What is the evidence that sound txui8r r)4vz:cnne i *mk/j 8e4ravels as a wave?

What is the evidence that sound is a form of 14g g;qy8qjqnr5et+0un4 jcf energy?

Children sometimes playuqor p1 u19kwfks9p44 with a homemade “telephone” by attaching a string to the bottoms of two pak1r9qp9 u41fsuw4 pkoper 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 travels from one cup to the other.

When a sound wave passes from air into water, do you expect the freq4 v:u7kzzf wg5uency or waveleng 7zzu4k wf5v:gth to change?

What evidence can you give that the spej4r m8 m4)6nc 9lvxg gtc77uqbxv(g6 led of sound in air does not depend significantly o l 4b6ng 6jc gm8mv7glurv)49 ct(x7xqn frequency?

The voice of a person who has inhaled heliumkpn 1**8-0cuh +(bmb fotjrfk sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch owt pghbg -1id9cf5*:af organ pipes?

Explain how a tube might be usedm/ yx dtu w,2r5q2tvt 0t-cko+ as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muvrt t d/0 -,qcouym22t kx5t+wffler.)

Why are the frets on a guitar (Fig. 12y g:4mm zk/. +4mki,jzqb)du+ uyhup2–30) spaced closer together as you move up thkh 4jpzgmi b/.q k,u2y +d4yz+uum:m)e fingerboard toward the bridge?

A noisy truck approaches yor;2 erl.ra * 0dox;notu from behind a building. Initially you hear it but cannot see it. When it emerrl2t*;r.nr e 0oax ;doges 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 to be due to “inz8xl9a,*klih*bh q2 -h+a thk )ex yy8terference in space,” whereas beats can be said to be due to “interference hh9x2lybykx)*a+ial *8e t,k- hh8qzin time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would thenn msc1 6*m3mr points D and C (where destructive and constructive interference occur) move far 6*rmmnc1s 3mnther apart or closer together?

Traditional methods osfe ifvbu6xub*u, ;-v+il6 o/f protecting 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 addition to the ambient noise. How could adding more noise reduce the sound levels reaching -evfbl;f ixi* us/b6u ,v+6uo the ears?

Consider the two wavj6 l:7wawkhrmj;a(ojgnux)f e.cs +9 1vrg-3es shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with oj(.cf )a+jm- h; njxvsrww9 g6: kru3ea71 glslightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same d (j nu,n mya+nqkzk6h3 l34j(direction, w,3d( 6n(khumnjalk3n4y+ zj q ith the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sounu r z+9bi:r0lqnuq8 m d*nv7qkt*sf0-d heard by a person at rest with respect to the source? Is the wavelength or vekdn0u8q s:*nql rr-m+0ftzq9u*b7 iv locity changed?

Figure 12–32 shows verel7yh;( oa3osv7 l a+3t6eoarious positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Expa avo tohr3(;l+7o6le 3y ees7lain your reasoning.

  A hiker determines the length of a lake by listening for the echo ofs;ig,jzu06 ; f nr+ivb her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lak6 0;r unv+,zj;ibsfige. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. Heymwk1s6snz -6 hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sk6 s61z-mnyw sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleipf /5rz c64kq+w,gl gngths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a schoo ma:ux zjeg3xy,jf+ *(pkh)k,l of tuna on a foggy day. Without warning, an engine backfire occur :af3h)k,m,*xgj+xu ekj (pzys 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 fw w10, qykst*jrom the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How hi1w0j,y w k*qstgh is the cliff?    m

  A person, with his ear to the groua.7fsdue6/s(q(jy vo :j b3mv nd, sees a huge stone strike the concrete pavement. A moment 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 oj(m3uva j 6 dsebqs/v.y7f:(occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance(2(ut3m;+xtmr ;ia1ypkvrx.w x0x -i l ugy/c by the “5-second rule” for estimating the distance fromuxr3 lp1a;vwr-+ ximut0(ik ctxg m2;y /(.yx a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of z56 9 q(mwukuza sound 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 sound whose intensiiapu5lppkdn fb+3c8 tv i9)19ty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound*( y.y+ob(l2r z-va jwf7p wsp level of 95 dB when fired simultaneously at a certain place, what will -y*(wpzb2+ ly.paos f(w7 jvrbe 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 four equally noisy jg- vef j8i;4lf*i8b dcet 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 84ef*f -ij8 gb;dlivc one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signd c.h5rki; z.sal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =hzr;cd5i .ks .    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in norm8 yd xde fot.s/i.z9n*al conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere center/ .izd.txod*89 nfy seed 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 ea fml *tb(vx.t.v/9uvhrdrum 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 isbau ;hoy:8bf*p dks.4 rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each a8.f; :sadbk*uy obp4hmp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registq+l:9+ grj xfoered 130 dB when placed 2.8 m in front of a loudspeaker on+:oqjr+l9 xgf the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound/p-t rh2z1 1l8tau erw level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hi a/eur18-1 tplzh2wtrnt: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wkr)kctc/v 0k xus1/ r+hat factor will the intensity increase? Increase by a factorkrxc1sc r+k/ t ku/)v0 of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice t- .qm pm00azcvhe frequency of the other. What is the ratio of their in qa.zpm0 m0c-vtensities?   

  What would be the sound level (in dB) o(j);oidsdiwo+q04c lds kt zud:qk;b 8 gd-3*f a sound wave in air that corresponds to a displacement s-o*;4q kzd(duq lid dctd0o wjig:3 k)+sb8;amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must havepiat x(z8(k(qj6yp9 ;o(l x np what sound level to seem as loud as a 100-Hz tone that hasx l ;6ptk(zyo8qj(p 9 (xina(p a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies tha .cr-hfbd81i o,lw5 ze t7g/byt an ear can detect when the sound level is 30 dBrl/fh w- t5,b1g8 iz.7dycoeb? (See Fig. 12–6.)

  Your auditory system can accommodadwfv q8 ,3p:omte a huge range of sound levels. What is the ratio of 3pm,qd wfo:v8 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. The len8 vvtn94t:ztc 26jhl hgth of the vibrating portion is 32 cm, and it has a mass of v9jth2 chv46lz:t n8 t0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the funj - ,8un(q)+paggn ght rz,c(fdamental and first three audible overtones if the pj ) ut(hn,rgfg-, cznq p+(ga8ipe 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 wou6psegq3lmz 7/7kj9 u xld you expect from blowing across the top of an empty soda bottle that is 18 cm d z/xlj7 73g6 epmsk9queep, 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 m5*f9) mrztdnspanning the range of human hearing (20 Hz to 20 kHz), what would d)5m tnm9fz*rbe 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 q .- 9uzi8qafxHz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lenaqu.- f8z9xiq gth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to(gm 4op 4 yl(ytg6lwd4 play E above middle C (330y4 4lg( p tl4my6d(owg Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emi.s g+qbqpg/9y ts middle C (262 Hz) when the+qp9gb/q y. gs temperature 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 20yq l5h 6qrgb(9 $^{\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– q;sd6as-zb+b f 3ok*z6+d irc(exj4m10 should the hole be that must be uncovered to play D abo-*i(k63 o6zr+dz q4b;fa ss +cdxjembve 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;+v; ql3oik slxta: f;, and 616 Hz, but not at any other frequencies in between. (a) Show why tlv;f3xoa+;s: l q;ik this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It re a:9ojnj +sfr8ceh2w -sonates at two successive harmonics of frequencies 275 Hz andf-r2sn:jaj9w+ec o8 h 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 pg5l0y weg1. 1 z-rc-fe)dwd fr)vzw2$^{\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 rang ,mltw:ht2e* fj2cfs5e for a 2.14-m-long organ pmlftctjwhe f ,5s*2:2ipe 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 theze 83,:caw i8kb*cac 3 twxoy1 outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of yca3cw: kz,ta ybic138*e8 woxour answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust)1hxsrfpfpj8:9h qw0 two strings, one of which is sounding 440 Hz. Ho xq)p:0 ph s18whf9fjrw far off in frequency is the other string? ±    Hz

  What is the beat frequentsn gjf 1s*,41ty3b g4rswb6w cy 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 operat / 6s6ab)swrsjes at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played ssr /saj6 6)bwsimultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded wit yftgtj2l4r,* h a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz f, *y4gjr l2tttuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tumh6dc4va uvpf78 vkp*; q rc*:ned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. W6hcqf*rmc pvakv:u *p d;7v8 4hat will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try t8dpvg3 lh5o3nc5 ;bcdo play middle C (262 Hz), but one is at 5.0°C and the other apodvb5c;hl3dc 3g8n5 t 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, a a 9f0ph9io . iu8nr+hk,-hmf+ ,qoemv6 e;lrwnd C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B anl+,u 6fomrp8q9iihv +-km,r . 0;n ahe oehw9fd 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 ap 2o4kaz 42vaxoart. A person stands 3.00 m from one speaker and 3.50 m froak4v2zo4 2 axom 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 b:q0s ,fj8 ng -trtlx4je vibrating at 132 Hz, but a piano tuner hears three bea j:f,ts8x0lqr 4 ntj-gts every 2.0 s when they are played together. (a) If one 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 wave9al0o 4k eja 9vg.k-.niwt w 5q3zofn(lengths 2.64 m and 2.76 m in air. How many beats per second wk49lqke. 9 o50n g(i3nftjaz.v ao -wwill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenjo*97u nf.p tpcy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/s tj .ponfu*7p 9
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do youo m y)h/q0 gyvb1/n (kir+zgw2 detect if a fire engine whose siren emits at 1550 Hz moves at a)wg/ /k m0+y1zrb2oyvn(iqh g 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 towanofk*+lb ht8g0 xoe k,;-wpy9rd you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly t *eb kklhgowpx8 y,;+-n90f othe same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When onet ;ahtvu+ cyd.n7*om/ is at rest and the other is moving toward the first at 15 m/s the dri;yn +ho 7mdta*/.cuvtver 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 sopu)f ahw be(qe3;9 t0mund waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the recei ) u;bmwf9q t0e(a3ephved sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the b2 xshe6+i p zs :3joot1ib1;kpat emits an ultrasonic sound wave with fz6je2 ibo11;:sp oxt +3h kpsirequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playxcy hl :1qh10ied on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10hlq1 h1 y:icx0 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood- ja;27ir/8(oed xkus j:d p0zfflow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is take:fp2 087oz(d/jdju i;xkrs ea n 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 ;dg83pxu5t ;+ g(kmkwavz 7dx ultrasonic 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 emitstefsbsyt/2i2f2 5b c- sound of frequency 570 Hz. When the wind velocity is 12 m/s ft/ sei2c-2ty5 bf2f bsrom the north, what frequency will 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 yu3r7opd ezw(oe 6a 7/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 3 z ca) wmk9tiqasz36 )ajhy .,us:su*+10 m/s (a) What is the angle the shock wave makes with the s6:.q,9a)ka cz*a yiu wshs)3+umtj z 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 :md xytn.swso )j 99*iatmosphere of a planet where the speed of sound is only about 35 m:)ixd9s*o .n j9ytswm/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave 2h mix, yob0.zghdv npfg87q6c( 9d3k angle it produccd2fgk6ip.,b yz m3vx h8 0q9g(o7ndhes
(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 ow gcod) o k3bd 6osv,4+v5y4f$/theta$ 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 abovd7 ebffsx-kba*2 ;om1u7br0egyu6+ke the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a km ab;1f xu6b7gyrebfdke+s 7u*20o- 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 sentm+anb6oxmhcxv9 *3,n )ppc 2ds 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 ) pompxn2nmt vh 3+ b*a,xc69cpulses (in fresh water)?    s

  Approximately how many oct b6pcvh7kor :2aves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipsfw6s x9lu)d9t -yn+*z7thw 9bof(tpe symphony. It consists of many plastic pipes of various lengths, which are open ont9-7pb + znols6f)fsuwt dxwhy(t*9 9 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 makn2g38z d0oob aes a sound close to the threshold of human hearing (0 dB). Wh3aod02zn8 bog at will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound y8 gojvr+k3 4dm5e* /t)rqzx glevel when an 82-dB sound and an 87-dB sound are heard simultaneously?4dz*y8govtj5 km)3rge+ rqx/    dB

  The sound level 12.0 m from a loudsp t vckqhi98q99eaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in 9tqchv kq8 i99all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outpcj.-s.h u1 nobut drops by 10 dB at 15 kHz. What is the pobj .uc-s .1onhwer output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protecb5k*+acq mlc8;k2u xltive 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 k5cl8b2xu+;aql mkc * would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gaiz v(7ds61b p-0 szyfv,cg2 hvfn, $\beta$ 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 kqic; kluanp;e3:ue/ x1. rq+* jhh;rto 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 hk:sem95 :w p afn;0y.qei2caa fundamental frequency of 4402nf q;yia 9: k5scweh am0ep.: 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 verticalp q48f2 e(o9q6wpgk jd 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 thqpf42 e o9wg68kj dp(qe 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 tuy6.uet., r y5;jjlc 5oeym8 vtbe that is open at one end and also 7m5 ylyt8c 5;.6.eyju ,ejr ovt5 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obscm; , ean*ct,m)t5ivvf z ,;;kgdr2)s blx7qcerved 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 ir,oxnkq96l +v2kmui2n 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 one source than the other. What u v,rq m 92n6i+kokx2lis the frequency of the sound?   Hz

  Two trains emit 424-Hz whistl3 )g(xag xf3r j4t+lsxes. One train is stationary. The conductor on the stationary train hears a 3.r(4ax3x tglsj3+g x f)0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yo,h zdw3ntv:8q u is 538 Hz. After it passes you, its fre,tq:hd83z v nwquency 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 of cars just by listening tuv. ) d6a76d:e owzupco the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a :6dp76a ceuv.uz w)do full 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 beat frequency of 11 Hz. Tg1 wa,4omrh 3gq:iwh/ he shorh oa,qw 1mgriwg34/ :hter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad cags8slfkbt-.,sp +2k er as 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, (s-p.gsb k+sl8k ft2,eb) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0jh99q 75uz 4vq): 1qrqfrs;m3zop iln.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were direcoqvlrz r: zmj;uqsp 7hqq 9) 43195nfited 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 j86cxe2uibk69 uvlx(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 after that wave reflects off 2xil698ku ubcx6e v(j the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approach 6nl 9(z/aikrses a moth. The pulses are approximately 70.0 ms apart, and eackrzl6(/ ais9n h 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 emitted?    m

The “alpenhorn” (Fig. 12–38) was once uso67aun o.mxk 3+0-jk qwvc9 need 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 res9k.m0 - auq e+o6cox7kn3vnwj onating. 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 compromised by the presence of stando58sy lrjw;d/o:s 9biinjoys l5wbio 8 sr;:d9/g 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,” h0 jk,1v 3pb)to5zm plinvolves 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 90-cm-lopt5o1 m)jk3hzp,v0lb ng 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 ear at a frequency abqg* n*asl*) g/ue:i+ a/5cepl*gwg of aboutaenwau*g*pil g*a:c5) gb+/ slq g /e* 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 observer on the ground hears the sonq553qtwc vwjnbd8 -- mic boom 1.5 min after the plane passes directly overq55-w3 mbvjqt8 wnd-chead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbpvg); av;ya k1oat 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