What is the evidence that sound travels as*gqned 6,rhx2 a wave?

What is the evidence that soundvbnbpz1np3 f/nws 3f88z/u 3y is a form of energy?

Children sometimes play with a homemade “telephonebx1s92 8/y9jm3b uy fr 66jvojy ;zpxb” 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 xb2y96o rjyju9/p 8bjyxv;sf zmb1 36at 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, dczk1l.9 fi4er o you expect the frequency or wavelengizcelk.rf 194 th to change?

What evidence can you give that the speed of sound in ai6:bi thp1jgws vx:8 8zr does not depend signifs 68xjzpwvhtb1:g:i8 icantly on frequency?

The voice of a person who has inhaled helium sounds veb4lloz (,l bdc(c( )qnry high-pitched. Why?

How will the air temperatur9t ,ajvuijtb 1rp4,mx d+j t 2g-c0;aqe in a room affect the pitch of organ pipes?

Explain how a tube migh)zb 2l:,cwrhk t be used as a filter to reduce the amplitude of sounds in variouh2:lw,k)bz cr s frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fi/y1lxbw r 3poz 3vxjd5.+i(ny g. 12–30) spaced closer together as you move up the fingerbon/3 z15v(3 xdyw jrbi +pl.xyoard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it b4+(5lhc,hf lwi lq1fmc:witnk0ng j0pr9 c4/ut 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 onm45/ri9f:,+tc n(l4qcj00 lkwhglhpncf1 wi diffraction.]

Standing waves can be said to be due to “interference in space,” wherenb5y unz2d/ 8gkf: it0as beats can be said to 80zi:gkbn 2yu / fdt5nbe due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lonq 2w rso/q-(cwered, would the points D and C (where destructive and constructive interferenc 2wo/r s(qnqc-e occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areasl) ;uwguprwh9ir 25/x h70ub o 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 wi9/2xpuu7l0)h;h r wgrb5oudetects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown inuaciubz /.7+ag n;ah6 Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly dif+a6u 7cabhgn i a;/zu.ferent 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 shg):ctey.9v qx bo,qi; ift if the source and observer move in the same direction, with the sameeiv ,)q .9q;x:obtgyc velocity? Explain.

If a wind is blowing, will this alter the frequ0qzz/1yy k ;usectt wep 517,pygi1n*ency of the sound heard by a person at rest with respect to the source? I z1ztpie ;y1s yw1gkyu, /*7p cen5q0ts the wavelength or velocity changed?

Figure 12–32 shows various positions22cdlq gyj p.) of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the gro qpl.jcgy)d 22und. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her vil0s7g 2uby: shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimateyu2 i7vbs0:l g the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ) o)ygb78d xliship just below the waterline. He hears the echo of the sound reflected from the ocean floor dirxy7i) ) 8glbdoectly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveloxzqcp-6z +9sengths 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 schb6 rtvksv ow. d5h.7:oool of tuna on a foggy day. Without warning, an bh6.kdoo 7:v.v r5stwengine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splapp;dgn(1annqnn i309 sh it makes when striking the water below is heard 3.5 s later. How high is the cl;qn a i pn0(n9nn1pdg3iff?    m

  A person, with his ear to tcs6i lmjn abb 02+0wu+he ground, 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 th0uws+ 0+ni jabb ml2c6e impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent erro1 iqz 8:4 psrr;:j)pcwuq(wnwr made over one mile of distance by the “5-second rule” for estimating the distance from a l (z: pr)8iwrwc q;sjqpnu1w:4ightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the,a jmc- ;4ep:w/d9wscb*mu c y pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity+eoa*jf5wrdv8rpl 9y ; ;9i pl is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulhppz+d 99 b2vutaneously at a certain place, what will be the sound level if only one is exploded? [Hi92dv+9uhbz ppnt: Add intensities, not dB’s.]    dB

  A person standing a certain distadh orq 0.1od(unce from an airplane with four equally noisy jet engines is experiencing .o0u(d rq d1oha sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio ofi8ki ;0-il4do/sc i gy 58 dB, whereas for -8l;iys 4cok/g iiid0 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 =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person s7qj00oqnoxk8 kb rmp:4f( xj 7peaking in normal conversation. Use Table 12–2. Assume the sound spreads xj 4(0pr kk7fm:ox8jb7q0qn oroughly 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 aqc o-tpg2qimrf p244/o 64fjrrea is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more mo0faw fs lp03b oyu)7r7dest 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 loudsu l073ro)w7apf f0syb peaker 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 whkvlr-jsv v;6 +en placed 2.8 m in front of a lvsv+ rvk6 -jl;oudspeaker 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 s kmv8s+)f)cnyn +: sljound level of 2.0 dB. What is the ratio of the amplitudemn)jnvyfk l+ ssc8: )+s of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is triple u /q1;iz1goozd, (a) by what factor will the intensity increase? Increaseqzou;go1/ 1z i by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal s ai9-)7otm+yctnx, tdisplacement amplitudes, but one has twice the frequency of the other. What is the ratio-cany,st) +mx t 79oti of their intensities?   

  What would be the sound level (in dB) of a soundg3:t1, np- fv 2ixh2r i,osopc wave in air that corresponds to a displacement amplitude of p1oorn, tfp:sc-vx 2i ,2ig3hvibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem *o*6( yenbsy jas loud as a 100-Hz tone that has a 50-dB soune6* (yyn* jobsd level? (See Fig. 12–6.)    dB

What are the lowest and 2f cbwy6-5n4gllu1d g highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.5lg2 1by6fwc-n gdu4l)

  Your auditory system can accommodate a huge range of sound levels.hi ,mpeyj j59-h/xr3 h What is the ratio i eph,ym5jj h/h-9xr3of 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 ofknn)4q-re b yj,bi lzt..psd7e76 t/v 440 Hz. The length of the vibrating portion is j4nysdiv6qbprk./)bz -t ne 77el, t.32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 c4 yzept4e6r 4fpa9ww7 m long. What are the fundamental and first three audible overtones if the pipe fe97azp446w4 wtry epis
(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 4 ogxixj2wis.ekh(2u* 1/gdy the top of an empty soda bottle toxg yu g2(./hw4k i*1djs ie2xhat 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 h n56pfya,nx(;sp yn5 ouman hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requir65n fn ;x( npysypa5o,ed? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has t)k1o rdb/t;-z6axcx a frequency of 540 Hz as its third harmonic. What will be its fundamental frequexdo6x-abc )rz1t; tk/ ncy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abjk4 jku 7fl54eove middle C (3374uk kj5jfe4l 0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe tctr+j4nypeu,.pew6l*yl: (e12l s ft hat emits middle C (262 Hz) when the temperatu1 e ef.p *lls4t w+ycntj6u,pye:2(rlre 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 at3jjf wvqj7po ., ae9oq:rj,,s 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece oftvcw4)/ d*bvx- /vbj f 3s2fcv the flute in Example 12–10 should the hole be that must be uncovered to play D above middbtj2/*fws -b4v cxvdv )3/c fvle 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, :iw) hjdwk +zts,n :;z440 Hz, and 616 Hz, but not at any other fr zwns k ,)th::+dijzw;equencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long isg) g-qvb dw((b open at both ends. It resonates at two successive harmonics of frequencies)-b vwd q(g(gb 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 omg;-i(b0 m -vp44 tiv7rrnaf$^{\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.83x*b d: 4ng3x/hm a pmexzkf-long organ px3 *xnpbedm3gkm84 h x.faz/: ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm ljob k66kf-0 swq+zrj 0ong. 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 relationship of your answer to the information in the gk+0sqjzf6bj 0w6rko -raph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryia ty(abxi)v1 b)at9q:ng to adjust two strings, one of which is sounding 440 Hz. How aqbv b( )axy9t:1a)tifar off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (:y y.(ygi/m+y1ge 1t h.qed io262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another0dfd /xe0 - oruu9u0hk (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 occu0 e/dr-0uo d90kfuhx urs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s wh6nzlj4ig 2f;m b2-p scen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational freque2fb-cjn; 2s 4mlzpig6 ncy of the string? Explain your reasoning.    Hz

  Two violin strings arez; shueu9bh+g,gv*n91 x b d:g tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playdhu:hs,b*;gue1 +g9vg 9 nxz bed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle C cjjgp+c 5h6;y i+hjv8(262 Hz)j5hjv+8ygj; +ichc6 p, but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fn ru*t - jv9wn0l,ol id+n.v6oork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard.l6 t +nl -rnnj.,0*ov ivwoud9 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 oneg3.zp,h 9f7rvz )ffmy speaker and 3.50 m from the othe9zpvf ),zf7 y .rgm3hfr.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, v5, l9 mwypsg/9n,gngm i*c o;but a piano tuner hears three beats every 2.0 s when they are pl9g mvgo5;ps ln/ym*cng w ,i,9ayed 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 wavelengths 2.6fu9c2u esocyr0:g+g8yt4, sy4 m and 2.76 m in air. How many beats per s y ,2uot:y rfegc s4s8y9cug+0econd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cewof s q(1vqzf 9.+u4do*z*e nvrtain fire engine’s siren is 1550 Hz when at rest. What frequency dofs*v 1f.9ue 4 zvdnq+(oo*wzq 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 sc4enbt) r8.8pdggawavn96 ;riren emits at 1550 Hz moves at a speed of 32 m/s 8dwt9 ev) gn8g. cn6r pa;b4ra
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if . *0,jeh,penl3o fhqz a 2000-Hz source is moving toward you at 15 m heq* j3lz,nh.pfeo ,0/s versus you moving toward it at 15 m/s 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 equipped with the s 1,lx9f yyz 40xyyie151cj wzzame 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 frequency of 5.5 Hz. What is the frequency the horns emit? fzxy1 5xy9,yle1zyz1wci4 0j Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz aew )-na-ms1 ki)zx ap8nd receives them returned from an object moving directlnasea-)- xz)1m i kpw8y away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an rfel,0yq8j 7wba9m -lultrasonic sound wave with frequency 30.0 kref0 waql- ,978ylmjbHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopplu/01ezlrsn6z0il d 8 ver experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station a vz1u0 8edlz6s /0rlnit a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to6 xjg.-o s-mcnwe;k)y+2 iqtw measure blood-flow speeds. Suppose the device emits g .e wns tq6i-jo-wc+;2mykx) 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 at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves o3ym9 ,sjb d+miqb+g7nf frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency a6e9c yonlt*,la+jnt / 0k 8ti570 Hz. When the wind velocity is 12 m/s from the nor 8n n+to*aelayt,0itj klc9/6th, 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 if -slmd0+(h mr*bss7x1 *,v5vlwgxez k 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 a:xpitgbwux h(d5gho, d 6 1i*h6 r(-dpt Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the aih ptrd6,5(gh:gd (p*b 1d6-wiuhxxo irplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of ap7 ci d(ex+h4ze;/4yp2dd ydf planet where the speed of sound is only abzde yh4idyxdf( +ed7c /p42 p;out 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. Determiny8+j)g x7 x1c v ywcyhwaok(75e the shock wave angle it pyvj)7h8 1cyyxwg w5 k7c(ao+ xroduces
(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 z,b 2doz;ijed3vtn; 0$/theta$ 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 zk2t cf7.vhj,8vp+zq 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 km. See Fig. 12–34. fc+pz8q kv.7 v j2hzt,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 do/ ef sn5zst.s1wnward 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 timezfns/15set . s between pulses (in fresh water)?    s

  Approximately how many octaves are thez;;,vgnxakgm4. h q *j1y0dh l)vdl7ere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewnl nde9xf2hpc, 8y4p )er pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. ehp9n)l2p8c x, fn 4yd
(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 thel1f8og)bur+ c *rm+xe threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes? 8rmcure+l+1gb ) o x*f   dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are h 4 h8*3gomg id7ood:ozeard simultaneom8o7g3: i o4dozgdoh*usly?    dB

  The sound level 12.0 m from a loudspeaker, placed8 ika zac8;n1x+rk.;aybo qg; in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in azx a+nq;o;rb8c8yikga ; 1.kall directions?    W

  A stereo amplifier is rated at 150 W o*enm6((a0 msjqr bx 7eutput at 1000 Hz. The power output drops by 10 dB at 15 kHz 60n(rqa emsex*m bj(7. What is the power output in watts at 15 kHz?    dB

  Workers around jet ai1,j j6sg2vd;wmwz5 xt rcraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the wtgs v 2m6 1;wjxjdz5,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 communications systems, the ga3+f,cb fn nt3p5)n9wy 6in plbin, $\beta$ 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 frequency/ ;t8 ,mqfvyt6bnm th5 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 fixeej. ; ezo49*y*b hvescd points with a fundamental frequency of 440 Hz and a mass per unit leno 9*bz; 4ee*vse cyhj.gth 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 inthb2 3z4ac*ri ao vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it*hizara 42bc 3 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 thzah j3 l19r93jaku:fgt th2*tat 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 fundamental mode) with the third har321h af3gz9 r*t ul:htkjt9jamonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate 6uc73z .xk* upv z8au;e hmkr*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 sources./p+u f*xcckv idl5h; 4ee zg3+ The sound is uh3kplze4;xf g/+*d c vc+i5eloudest 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 is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train kiim-zb 9:1ut :xx(pyis stationary. The conductor on the stationary train hears a 3.0-Hz -9i(zit:bxpu :x1 ymkbeat 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 2) qph 0j)afcyyou is 538 Hz. After it passc )pyf20 j)qahes 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 of cars just by listening to the j hta/(ffyn10phfh2 ;f 0dqq 5difference in pitch of the engine noise between approaching and receding cars. Supd5fffthp/0q;q j0n f ah(1 h2ypose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce ywm8a *7x7rc +1ohpg pa beat frequency of 11 Hz. The shorter one o 7p+c apg w8*1mr7hxyis 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad cxq.vz5kc v9k;ar 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, (b) he is between the speakers, at B, and (c) he hears the speakers after they hkkx59.qcv ;zvave passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m8wbo 8es/ytmh.aq , x2/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that tha,xq8 8mt/.osh2 w eybe 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 fly kc9 n2i3vgr p1wj8u6eing toward the bat at speed 5 1ji n83 u6wkc2e9prvgm/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 pulsesi1ev7lrew9t(o k1v 8 t as it approaches 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 dett91(t1okv7lew rve8i ected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was x :n;wqp)pa3 ponce 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 play n:3aqxp w);pped as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromis7za shx-v7c 3kb)jn1f ed by the presence of standing waves, which can cause acoustic “dead spots” at the locations of thvnza 7hs -1cb)7j f3xke 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,” involves a lor:rrdkk; ldtn/;g8j :ale5l4ng, 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 bl:l:8ddk r4lg; rk; e j/na5tre 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 hearing for the hu qwzw/9 *,dnsxman ear at a frequency of about 1000 /qn*,ww 9xdszHz 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 obsetu* hdrw:y d 86jh6t-frver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? rtw:y*6fddhuj 6t 8-h   $ \times10^{4 }$ m

  The wake of a speedboat is 1bzcag czb5o x76sy.3 45 $^{\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