What is the evidence that soungz x+8clzbg;6 sz+c1iy kec4* hy:k7ud travels as a wave?

What is the evidence that so xs 14b-)d8kg +)kljhuqu.pbdund is a form of energy?

Children sometimes play with a homefk04 8eg9iiit made “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other084gift 9 keii.

When a sound wave passes from air into water, do you1of 7ln4 *f-rpl6m jbj expect the frequency or wavelength to chan j1 plj mfrb4-6o*7nlfge?

What evidence can you give that the speed of sound in a; k3jifmafh zxtovl+)y t2s7g17w 0m1ir does not depend significayjz1l+f0gw 1 s;oa27f kmtt3)7 m ihvxntly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Whap l vq(buh 3fiv*77u1y?

How will the air temperature in a room/ 9 iy xy/*kpr*g0brrq affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude o)n itc50jk(; cowt*tm+1ftv uf sounds in various fuv( o+m in )15kjtc;ctt0wft *requency ranges. (An example is a car muffler.)

Why are the frets on a pz j)io -z p9twusi436guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bri)zsoz6ij ptw i-pu43 9dge?

A noisy truck approaches you fj.80rctwo c c5u-u 60yxp3elcrom behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its souytu8xe .56o-cr0cw3c pj luc0nd 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,” whereas be8/yy/e3o)x rhui 8dwe ats can be saidx)yweuoy /i8 /eh83dr to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency 53*gvvdqj 0e yepy5 a5of the speakers were lowered, would the points D and C pyqvegdav y355e0*5 j(where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectin 8 5c-ubcny1dbg the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears5nd 8y1cb-buc ?

Consider the two waves shown in Fig. 12–31. Each wave can be thoeh3r j xs9.e xwo5:gj,ught of as a superposition of two sound waves with slightly different freques gox 95 jhe3jx.w,:rencies, 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 shiro5ueg1(/ c zjv5s mp/ft if the source and observer move in the same direction, with the sg5/jrvc 1 sp/euo(zm5ame velocity? Explain.

If a wind is blowing, will this alter the frequency of tjuv2kf ed-(qk fx9,yj. dykfd1p-g6 ,he sound heard by a person at rest with respect to the source? Is th k6k 2f ku-,y1e.dpfqgjjy x d9,d-f(ve wavelength or velocity changed?

Figure 12–32 shows various pl fmfe2*fq*nze1)4h p3ff7kzositions of a child in motion on a swing. A monitor is blowing a whistle in front of th4ken3ffmq z2epl7f* 1)fhf *ze child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout rz tqg+( e) 99bc;ufpymeflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the9p+ (b tym)cgef;zuq9 lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wat,5v rlhbd )cs7erline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is tc5 7h lbv),rsdhe 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 wavelengths in air a6os+. gu cp-nx*ryj r-oa5 v9mt 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 tuna on a foggieg:lff*m) *x91v zgey day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before thef* f:e9)vgze ixg*1lm backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The sps 0l 2,zy4f-gitr xc*elash it makes when striking the water below is heard 3.5 s later. How high is the cliff?i,*e-x24tyf s0glc zr    m

  A person, with his ea1yi7d 5ub8)6 eqyq lmyc-o2ugr to the 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 ap b5 )q2e6 guyuycmiy1-l o7dq8art. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made o; (i 2 5iluumxy,bso5rver one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the tempesyoibu 2l(5;ru,x i m5rature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 fgurk5ga :5zit:p. 6q 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 intensi .vkf: x7i+ximopj3xxb6fm :5ty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soun zpn h5c77,um:ta4rx jnp3q2ac.e )ic d level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is explode4 .rh)c3 5jpau ,7n i:7cxptanqzc2med? [Hint: Add intensities, not dB’s.]    dB

  A person standing a 5uz:oe1sfy: y 4ur)tycertain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if tz4 1:o)yetsuuy y5fr:he captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-tox xnbu;gmwg.nz/7p x*7nn3 :ssu+ko ;-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the back; 7skmu pxs7*/ xn.znxn+ ;g w3u:bnogground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conv+9n+ yiw:wt 8ehsb thqb2f8+ cersation. Use Table 12–2. Assum8+ns 2feh8bbw:yhw q9 t+c+ tie 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 aa mfm2f 4r(i4vwv.pq,n 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, wh 8yo3nky8mm/s,/9l ml8cql yp ile the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in/l98yqm8 /lc 8n yy,m3pslmko decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8nfuw,yazqaou.9 hm ir+(*2 j5ha 9:px m in front of a loudspeakapnoju wa .fh9hzi rx*5:2(q+uay,9 mer 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 differejk4: zl2qjxw(p4 rpv:nce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diffej :(2xpr4vwzpj:k4l qr by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factorzb8 affg* n7j4 will the intensity ing znf f8ajb*74crease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, bu(mi)tk 3/h)x 2 rw,-zybtgflzn w z)j/t one has twice the frequency of the other. Whal,zbf 3jxw/niz))2 )wzr-/ (t ygh mktt is the ratio of their intensities?   

  What would be the sound level (in52o 7bizwgmm,cuu + j8 dB) of a sound wave in air that corresponds to a displacement amplitude of v7b,zguj cim5 +mo8uw2ibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level 2ucn n w0yzoy3owd1z-k/,w7qto seem as loud as a 100-Hz tone that u-zqk zwc12/ w 7on3nyyw,do0has a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequ9v/i zipfb3 t/encies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.)i 3zv9tbi/fp/

  Your auditory systempkya d6i-u4 *c8dr3am can accommodate a huge range of sound levels. What is the ratio of highest to ir* 6aa dkd-48cym3uplowest 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 thgc8 4y-*(m djp dle ;k4alyhi.p++4qf /vf sof 440 Hz. The length of the vibrating portion is 32 cm, and it has hhpdlei4 4f-y 8p/+gc*ajmq( + d.tlk fv4;ysa mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible ow1sb* lst m04nvertones if the pipe is s tw14* lmsn0b
(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 ksfywkx5+g7 / pxlr9dwv+)(a54at ueblowing across the top of an empty soda bottle that is 18 cm deep,9ey)(lk5kx+r w+ taapfw 74/xdvu gs5 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 t:p-dobulos g o5rao .brw 3)/7n2oz7open-tube pipes spanning the range of huma7na)bdbt7zl u -srogr/.opo2:w3 5oon hearing (20 Hz to 20 kHz), 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 H 3wcnjn27i1 te8b/ rdkm; 2bzf)vlz +kz as its third harmonic. What will be its fundamental frequ7nb z3m 2kiwrl kc;/8nz ftevd+ b2j1)ency 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 pla6j 7h l2q-ybiz 0,mjlf .2ji7 .o7huy1gtjgfny E above middle C (330 Hzj ,bgi7 72th1.fjjn h-qg2flj y6.7uziy ol0m).
(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 orgz;np 23a q04wys 9obiban pipe that emits middle C (262 Hz) when the temperature b s93wqoizaynp4;02bis 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at kt c;ypw7)e* ks asy4020 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be thw mab fis4)9htujp b/2ug 7-c;at must be uncovered to play D above 7a tw;/spbj9-fi u2bu ) 4mgchmiddle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, anddo4j w5r r(+oo22e tbx 616 Hz, but not at any other frequencies in between.ro+j425ew(oo 2 dbx rt (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 is opec)z0wq)rve9ykqpxu n*z 3 8s 3n at both ends. It resonates at two successive harmonics of freque yx0eq8zk)9c*3)qzvnu3prs wncies 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 wpr twjqdyxa2 8w61nm-*fqz k5 :/ 3op$^{\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 2ou+ta02vi y 1h.14-m-long organ pipe at 1 v0 oyiu2+tha20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm,u ta;qs1d. (fic0u jm 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 relationship of your answer to the information in ta.t(1jus q0d icuf; m,he 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 ,0rqvfd/itrm45 ; daxj3 2 brpm9cyr+two strings, one of which is sounding 440 Hz. Ho,+b4;arm 9i5tc3/ rrp0djrfd yvm 2qxw far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262j2 i8dr9apsud aokg6c ;h(;6r 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 anotherjyl0 f4.bj7ie6a 2gt r (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estim tae64 bf 0r27gj.ilyjate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tunlh: uzv x y55(t9(rpamd6n7k ving fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is thzruxmy n7vtd (hkp5 9:6va5( le vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequenc+ops4hq1 5nr mij/h 8dy, 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 played together? [H4in drm ps8+j/ho51q hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each tr h (bz6x;v7haey to play middle C (262 Hz), but one is at 5.0°C and the other at 2 hx6az e(7hbv;5.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; ucj/.9nle x:e 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 frequenciesne :u cxl9/ej. of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one s+s k(5,;8a pxagfkrwfarq+ f7-gzx :npeaker and 3.50 m from the otheraakfr :r5q;fg w-8kz7fxa +n(gx ,s+p.
(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 vibr4ih( /ybq2: auim pr8nating at 132 Hz, but a piano tuner hears three hp(:/an i 2qrbymu4 8ibeats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air.k/*ezojoq o *0*.qam a How many beats per second will be heard?qz/*oa a*oom* jq0ek. (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certaino3c+ bek4udip1nv:a o e n/7;g fire engine’s siren is 1550 Hz when at rest. What frequency do you34 euep1vi dkon+ gca:b;7no/ 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 w8m go;hwcp) 2nhose siren emits at 1550 Hz moves at a speed of )cw mgh2;8pno 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency i vjld/(fbpsjli64:0za:(7n3hk3k x: q vjmzlf a 2000-Hz source is moving toward you at 15m:jbsj/xi 4qnj: (lv3phz l3 f( 6kk:z7da0vl m/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 wit;ztiz v1bid i.,b((zgh the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver .db;z1( ,gtiizzvib (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 uldwn8,yb 4p tz1l ,p*v:ez nv(qtrasonic sound waves at 50.0 kHz and receives them return8b 1vp*p:d,4lvz,yt nn(wz eq ed from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speedqr0,l4s * eloh of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does srlo4l,h *e0qthe bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopr +93ul9nwj lzpler 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 approache+l jnl3wur99zd the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses u 1if(sc0t8f6voc09z q(xuv heltrasound 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 flowingoztcv 0f(eh sv06 xcq8u91i (f in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves u*69cfoa 3 utjlak(,l 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 og ;/6 v/o7djkybqb:gfrequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear w/y;q j7/obg6kobg v :dho 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 movingvut(fbehuz .;:nl o ca1; pd.3 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 where the speed of sound is a.pf 0omy(1d*tjl0o6mn;w m i310 m/s (a) What is the angle the shock wave makes with the direction ofj* f00 ;pm. otow mid1yna(lm6 the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thqdhokn 3l-2 p2+czm-iin atmosphere of a planet where the speed of sound isho dz-2pm3-2 +n clqik only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikxpu;e u3 /dklq kw1/*yes the ocean. Determine the shock wave angle it plky x u;p3d1uke*/q w/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 p51kejncnkbi t4/p(nivb: ;,e q +z 9p$/theta$ 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.z3jepz/wl54 f 5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has5pefzjl 3/4 wz traveled 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 songg:5*yj zjmv1fa9r 6 und pulses downward from the bottom of the boat, and then detects erygm5jz gvf6a91*:j nchoes. 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 ther :u+z b( 7fgzod01wmtfe in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sear8m:yf /zj m l.+sdck*; ub+ ec7sf6iwer pipe symphony. It consists of many plastic pipes o 8ka6fr7+s:cmydc/f+ smz .e*;ub jlif 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 dl7j gt7nl:j :a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound l7l:lgd:7njjt evel of 1000 such mosquitoes?    dB

  What is the resultant q i5qwj idra 0neh(7ye+9,kf *sound level when an 82-dB sound and an 87-dB sound are hear0e,5wqr+7(ha *f9dki ei n yjqd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 10 a1nd n(o+o:kav1d /h2wdnr1k5 dB. What is the acoustic power output (W) of the speaker, ass1k/d +(v 2:oa whndda 1k1nnoruming it radiates equally in all directions?    W

  A stereo amplifier i h/giw(,6x/bv (zu uuas rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in wat/u i(uwz6 b /xhuag(,vts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears.lz3gst ,wd2zlhk (is- jqutw7x 13 b47:jlc 4s 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 ear at7:gbwzts34tk q -zj3du4j7 wlxs (hc il2 1s,l a distance of 30 m from a jet airplane engine?    W

  In audio and communications k al)sg j w+;7hes5w9wsystems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequencush4han q7 *wx70fziv3q o7; qy 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 xu mdqhu:5;e2xtoj1l:b8a7 0mpg - pyj sy :v1between fixed points with a fundamental frequency of 440 Hz and a mass pey7y28 upql j;0xg 1h teb:5xv1 :mdp jmas:o-ur 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)7chqmp:j1 m- a1 mrf(1 ingba vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly.m m1a()ipm1b:17hg -afjq n cr 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 aj(js*28wwdy d(mydtli,.f,rm8+ ywk tube that is open at one end and also 75 cm long. How mu mw+mk82 j,wy d,t*yd(ji lfr8wyd.(sch tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop nwb,:yb k(ix 1($\frac{1}{2}\lambda$) 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 inqi zss9)z;7vr7ep.()viue nmz- w+ d g the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the pe pi9m q7; g)(z.sv)z-r uei7 vszn+ewdrson 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 is stationawlsp5j8twl7xcm35d2s a.fk + ry. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other tra5wpw j2xlsfla5+ .8k d3cs7mtin approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachesp2:iu5s *dbu h you is 538 Hz. After it passes you, its frequency is measured as 486 Hz.uipu:hsb 5d2 * How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listen2 je vr )5i vjwdoj8y)/:an;iging to the difference in pitch of the engine noise betweei8)nr5)2:jw; iye g/ vvdajjo n 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 j.8jj:dlt s: wa beat frequency of 11 Hz. The shorter one is 2.40 m long. How lons: j8jlj t.:dwg is the other?    m

Two loudspeakers are at opposite ends of a railroad c*q,;(wokz, gk xm7mku 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 frequkw ,q* mxzgu;m(,k7koency 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 about 0.32 m/s ot/59sgly lchm u-9f4what beat frequency would you expect if 5.50-MHz ultrasound wave/-fstc59 lgu9h oy4lms were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s d bqd8m7b- wmjk3*e(vwhile 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 waj *e3qm(db87wbvk - dmve detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it)+f bzb:8qomk approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away cam)kf+ qz8:bo bn 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 from one Alpine vb8v hd6vw (1: r 1q;cds5mr f4pwwmi1cillage to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such aw 5vwd1 c8mfw;b1(6ivmph1r s c:rd4q 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 ffp 3cu wk509 a3g )gwcc;wo4scan be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves a csu 3ofg);cwwcgwkp f34095in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rog5ms oci ++iw+ds,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rodsi5o+c+ mwg+i is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-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 thr j:i4yjcit 1l-a(es ,ueshold of hearing for the human ear at a frequency of about 1000 14( : ,jtieis juacly-Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the1ysvkj m*bx-lo)h7k si k;4/n ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is1hk oms vk4s*ni -x;k7)j /bly the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat 2x9v jsvvc*4k is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h