-) c 6o7msklv(k0z tone that has a 50-dB sound level? (See Figljkt( 0(k) rvvfs62u7doc mp-. 12–6.)    dB

What are the lowest and highest frequencie*-g b :dsnt;-+,tlh ooycmq7 fs that an ear can detect when the sound level is 30 dB? (Se cm s- yoo-:dl7*n,qt+;gf hbte Fig. 12–6.)

  Your auditory system can accommodnozqn /an /wo0zmxh2 w:+.+ xiate a huge range of sound levels. What is the r2:xaino.0hnqxm/n/ +wwz+o zatio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequenc qc pl.iz--(rry of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.3cqi-(rr.zp - l5 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long.l4rd: -u q.v+dgjyt8 y What are the fundamental and first three audible overtones i.dyvl4+jrug q-t:d8 y f 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 tuy*5u3l9q7 u2 w irogblowing across the top of an empty soda bottle that is 18 cm de 52tw o9 q3ui7gulury*ep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning thuqe(+ jfo,ump 0u)al, e range of human hearing (20 ef,mj0l( +)uo q,apuuHz 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 its third h2l/v(r; vjh am5 w:eocarmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original le h2 vr oawl:mcj;v/e(5ngth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E ab 8: e7ovjwjb fvq8d7j,ove middle Cbvo 7feq ,vjwj78d8:j (330 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 thatn8pj 7uv kjwdlb6 dv2)vd a4(a;o.0zu emits middle C (262 Hz) when the temperature i4pbzvdnkvd (6ajl7v 8o).udu ; j0wa2s 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 181q ib 8fym3jb qn0iaat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole b*e xfqa cx2gg1 04lzws8ekm8 bq:+ct8e that must be uncovered to play D above middle C at 294 Hz8c8ae+qx *mk1twz e:gb s82q gx fl40c?    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, q- s6j9sf0.9lvu pbvqcbsi-7440 Hz, and 616 Hz, but not at any other frequencies i-6vv9ic p 0q.l-j9sb qfu7b ssn 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. z oy7 7,lze9euIt resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What isul, 7zoeyz79e
(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 bn.km:o 4 /e(lmk g36mpc.guc$^{\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 prese5j 46wp ih/9hufpqt 7td:u2ohnt within the audible range for a 2.14-m-long organ pipe at 7 625:i9q4jhtpu f hhu/tpod w20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 ,mllif) my qswukn :oy-q gq( (2.tv65cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frk2 m6)m5(wy t:q.q-uf l v(lginys ,oqequencies (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 everon t 1 x: r3ld,+-wm*if0mtowoy 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far o,ittxm 1w 3d0 o+ o:mlow*-nfrff in frequency is the other string? ±    Hz

  What is the beat frequency /x.l,gkhdwi:v: si/i 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 (vgn rtq (c.;doperates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans d.q(tn rvg;c(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 beats/s when sounded with .du)5 t2fp prma 350-Hz tuning fork and 9 beats/s when sounded with a 355-.m) 52dpptrfuHz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequenbxp8n3x- xx;wt686g) zhi t 0bbxsoe0cy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when bt0bgi6shtx x 6bz; - 83xx8wepn)ox0the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middly)asafo96z e7e C (262 Hz), but one is at 5.0°C and the o)sa9oy7azfe 6 ther at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hzax .2zc+*pod fsln7 2oj;4zoi ; when A and B are sounded to4;pzol c* sx+ 7j o.za2i2dnofgether, 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 perso-iy;( jxo)g)nqoy q y,n stands 3.00 m from one speaker and 3.50 )) ix y(jq;-nqy,gooym 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 tunerc1yrp, nfq a (:+qyzss+i) f(r hears three beats every 2.0 s when they are played together. (a) If one is py1)r:qr +i qczafss+ (y(nf, 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*9 ygx2cj* ymi 2.76 m in air. How many beats per yg 9c*2yxm* ijsecond 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 Hzvhj1 gl.1 rac94- orhd when at rest. What frequency do you detect if you move wi1r-a9hhvl1gjc ord .4th 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 5sbebp/ wbvdch; )x. :if a fire engine whose siren emits at 1550 Hz sb xc pdbh:ev;w 5.b/)moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if w (f* ,8x+r*ygyd lxlwa 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two+*w *( xrlfw,x dgyy8l 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 horn8vu1 gmt*yr,u;/h coy . When one is at rest and tht/h* m8vyyugo,r;1u ce 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 any/3qg,i tbilo,,mr;8 y1pgu xd receives them returned from an object moving directly away from it at 25 m/s What is the received sound fre 3q xryb8;g miu1gyi,lp,/ot,quency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m:yoh.8j63 vbr ybo gmw3w3e4r/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does thr38 ev.bybyo hw 346r 3go:jmwe bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopwnxjr3i:;p) ij+ l:yz pler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while jijx:i3n:z+lp;ryw) at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to meashnm y g /-l+c46tv6og1:ki d(gpz fyj5ure 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 the expected beat frequency if blood is flowing in large leg arj+ogi v cp zyg6 5m-/1ftn6h 4(:gdlykteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frepmsk 4fdix4.d +8m6 kyquency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind 2p, anywof58m* nq6 lcvelocity is 12 m/s from the north, what frequency will observers hear lcp,a6fyom 58qwn*n 2who 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 land8pbk- 9-wvlte+0tv- re vhxnb )s)3kp 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/s (a) What is sq u5fzj- e3.ch rf(0q1woqf8 the 3uqr-1sq0jeq5w8 (fffo .chzangle the shock wave 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 planet where the speed of s2 uaxluf,k 18zound is1kuf,x az 28lu only about 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 st2i1h d 1k0dqi oawjw-+rikes the ocean. Determine the shock wave angle1k +w qd-wod ija20h1i it produces
(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 a :0 txvo+bms;$/theta$ 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 gr;8ivh5qnz7zp ound flying faster t;zh v5n7p8 qzihan the speed of sound. By the time you hear 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 vfg309 .7w pblrukua5 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 designed to work is 200 m, what is the minimum time between pulses (in fresh water)k.vwu73u9g pf0abl r5?    s

  Approximately how many octaves are there in:ydzix4*q f jl )5s0jz 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 manwflfg.al5tn 25duh+j sq. 9-sy plastic hwg5n59d+afqf.jllt.2s -u s 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 th(v5(s; npe aqme threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoe;pnv( a(5m qses?    dB

  What is the resultant sound level when an 8 /tpjs(a jjr,*2-dB sound and an 87-dB sound are heard r* jp,stajj/ (simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whjgzao l9n2 /mpx-/i 07bzqzp:at is the acoustic power outputlz -g7/j9pxinzb0z/ po 2ma: q (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dropsghn rm :t6uc8.fuq e80z,py 1s by 10 dB at 15 kHz. ye:z8qrnpg8uht 6cm.0 u1sf ,What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraftg9bf bm5y4bm6x8n4uk typically wear protective devices over their ears. Assume that the sound level of a jet airplane en54bfg4x bym mbknu968gine, 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 communig72n 9zjy:t qpcations 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 violin is tun 8xxte1 5*a6 xr+amauded 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 c.lm m-de227puct 2m r:t4krkqm long between fixed points with a fundamental frequency of 440 Hz aeu.tmr4t22 km dr:pqmk2cl7 -nd 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 filled with uuvu 0954ttzxwater (Fig. 12–35). The water level is allowed to dr uvu0zx9t54tu op 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 that is open at onz mldps8 a8:a-e end and also 75 cm long. How much tension should be in th pz d:aa-ml8s8e string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wv2.x q:(b dw(w a7rwt3do qjh9as observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure toneigc -46z8g 3py;bsooa in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from oa6b8i4c3-sgp ;yzg oone source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on t )uyo w ulgplg o4i87y.rp-8+rhe stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moilpo.yuuog 87) g py8l+ rrw-4ving train?   m/s

  The frequency of a steam train 20 x8* 9zegfz0wuqlh2 )plnb ywhistle 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)?z 9y)g*2hleb8upzqx0 w 2l0nf    m/s

  At a race track, you can estimate the spluag/ a kl3a ;39to2xieed of cars just by listening to the difference in pitch g uiaal 3x2 3o;atk/l9of 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 it going?    m/s

  Two open organ pipes, soe8i ig z9ic0k9uone //unding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the othe/z 0 gkii9/98iceonu er?    m

Two loudspeakers are at opposite ends of a railroqnz 50s2tse;pl 549dzhhx (7h(mmochad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequenc(4o7t e5 m2n9x;mz05hpzhq(sl hs d hcies 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 flow in the aorta wz:d9n e xwv5*o/l2t qun ;.nw94ejqbis normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assuo:9tw /u. 2;w9qqne*wx nj4vbzl5 endme 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(nw3.cl5i tb .6x)vyu6gcuy +iq su 3a/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 thc 6yx .nu 6i+ wytg5ic)3u .3qbals(vue wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high f8fv., vuja yy,u2 /qpprequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms lay8j, ppf2 y v.q/uvu,ong. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send*9tsn jv 9fqx,u hqg43 signals from one Alpine village to a,4*qgqhxu 9vs 9 jf3ntnother. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromisedl lt 4ams3:3(-beivqr by the presence of standing m(qv3letr4-b sa:i3l 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 in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invoc1 j 9j4ipbx4 4fqcp0zlves 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 clear, loud, ringing sound. For a ip1bp04 9j c4fqc z4xj90-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 ea6ir h)2g5trkeb 5 m,lwr at a frequency of about 1000 Hz ) i55bl wg krt6rhem2,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 gwi39.xf7 /qw iz1qr9 a. rczferound hears the sonic boom 1.5 min after the 7. 9exzqiwq za9wi/cf fr3.r1 plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbogx-rvj: 8+xpy )l p+ri*m;tplat 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