What is the evidence thatkg bt8h/b/5(oj f+ :nxwdk/ vb sound travels as a wave?

What is the evidence that sound is a form of ene4dsajro0ub3* psx h4au) tt:(rgy?

Children sometimes play with a homew l,q6nwjh 3u/+gru i8made “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearqn6 3irhjwlu,8w u+/ gly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or wa 2hh *,*pj2vrfdvvhf7 *a-wsj velength t v-*rv,h*jv27w pdhsa2fj* fho change?

What evidence can you give that the speed of sound in ai cw tmqm* 2rehli(/w4(r does not depend significantly on fhw2t/c(lq*r (mie4m w requency?

The voice of a person who has inhaled helium sounds very hi9zxtu) 6ybo 9 ehmi/8igh-pitched. Why?

How will the air temperature in a room affec eh;stx 6gi(bd-fz):f48wacct the pitch of organ pipes?

Explain how a tube might be used as a filter czdds0cp l)4t;wd)s ) u5bk c.to reduce the amplitude of sounds in variouldzpc5s c bu4.dcdk)st 0w);)s frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spacedshih1 n8m 6pqlk42pdpg;sg) 5 closer together as you move up the fingerboard toward the bridgeidm6hk )n18p5 ;lgpg 2pq h4ss?

A noisy truck approachwc) zyo4r:0w; ip-tiyad8br7 es you from behind a building. Initially you hear it but cannot see it.droi b;acrp 7t:iw4w0y 8zy) - When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfekenqujt gk,3i. j4e88 fhnm-/ rence in space,” whereas beats can be said to be due to “interferencen3qh8gj/k e8mj 4.nitufe -k, in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowere(z/ob *;awu ,esvk7pyd, would the points D and C (where destructive and constructive interference occur) move farthekv*u;7be(py, awos z/ r apart or closer together?

Traditional methods of protecting the hearing of people who work in areas witez0 jus2gv *xpp8).b xh very high noise levels have consisted mainly of efforts to block or reduce noise l*ju2xsevgpp ) 8b0x.z evels. 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 the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thouggcbk c5alj(2 +ht of as a superposition of two sound waves with slightly different frc+kc jgba 2(l5equencies, 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 anxxm4q.v5 sz+d)c hu/ yv3eal5d observer move in the same direction, withs l5v a.)4d+mche u /3xvzqx5y the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a persut;hb,r )tl4aa- ( gpfon at rest with respect to the source? Is the wavelength or velocity cha(bg;p a l)-tfh,4u rtanged?

Figure 12–32 shows various positions of a child in mo t;chhgivymx70d*v/-m 3xg/ ution on a swing. A monitor is blowing a whistle in front of the child onh;3/xi0 */tgm u7vhv xgmdy-c the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the i9 l7ogy v+tamhz3rl160e7xe length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s aftee39m7ol +rixy va67 h0e 1glztr shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belo yf7/9u g5pzndm,r(otn.o 0kgw the waterline. He 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 sound in seawater is 1560 m/s (Table 12–1) and does not vkf9uno.y/rd 5g7,p tngm( zo 0ary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavecnd8xz2uf30i6 i ml9i,zyk 8 zlengths 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 school of t,81jk/a;vl x*aivrq sz8zy* muna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a)i s ,* r1jlv/ mxz*;azqv88aky by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splashcgx d.l) d-+wv it makes when striking the water below is heard 3- vlxcw )g+.dd.5 s later. How high is the cliff?    m

  A person, with his ea-5tg5i,xv8kq c z 5 owr;lqrd-r to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds 5qkqrgwv,ld8t oix-r c -;55 zare heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-j 8w2qwx+ok77- pmfye u7x *besecond rule” for estimating the distance from a lightning strike if the temperature is (a) 30 *ue2 x8p + keoy77wwf-qxj b7m$^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of ay 8wdt9g 26hyk 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 intensit-/( .o y)iiz/rqjj68k a,nxviwg 4 ttyy is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously 5o3 cxd*yev2,(es/vgxul1r c at a certain place, what will be the s,y ugx5dse (c2lv c1/rex*v3 oound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wmij 201ip9nm3mdtf7pbqq;- tith four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What soui2m ; -7mbqp30tqn9ifj1 ptdmnd 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-n-jlfi5 r ek0y;oise 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? 585 fl 0eij;k-ry dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakhw,hoam1rrcv l-k *-gzqw9+j at: nnh-/c8v* ing in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouthhv +9 -wozk :h8m-rhnja *c/agvq,wtn1lc*r - . $\approx$    $ \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 strike eq 0k q.1amc3ofyw1(qs an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while tyr.x uum0 gm;1 ar ry5:w7x(dkhe more modest amplifier B is rated at 40 W. (a) Estimate the sound level in deci0w d ;y.rumuka(71mxxy rg r5:bels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front p. f90y+ 1wjvqzmo9rv of a loudspeaker onw1 qy9.f0jp+ ro9vvzm 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:j(i6d*b.nom e gwv bjl0,i-f 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by fdi06 w,:-(o jnv b.jb imlge*this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave5y k4ia/9s-d rsjn zc4 is tripled, (a) by what factor will the intensity increase? Increase by a facto4sja5/ c k rnsi4zy-9dr of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hqq0jw*-re7.6cd vga uii, h l*as twice the frequency of the ovj7.c iwq,u0d ihr6a*l* egq- ther. What is the ratio of their intensities?   

  What would be the sound level1p0zz6 :cdn wqi* yva. (in dB) of a sound wave in air that corresponds to a displacement ac:d qa.ynw 0z6i*vz1p mplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sou5- ;s/out(8i dcvr mbxl3mu3ynd level to seem as loud as a 100-Hz tone that has a 50-dB sound sm5;v/- ml8dbuir 3uc3 ( yxotlevel? (See Fig. 12–6.)    dB

What are the lowest and highest frequeu3 3 2x stvywd0il wzd3vr/::jncies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6lxw /2z:33si u0vrtj vydd:w 3.)

  Your auditory system can accommodate a huge range of sound lsqo m1)n(el1x .xv, aoevels. What is the ratio of highest to lowest inom,x)(enqaxl.v 1o1 stensity 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 frequenrd0pc t5,y0ph r1g;ipcy of 440 Hz. The length of the vibrating po,ir1p;h pp0tc 0ydr5grtion is 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 csnznq/7s5wls.*e:oq ,e l p)w m long. What are the fundamental and first three audible overtones 5no*l7ew q qnw) .psze/,ssl: if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would -iar +u4egvg 2you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed t g-g i2arvue+4ube?    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 spannin2 pxai1zvzobj9* n,)vg the range of human hearing (20 Hz to 20 kHz), what would be the range of the lezza21, ionp*j9bv)xv ngths 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 harmonic7zqga/xrf//x+qr,3j bpq: r e- h cgd.. What will be its fundamental frequa- hr7b .q3gx z:je /xq+drrcfg, p//qency 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 playnqv4 ; go;p6tt/maq ,d E above middle C (33;;/an,t6vmp gdo qt 4q0 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 ofyy 51bva2*peqgt 5qv1 an open organ pipe that emits middle C (262 Hz) when the temper5b2p1 tqavg*yqy5ev1 ature 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 l sj:p7wqc n()h2g.ccat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of /28w7l3vejov x-cbrfthe flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz? j8evcxvl-f o3 7r/2wb   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 r8* o.xm((nlha9 w0 mbgpu m*pcan resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is ln9pm8m(w0upbr (. *amgox*h 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 lolj)t5a) ev+ efng is open at both ends. It resonates at two successive harmonics of frequeae+f)5t) evjl ncies 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 u,e n1sj: niyjsvt ;68$^{\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.r.gr.qylm1 qsi4y2 9x 14-m-long organ p2xsgy1i m.r ql9.qy4ripe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is a 88)yfoostnr7/wv8piq yo)b1 pproximately 2.5 cm long. 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 relit)v oyo/q)wyn88psb8 1fro 7ationship 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 q21/fxgwq1,c,da z di-qaj3i strings, one of which is sounding 44,c/agajq -dzi, 1 qix2d 3fq1w0 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (2;w owt,z041 bhdsuxvv h/ x8-j62 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 another (broa3hx ux0yk, s u6y8/zand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separyy0 hask/x86 oxu3 zu,ately, 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 tuninow yvj5/ 7sqkx4nbh3m o01jf2g fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the str o nx4w1f2o vh5s0b7mk3q/jy jing? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one y/vvcjjgbrbf h.*w /u68m - pq. j3is4string is then decreased by 2.0%. What will be the beat frequency heard when the two strings arey/c* gv/f4wsb.h.mjj p- 8bj6rquv i3 played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fl0hw79l vf9o*cr impy8 tu-;y yutes each try to play middle C (262 Hz), but one is at 5.0°C and 0cvymfo-tw r*7p y9;lh 9yi8uthe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and Co)ud3 4g0pz*z9uha xn . 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 gp hx z4zoan 0*du3u)9beat 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 o3mj;wg b w:b2s ywwl3ded9c; )ne speaker and 3.50 9y3sgjwdl w 2me:w;)b;dc w3b m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner4 f,hut (fzi(- -qfiih hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequ4 i f-quizif h,ht((-fency 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 wav; y,;/i 31)gsdggellp jqrv g2elengths 2.64 m and 2.76 m in air. How many beats per sec,2 pil gv3r;;g/g slgdy1ej) qond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz buepb054p m( jwhen at rest. What frequency do yobj5(4pmpeu 0b u detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you d s er)lvz.x*pre o/m*4etect if a fire engine whose siren e4)e/ lzv. r* omsx*repmits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hzv5ii(xw2nb *a7 3crt 9f.xsun source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they clo t27ar ux9nn3wi 5 f.b*xc(isvse? $f'_{source\,movine}$    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 cuzs:un/ nn s3p 650gione is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat z n6s0csu u ign/p5:3nfrequency 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 andl(( n81ltkkuy receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequeluyk1n8lk(( tncy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flie y(uw--bi )yzws, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in t)b wy(z-yiwu- he reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubn7gw 5idc9t )fh x5c7ba 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 nthd7i 5fcx9bwg57 c)the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound nadqz z*n72wz j*w* 9m0pmqm2 waves to measure blood-flow speeds. Suppose the device emits sound at *7 20jnm2 az9dwmzqmq*wnp* z3.5 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 of frequbm1)* w8yh3j(x11 c m bmgrgdlency $2.25 \times10^{ 6}$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 su )(/dzbeu1p vc7h;r gound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, h;gz 1 dvr(7) uubcpe/
(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 objecepy / dhlxy); 0z;: gb.wkoh by4lg-.tt moving on land 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 w(.+a4tybnbyg4p9 o 5o+mitbkhere the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s m otig (y ya b5+4+pokbt4m.nb9otion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of soun*nb jl u 7;0,v2vdkaxqo:ub *h kp(s;dd is only about 35 m/s *uo 2b v7hvld :n ks;(ud;b0xk,*pa qj
(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 strikumsy+3rxmr(-r d: m4d es the ocean. Determine the shock wave angle it producesyrum rs4 rx3+dm(d:- m
(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 y;5u 7 :9. vucvwjqr1shso oim9hj/a($/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a planeh(lq zf4zq f+9tkn/;q 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 trave/q+(z;qf 4 t nzhfqkl9led a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pu3nz 3,pyq2u dfm:zb -ulses downward from the bottomfnubuz3 ,yz :d2 pq3-m of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many o q+bah zgk;e,,ctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe 52m y zxrpdc,,6qbu:psymphony. It consists of many plastic pipes of various lengths, which are open on both endu ,qcp 2brd:,m5 zy6xps.
(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 cinp.eb ,9;c mh :/8,eqp zxthulose to the threshold of human hearing (0 dB). What will bb,m9e :pc t/8xqhz .pih;e ,une the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82 ramc3 v2fi 7q8jb+g6y-dB sound and an 87-dB sound are heard simultane avrqi2m7+3 f6c8j ybgously?    dB

  The sound level 12.0fc5w4(hucj64* uscae m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direu*(ujsc56hfw 4 ccae4ctions?    W

  A stereo amplifier is raxygn.c oy ig 3s6,8c*m .uae+vted at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at c 8vmecg* +sgoua.in.y,y3 6x15 kHz?    dB

  Workers around jet aircraft typically wear pro92 2 nm4qnkn//md sszftective devices over their ears. Assume that the soz229/ qfmks sdm nn/n4und 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 ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicok*fu 41eo qqtz(tpy*vvxw q8,6) w/iations systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin ismmmzcp2 zvx3uh ci)6he0r cz/5 np2e 50tpb.2 tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamental p hhpc;)8:f.;ztrwt;u7 zny y ujx6cs6+iba 6frequency of 440;p zjsy).6 ;rcut8p6hbx:zwchf 7un; 6+ tyai 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 vibrapm4vf zf*k m)buoowco/1 6)y2 tion above a vertical open tube filled with water (Fig. 12–35). The w )op) 4k2bzvf*uwcofo/y 6m1mater level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube 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 mj(w jlzj:lv:82xte,string of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonaz(8w:mej lvjxt:2 l,jnce (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lov1d0:kc bpzhi:tazcvt:s2 k+c)vy 7.op ($\frac{1}{2}\lambda$) 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 y g8gcj60nb8fxi48wfpd6n 7b+d 7pr uuk:c0u-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 is the frequen8 ub p6i: uyn80jfck d+f6px7b7g0 ruw d8ncg4cy of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on th -2icbxi/kju 7e stationary train hears a 3.0-Hz beat frequency when the other train approaches.u/ x-bi2i jck7 What is the speed of the moving train?   m/s

  The frequency of a st)y 1jtph v 5nfvsj.m,-eam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast -vfsn)t 1,5jh jym.vpwas the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lis ;1eg33 sfurq7sm1bgj tening to the difference in pitch of sgm3b1r;sfueq7 g31jthe engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beao,x 7xjqnzveog /h2c (5) xc+pt frequency of 11 Hz. The shorter one is 2.40 m long. How long is oo/ c 5v,xnjxzch+g 2px )q7(ethe other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past:+ x -o-sqa7hne/*qcsw /( kigbtsi(s a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what issbxc-7/n-:*(/ eiq wahs it+(gskso q 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 aor8vv u 0cinh9p9ta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wavepi0chnv9vu 98s were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 yse lk6y/(j-mq vq /nft. w;a1m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave re aj nq;fekq1v/- tw6(y. /smylflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it appronc: q9555mdxt 6 digfdaches a moth. The pulses are approximately 70.0 ms apart, and each is abnmdi5g6:d 9f qc5xd5tout 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 used to send signals fromkgh qr*xzv7/ 6o a(r74;qyxai 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 y4k7xg/za7 orrq xa(iq;v *6ha 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 liwl2p) fur+ca 9ocmm u,/c:xof*dtl;2stening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of 9xmo/ :flc*mcwc2ur2)l+,dtpf a ;outhe 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 lta.5 to36m kh )zs9spg)g6k peong, 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 emit66 hst k.pekg3zma)5t9 gpo) s 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 human eft l hm:bn8.a0ar at a frequency of about 1000 Hz a8fmht .l:b0nis $I_0$ = $1 \times10^{12 } W / m^2$ 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 thl o73aed-c y1fe,/0 6jpr ockne sonic boom 1.5 min after the plane passes direclorpde a6 -jy7k,/3cf c1on0 etly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ius hw )j3og 0rus75ou0 zv5b.ws 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