What is the evidence that soundj8 z9,mdy)qkt travels as a wave?

What is the evidence that sound is a htmr/ys8q 42 wform of energy?

Children sometimes play with a hfmo7-h ( nos3c;m bsp3omemade “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 ;h ossm3fcb 3om-np(7travels from one cup to the other.

When a sound wave pas*v / -gt(0l5i umeygm/q ,tdwx lz+5ytses from air into water, do you expect the frequency or wavelength to change?l (md+wym5/glt0g/* z5itv- qeyxtu,

What evidence can you givetkksifnd 0: y2e6kv63 id-ec0 that the speed of sound in air does not depend signifk k230tdd si66inv0y-ee k:cficantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitch;v.(j8cgsi; sjabfu 6ed. Why?

How will the air temperature in a room a *dx3sl b80euwju t3d+ffect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce t) 8rvl5/0tq nrwcdml )k y//llhe amplitude of sounds in various frequency ranges. (An exa/ /t8) rnllw dmv0ll qky/cr)5mple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as:wtp yup;ell+ r 92e+u you move up the fingerboard towp pw lte+;u9 lu:e+ry2ard the bridge?

A noisy truck approaches you from behind a building. Initially yu)1+cu z nflm60/v bdkou 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 Section 11–15 on difflbdv n0 )z/ku c1+mfu6raction.]

Standing waves can be said to be due to “interference in s jlg628ybau a wkb.2jp(c+oa;pace,” whereas beats can be said to be due to “interfe w.c(;yoag j2a+6a2l pbjbu8krence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were 1 72eq -(zugj)lk su jc1i+pbnlowered, would the points D and C (where destructive and constructive interference occur) mu -gp) z+unl12jjsc1ei7( kbqove farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with u4zjw 6fx,6 1q)yrhwx 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 noise reduce tfz6 u4qhxyx)w1rwj ,6 he sound levels reaching the ears?

Consider the two waves shown in Fi7ht s7 7dqi h bas :i5y7yl0xmcdk/-.dg. 12–31. Each 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), are the twqd k7h.im0t7bl7yxs yi dh7:ds 5-ac /o component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the so1nox qiy9,l0u cfvs3) uk* q0lurce and observer move in the same direction, with the same velocity? Explaifq o li1* nk )uvxqy03s,0u9lcn.

If a wind is blowing, will this alter the frequency of thezj o ,,7gecxpz,kfn5 * sound heard by a person at rest with respect tpgcn *,k ,5zjxezof,7 o the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing.hx461tjyg 9it A monitor is blowingiyt6 1jg94xht a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of qc.ngt /zcmu*8:axn-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 2c au*nq/-:c8 zmx .tgn.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. Hezo:d 144x mkch -i16ijl/ffuza 9nn1v hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this pv ni44noa 61:ihxzlju1 zm9k-f1d f c/oint? 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 in5gn0/b;lc cjk 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 lmh.4l5 v hzc+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)ml+5 . hlvz4ch by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when stri+ ue wogkmg+bn-nk,*/ wj0d;fking the water bel; mdu +k kn eg-n/wwg0fb*+oj,ow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stritd.q* fgx,u0j +.2vtlyq d l:gke the concrete pavement. A moment later two2, +ly:*d fuqt.xl.gtdqgv 0j 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 mi4.o 8+nuyf. hcw4x f8fzya*drle of distance by the “5-second rule” wd4 f+88za4o.y fuc.h yxnr*f for estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a s+jq +a :ctcg).p-;wi, w putvvound at 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 sounrz9u1;7g1 hrdzfrp 82itdzjz- 4ff b)d whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produ8q39w) vprd0sc)faul0 yzb;lce a sound level of 95 dB when fired simultaneously at ac) ra 8dwfsvb 90ulpz) ly;0q3 certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with wre3blu 7cu 4w;ul9.xbu (ci/four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound levell4/euu7;ib(lcwrb u c3 ux. w9 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-to-noise ratio of 58 dB, whereas fo) 8 , -d( 6tazmgowjhn1 b9k)j.qsffwor a CD player it is 95 dB. What is the ratio of intensih.9,t-o8w)g jbm6d1zsa w f)kon(fqjties of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output5 yvb./ .12cacqr3vweacoc8 e of sound from a person speaking in normal conversation. Use Table 12–2 . 8 avew/yc1rac. o5veq2bcc3. 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 whose area ifepw2l50 qqltg9g12 rs $5 \times10^{ -5} m^2$ (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 Akip5)x)r ram3 is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) mixp )r)r3ak 5Estimate 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 when placed 2.8 m in front oi4h+w9 i-yr bsf a loudspeaker on the stage sy+br w-i4h9i.
(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 sound level of 2.0 djhnwqqsf9d 7kv9p + ;/B. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]9/7kf9wh+v;nq sqdj p$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will thumpa9*1p 0 lgbe intensity increase? Increase by abl0amgpu1*9 p factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equat rxgx,mx2u11 l displacement amplitudes, but one has twice the frequency of the other. What is the ra gxtux1,mx2r1 tio of their intensities?   

  What would be the sound level (in dB) of a sound wa;ak:u6 rq,1pi yqgx) *kec 6heve in air that corresponds to a displacemar 6p1uyk)qgh6x i ,e:q;k*c eent amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz t (j.aj owgt/6o 1h40a6x 0fqzkvm/0ncrn 2lrmone that has a 50-dB soun/vmo n cm.tr20w6k rqah0zl6jaf(/o0n jg14 xd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear cac00tu8; p errcn detect when the sound level is 3 cr0rep;uc8t0 0 dB? (See Fig. 12–6.)

  Your auditory system k0c0sv7 uqsbegex/da,m,o4 ,4a v8 p fcan accommodate a huge range of sound levels. What is the rati bac0pdqv0e x,/84,k 7 sseav ugm,4ofo 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 frequency of 440 Hz. To9a- h8mfd42ui kf j/she length of the vibrating portion is 32 cmh9kd /ffa-m 2o8i4u sj, and 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 the funtwcsb)- 2f0sox1 ( yrpdamental and first three audible ovypsbt1- ( 2of)xrwcs0ertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top-hahhd dqq 5n+ /qj*c0 of an empty soda bottle that is dqd jhac*0q5+h/n q-h 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pip 2rikjus;l)uy6 c(+szh-br aj/ + gi5kes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requiz g+lsr rc2;kj-)husyj5/uki6b (a+ired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz+ 1xt hw),sqlv as its third harmonic. What will be its fundamental frequency if it is fingered at a length of onlq1t wsx+),vhly 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middh- xvqv(fq u:1le C (1hx:qqfv-v ( u330 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 h 6l8(mny2 . pq.q 6tufjhs6qjan open organ pipe that emits middle C (262 Hz) when the temperaturj686n6hpl2 muj .tqqsyq.fh( e 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 a:wollcg0 *(ztt 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 thn.m-6psl n-r oe hole be that must n-pmr6 sl- o.nbe uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ ptkb :76yztu 4 cp0gsv6ipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show wh tk: btpy664uvgzs7c 0y 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 botm0(rkk1fo; z0kp,pv ih ends. It resonates at two successive harmonkkvrmpz0( f ,k;io1p0ics 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 *u62yfz uwv,mqcsuy/e( umiu )/2 ht)$^{\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-long org,m +7 nqs1;lzenciwxo- 6d ez(an pipe at 20 - wd6c7(sizonzq,n lx;m+e 1e$^{\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 and ubqr bxf/3 q ,jk1y4j(is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the stanb,xy 3bjq(fjr1 kq4/ uding 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 every9s15-amd8xp gzg.x ij 2.0 s when trying to adjust two strings, one of which is sounding 4z xi98gj.15sg -amxdp 40 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and.hlx2mhir,z 7 $C^＃$ (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 kHzhs9a 72:kwa7prny5s l, while another (brand X) operates at an unknowsa 5pn9kw7r:2shly7a n 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 operating frequency of brand X.    kHz

  A guitar string produ+j3 jm6lq) j:cas 5;sj ienlo5ces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hc5j6o5; j sla3 snmj i:j)leq+z tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The t(vg y1pwuq +qpnij2r7ph b3- 1ension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? 7p31i(wv2 b- ph1grnjpuq+ yq[Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fl/ pyejx0-2wa9/bf 4+ze c bxozutes each try to play middle C (260 bxx-y/9 ewza2+e c4zob pfj/2 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forksuo)vt 9ieobg3dh ntdj l,/p40 h: a0)j, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are soundedj9lj0b ):h3tdnv 4epah /td o0ugo) ,i together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker an)mi. rlit2l g2i-omr bx/qa+ x772aacd 3.50 m fmlirx+t2 la)qia7 . ca-2i/gm or27bxrom 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 13d )d-1 jxgetw62 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibratingt )wx e-gd1jd6 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 agoax76aarh3x (4lyb .nd 2.76 m in air. How many beats per secorxyahbx3 6 glo4a(a7.nd 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 r5zq,dkq2(91;ekn xl hp6q yx ;a.7kwpg u8ztis 1550 Hz when at rest. What frequency do yowz1pkh,(n q789; yl2zp kk.6dagtxq5 rqex ;u u 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 stil2/ebl-j9ud z:se x.r0:x vvdhl. What frequency do you detect if a fire engine whose siren emits axdejhlvr2 :e. d9 0su-z/x:bvt 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you ;lai(cs.ri.e at 15 m/s versus you moving toward it at 15 m/i.ar;(. icless Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equippelbsbdw1qm(a*8xc* i --s0 u ped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat 0*p mwc( s*lbs-e-b8iud1 qxafrequency 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 andi,wr6l hlpgxn+3 k)j, receives them returned from an object moving directly awa63)k nl lr,jpih+gwx, y 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 emits an ultrrbh /:+suj0u)x hs gut)hk84ig km)0f asonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave? r08 sbg4u+))h: k/j uk0gt mshhfu i)x   $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba edppp o8,c9 tk 6::splwas 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 wa:k,:ppsdpe869 clopts heard 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. Suppos* ueiyd ( ovl/f0;ovx*e the device emits sound at 3.5 MHz, and the speed of sound in human tissi;(o*lx0 * dv fveu/oyue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves off9 tw+lxj7t ;1) jdmwu 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 zpr,h :3/ fxr08y2h :vg u-mh2sndwqtof frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency wi: ymhts,8f rzw h2dqu-hg x320p:/nrv ll observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at j8epcs,2 q qa620 $^{\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)udx95lzefj eiu h(-/) What is the angle the shock wave makes with the direction of the airplane’s motz(x ujehf ei/u9d) -l5ion?    $^{\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 whkk;qt2x6fg n 5nje 35wpoh+j 8ere the speed of sound is onlyj558q 2+jfkht 6knnpg owx3e; 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 strikes the ocean. Dedzqq(5 6 5 kr-xgfvyr/termine the shock wave angle izx qfv/g5 qry-kd(5r6 t 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 /t/zl9teyw, bb.a kr6 $/theta$ 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 gro j+bgl(+ fr.4d px hp77sza4+ac5vrkbund flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.+p5z brfpa +g(kvbasj4 d+ xlr47ch.70 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 de6joy c,57zcg,i.hixr e/a.tjvice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detecrjgjo. 7 c,.5yah/ , i6tizxects 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)?    s

  Approximately how many octaves are there in te528l tf3dcmkhe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dhz7 k ./)nkuvg2kk974xhxtvkisplay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, whitkh/xkx7 9 uhg7k2k.)4z vkvn ch 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 the95 pik +1mwoey threshold of human hearing (0 dB). What will be the sound level of 1000 such meoik1w5my9+ posquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 871 gh9;nu1/b ux*d6o/boblt w n-dB sound are heard simul1ou o/d/t*x9hbb ubg l1wn;n6taneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the op*pqc4fo(9 nyq en, is 105 dB. What is the acoustic power output (W) of the speaker, assumiq9 (q fcno4*ypng it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W o z x/psfp0hi8)7g1m om 5gfe cc19vi;wutput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is v9 pwc1h emcgf/mifop)7180sz5;xg i the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear 2.x p *8)cllkqh:t kfxprotective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dlcx*k k2 8:q txh)fl.pB, 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 communication gonm im5j+-q+ao*78x5ypkb budl); ts 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 tuned to a fre b3e)o :da uyk/xw;n8 aclho./quency 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 lotv)rf sv1-ga6 ng between fixed points with a fundamental frequency of 440 Hzg v a6tvfs1-)r 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 vibra4ckp:-qgi(+i:y z qujm-o oo0 tion above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube ope 0ijoqyk+ 4iqo-( ozp gm:uc:-ning 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 mh;-jra5h nl2ktrr , g2ass 2.10 g is near a tube that is open at one end and alsh22-r l;k ,5trhrangjo 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass waselq1sqpcq z ls1)qt) 8r; e9b k-:.go 52pxlwt 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 tone in the 500–1000-Hzlza67 unklj )c 4 pp8icsb3sj1fte1-, 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 cl31-j8 16tj s zplupb)7na,ecis 4kfat a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hhfm4l25 5 o kfvcbw:h;lop b+(z whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beatf;c h oom : 5bb+w5(24klhpvlf frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam trn 1ky6cl+dyed z-7- jwain whistle as it approaches you is 538 Hz. After it passecel nz djyy1--6 k+wd7s you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed srw:hw,fw. yl wult3rg8d (50v u) ld*of cars just by listening to the difference in pitch of the engine noise between ahw5ud3 ylw*wv,u8 rd) s(lf0rl :tg.wpproaching 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 pipes9en/nvswpt22azkgs; h 6 f 63x, sounding together, produce a beat frequency of 11 Hz. The shorterkgp23;9sn vaetf w6s 6nx/z 2h one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car h-ow;ku t+.o jas it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have pas+ ;- .wtuhookjsed him, at C?

  If the velocity of blood flow in the aorta is normallyg 8f7meq d:-rb-:c 8wezal tfvn t0a.k4fi(7 n about 0.32 m/s what beat frequency would you exte fai0e f88tdg m.:-kfbn- w n(qz7a:l7crv4pect if 5.50-MHz ultrasound 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 flyi bd4 zl umr0rpham/,*4ng toward the bat 0 ,4 *bmp4urhra dzm/lat 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 after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approach sxtwm0wx,a0 qphh0 iob of+mx*+ +(9tes a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emittetxma9xhio0+hbmsx 0q *ww0t+ o+( ,fpd?    m

The “alpenhorn” (Fig. ;,sq frx zo3j-12–38) 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 t rs ,x;qofjz-3he 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 compromised by the presen7zkd zr56e( )n 8cqtuice 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 z758 )rudnzti(cqe k6 waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstrationbpvm8o q4e5;no9c5 v r, called “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 practir5co5 m4ev98p o nb;qvce, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of qm,/ 6o16 ostfptx,f xpza5sp +ot5g.hearing for the human ear at a frequency of about 1000 Hz isop5 6+5zgmt/t opfx6o sqx.p f,at,1s $I_0$ = $1 \times10^{12 } W / m^2$ 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 groung6r-oq/-odl7 q(gxzrd hears the sonic boom 1.5 min after the plane passes directly overhead. What irq- x 6(gor-g7dz/olqs the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboahpszb :;/x 8b)+ 7qn9kldyyoit 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