What is the evidence :mz6ke;6xpbpe gg0 m/ ay/wn ,that sound travels as a wave?

What is the evidence tha*zo1l.d7ute k t sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string tjs8pp+(8br+;/ aex6 kga aalz o 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 clez+8px(gs e+ra8 ap6;a/ljk abarly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, r6qw/ak;o8 v t2blxz;au2 c( hdo you expect the frequency or wavelength to change?qar8/o;2v(ukb6;al ztc x2hw

What evidence can you give that the speed of sound in air does not depgh h/lf ,szu 2qe4d,3lend significantly on freque/,lqe 2f 4dgshuzlh3, ncy?

The voice of a person who has inhaled helo 7(wncvq6x 3lium sounds very high-pitched. Why?

How will the air temperature in a room affect theiq qkd7cq4 ).h pitch of organ pipes?

Explain how a tube might be used as a ) .cvdcb tu1.uc jdawk360:go filter to reduce the amplitude of sounds in v6 ubc ).j.vadocgw 3:0k 1tducarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guit 4 c cx9voi d82hti6)rys(/tcmar (Fig. 12–30) spaced closer together as you move up thevht2cc m/d)tiyc 86 xr94iso( fingerboard toward the bridge?

A noisy truck approachv;k + 2xgz.c xc ;vpy7wj-q;uoes you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, iq +z;;w2 ojcv-x g;xky.cv7puts 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 “interference in space,” wheretnpkdhif ye2-f3*7f; as beats can be said to be due to “interference in time.” Explain.yh td; e3-fpff 27kin*

In Fig. 12–16, if the frequency of the speakers werenf6 f9h 7t.km).6c4am. m 8znptk gwbp lowered, would the points D and C (where destructive and constructive interference occur) move farthertknpkz 84htfwm. 79 m6 bg.6)an.pmc f apart or closer together?

Traditional methods of protecting the he- )tpghfyf9/z0 uoxq(aring 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 ambien(9pzoffq y )/guxth 0-t noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shownfo epj3kd.2hs :p, b)e in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequenci,p 3ebde. 2 hpo)kj:fses, 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 -w 48uwr:ucq hsame direction, with the same velocity? wwuc 8qhu-4r :Explain.

If a wind is blowing, will this alter the frequency of, 95 bkvllna.jx/)lfc the sound heard by a person at rest with respect to the source? Is tak/l5jc) b,f n.9lxl vhe wavelength or velocity changed?

Figure 12–32 shows various poshrpdmjr9. s g089l6 sditions 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 whlrh 8d0g6sm.jdp99 sristle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echoitnyj6e57 a n+l3hy4 c of her shout reflected by a cliff at the far end nch6nt a7l5ye+4j3 i yof the lake. She hears the echo 2.0 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. He hears tp3z(sit/xq 1 lq f/ng*he echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the oce13zntilqspxgf q(* / /an 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 wavevogk:21c8ul)dxgi az x 9 i*t3lengths 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 schlnp -tp*5g4v fool 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 4vnfpl *t5p g-elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clixyl+oke/ -mim y wq4ddg 5(k r*w;h+s2ff. The splash it makes when striking the water below is heard 3.5 s5y/ ls+wgm+d-( kqm4hkr2 i yed*;xwo later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone oc8 o,ukion; .v5b+q 5h5bhnhstrike the concrete pavement. A moment lchn5 +oh;,hv i 5konou qbb5.8ater 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 ofnw d7lyt(a;5** gr n +jiumx.b distance by the “5-second rule” for estimating the diurwyt(5;ndi*najx7bg* m .l+stance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound -m7ok9el ) pvpit y)o*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 wp4ximgb3 -c:e* td /uhhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levc(se96i t dp/sel of 95 dB when fired simultaneously at 9ts(c /dpe6isa 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 airpl9 t:gl ji1vby1ane with four equally noisy jet engines is experiencing a sound vg 11 b:iytl9jlevel bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is s,o)iv;+ogxod:bl sq6aid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the rbo o;gis+oldq:v) x,6 atio 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 spe,ogjwzos6k ( :aking in normal conversasz :,6gwo(ok jtion. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrkbora8t oq5;4hg,x1 r:mit-mum 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 * bo(ak0wul9c qx;x/x A is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate t 0bu9*c;xxl /wxa (kqohe 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 registerwm1 m j(q ;tkn(u+zzl*ed 130 dB when placed 2.8 m in front of a loudspeak ktuq z ;m(z+1m*jwn(ler on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Whwft +g3u mcr(yz; f)wm:t2 fy*at is the ratio of the amplitudes of two sounds whose levels differ by this amountfu)*t 3g ycr+zf(m;:yw2tfmw ? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whampcp+l)(vs a. be/ *ylukk(j:t factor will the intensity increase? In/s:k( uaycl ( bmklp)j.pve+*crease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, / 7y 9:b jw9vvrdre7dabut one has twice the frequency of7b r/rwdae9 yvjv79d: the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in8;mkpqg5j 7*s(c ess p air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 (sps8sm k; *qg75jepcHz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 1umlijjrg2ir c23 zg k5q-s:7wo-h1t100-Hz tone that has a 50-dBj1c25zlq t- kh-i:37 1 m ursir2joggw sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the soun)dq yt63gdjrv v:l5uuc)u) 3c d level is 30 djtdc6q))u33c rudyl vgu )5v:B? (See Fig. 12–6.)

  Your auditory system can accoms4 u4bcab8ve)y*; jzhmodate a huge range of sound levels. What is the ratio of highest to lowest intens)4vb; se * 4ujyah8czbity 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 fundazf)z/5,;qf .fj iry ry wr4k)jmental frequency of 440 Hz. The length of the vibrating portion is 32 yj .y rr)qk4 j5f /rfzwf)i,;zcm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm l3fln0h/g ;dmcti,-u long. What are the fundamental and first three audible overtones if t3c lil/0d,-n;gmu hfthe 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 lp a,6w zx5r+ngj/z7ilgmv5 -would you expect from blowing across the top of an empty sa6pnwl ,m5+vzz rxg7i/5- gljoda bottle that is 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 pipes spanning the range of cdanw6 i0l;t *tt mn*0human hearing (20 Hz to 20 kHz), **tt c0a0n 6 mwdntil;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 h+to8-yn.u y7udux hw (armonic. What will be its fundamental frequency if it is fingered at aoxwyu.ud -+th8( nu 7y length of only 60% of its original length?   Hz

  An unfingered guitar hfa7kf g- yuh,0i8,tastring is 0.73 m long and is tuned to play E above middle C (330 Hha0 87tgfku,y -hf,ia z).
(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 mpo)3vzpxu5j-*0 gfh that emits middle C (262 Hz) when the temperature is f0upmv5*o-)pgxzh 3 j21 $^{\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 9syw5py2mnj-wf( qr2at 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 Examplemgdjobbw f;q; )ch9:* 12–10 should the hole be that must be uncovered to play D above middle *mj;o:qd b 9bc w;hf)gC at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and + x j:ykufd,+g616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed+k :x d+uy,fgj 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 b0 u .nvre0*ddhw13o bmc..adh oth ends. It resonates at two successive *r .ou3me1c0nd hd.0b wd.hv aharmonics 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 6f cbx* 6p3cy v;+uyxf$^{\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 f1uz.v1bbe4 ns or a 2.14-m-long organ pv11s4be n zb.uipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm longd5cn ci 3cc(k2. It is open to the 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 relaticckcc(n 235dionship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two stj5) v ucn4o0mc8 +a5fe+qj bw3 prldz4rings, one of which is sounding 440 Hz. How far off in frequencpd4l m+oc fru40+55n) 8z3qb wcvejaj y is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and 8exnpf zv f.ym1)q k.h ,osi/9$C^＃$ (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 a21 eat,egjw+kt 23.5 kHz, while another (brand X) operates at an unknown frequency. If neitewk2 +atj1g,eher 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 produces 4 beats/s when sounded with a 350-Hz tuning fe(gpi/ 7eic .fi0+b, svkm,ekork and 9 beats/s when sounded with a 355-7f+me.s0pii egeb,k,/c i k( vHz 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 tension ia;)kq g9 8nix*+ta(6nwkv :jtlx1yx dn one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hin(w6a8)yqt nx 1k*+j9:iaxtknl xv gd;t: Recall Eq. 11–13.]    Hz

  How many beats will be heard ifj;+ a(he xw/pqd*h a9 6m5kmuf two identical flutes each try to play middle C (262 Hz), but onehdfeaq *mjpa5+; xu/h(9 6wkm is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, ck/d4ufy -x/pyw 74wxB, and 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 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?fywcd/xy-/44p7k w ux$f_A$ =    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 -oeu.vvwf.7g*j0e m vspeaker and 3.50 m f7 m.gu. v*vee0v-fow jrom 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 132anlfb4 7a.0l n Hz, but a piano tuner hears three beats e4abfl 0n7al.nvery 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 wavehpi++:y(yhd e* su8q6 fhsv8( ve:ogclengths 2.64 m and 2.76 m in air. How many beats per second will vuy hq8 fp (h8*vygh:sd 6sc+(e +ei:obe heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequ8aj- s1z,ymjw ency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency dozmj-ya8 sjw1, you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose :la njfjqzvo(9ri94x6 cw(p+siren emits at 1550 Hz moves at a speed of 32nlf4jx a9jo6i9v : rq(czp(w+ 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 at4ums(6n o ty25 se+ 07uvjyfeu 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactlyj546ufe (+eyys 0 utu 2snm7ov 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 sj.8ii;u 32s2qsvb bl bame single frequency horn. When one is at rest and the other is moving toward the first at 15 sis.b 2qbv;j l2bi83u m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives p/mamvqf 4yd ;5f:i,cthem returned from an object moving directly away fra mf;5fdq4ip, yvc :/mom 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 qq/*hg 3ax p/mAs it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat q/ hgpx/a*q 3mhear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a 4co7/ ) acdcem*v cuz9moving flat train car at a frequency of 75 Hz, and a second identical tuba played the sacu49ovmzd/c *ec)7c ame tone while 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 ultrie /zyx. xr9ivuegs;a ; c2,1ya,6 nw,xgw.mvasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries atx2n,61gvw i wegi;a.vru9s ,,/ac e;mxy. xz y 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultraso6: 3t gj4ft;6acmf4r qs8vgadnic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of -- /iw4y:qj)z yru oms7f;f zufrequency 570 Hz. When the wind velocity is 12 m/s from the north, what fr7ouz;/ :uw)mrqyz4sf if- y-jequency 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 if its sp/leahl +4iyb v-::n zqeed 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 t,a+sy1c enz+ fhe speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s+1ny+f c, zase 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 .lsn p/ 3 voj6sbu;:lnspeed of sound is only ab3n b:l/; lv spsjuno.6out 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. Determine the shock wave anglv ,abts/()sl zh5f/cue it psb v /afh5(zslcu,t /)roduces
(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 fg-cp( + oufd zq4:c4ermao4:$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and)n13y j8ltaq3d5x(u ra s2 rnw see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 kmn u3s32 jdwnralaq) x1 t8r(y5. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downwa,c4+fqk */ qle 7cqbyird from the bottom of the bo i bq4/7+l cey,fkq*qcat, 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)?    s

  Approximately how many octaves are there in t4exq2um/9qz gy,: bo phe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a kx -) hlj22a zqk8heu*sewer pipe symphony. It consists of many plastic pip)h u -zl jxh2eqk2*ak8es 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 l)r7av 8al (qke71snfbtfsy1g wt-c5914 liy person makes a sound close to the threshold of human hearing (0 dB). Wha1 7kls 1(1 ttnr8)fae ylc i75 g4sfalwybvq9-t will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB socpth9x6q0a b2y6x w,x und and an 87-dB sound are heard simultaneously? a 2wxp,c hyx6tb0 6qx9   dB

  The sound level 12.0 m from a loudspeaker, placed in the q5)q tv2,/ tvszn x(xsopen, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equa(s)tz2 , sxq/v nqt5vxlly in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops (q6lo +xml 6,2vj ix(h/redjaby 10 dB at 15 kHz. What is the power output ia r lq62ehlxvd(,i6j/ +x(jom n watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devic/jf15yk pjv6a es over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected eara1vf5 y pjkj/6 at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,1eu le;vc-d(o 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 tm6cvs7y,hafv0 vk;ij ( 7i7b puned 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 32er )p s6sn65 ul5yu4pawy 3g1i cm long between fixed points with a fundamental frequency of 440 Hz and a mass g3y u5i 6surp65pw14)l an eysper 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 viby1 c xboej.)4v,taoi9ration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop s1,ajce.9tvbox o iy4) lowly. 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 tfgyrlxg dl6(:o4y 2ucb0 + ;unhat is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundab6u:+fyl20ncd(g; o4x r yg ulmental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to d)qk0 ay7tg6-*el6glwc- zxs 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-Hz range coming from two - .k/dvoi2mny8 vnj-r 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 onevy -.2nk/ -r minov8dj source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One trainp t+ gv6d yt*vtmn5(ce2 eal8. is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequencyagv6(ttn*ey 2plm+8ev 5.cdt when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam agyswbsy2+,i6y* f7 r train whistle as it approaches you is 538 Hz. After it passes yy yiyf 2wbsa6, +*sg7rou, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you j ;4g. *em8q udqelgxi5vv5ch65:hnj:y;ok xcan estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octavecg54n 5;u;.l :kj8v*h:5vexixegdmh6oqqy j (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togeth,egkmq/(d4c rer, produce a beat frequency of 11 Hz. The short,(r/dkq m gc4eer one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a sta fjq*o 33g6m 0dbcez edl5a6hc-xa2(ktionary observer at 10 m/s as shown in Fig. dah e g 3cq6mz(*5c-3d6xo2lajbekf012–37. 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 passed him, at C?

  If the velocity of blood flow in the aorta is normally ab/4ng dfaa t0 f:e,7:8x nngwcyout 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 7y:wec:4/ t fgn,fg 0axn n8dacells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward thezgj3q/ rhpd *s)z ve;2 bat at s3r2p/j;d)hqz e *v zgspeed 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 approaches a moth. Td gn)f norh 86:dc-g4yhe 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 emitted?6)fo4hy:8grc-nd gnd    m

The “alpenhorn” (Fig. 1537)ie.c bzvtvfo d 3v2–38) 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 7d5zvi.o vcv et)3f3bmust 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 compromised by the presence rxo2h1pyrckw9 m9 8.l -x8tb lof standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Con rm2-y989o cpxwhr8 k.bl x1ltsider 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,” involves rzew*n 1n (0 .mncmv. 7nu f(gn*3difka long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked gde73 mn(rvufkfi. 0cn*n.nwz* ( 1nmwith 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-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 heaw ghzjh)6569i6 ypmrgn g;z4lring for the human ear at a frequency of about 1000 Hz6jzlm9r 6 yn zh h)igwp;g5g46 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 thk)q w4vhl4w,u e sonic boom 1.5 min after the plane passes directly overhead. v4q k)uwwhl, 4What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i ejkd8yv6 5*2s kk1atzs 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