What is the evidence that sound travels as a:j oh 3nse5zf+ wave?

What is the evidencebuscao ) yz9c0:fh 5)e+i+uwoq zq-6t that sound is a form of energy?

Children sometimes play with a homemade “telepht0s cx1ny +mvg*2c cn0vdxfu4 +8 q1jsone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one 1x+cfm004vcj 2+n8xv*gtsd suy 1 cnqcup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you exb6eh5 +xe21v8 osiiuopect the frequency or wavelength to che6i+2s eb5 oxihuo8v1ange?

What evidence can you give that typ+ fp82gg*vthe speed of sound in air does not depend significantl2g p*ty8gpvf+ y on frequency?

The voice of a person who has inhaled helium s.q uoi3 2*zxohounds very high-pitched. Why?

How will the air temperature in a room affect the pitch o(//j j*h8xjo0g8 trcicg g :nyf organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of srtnoqi(86d .. srs *zjounds in various fris(z* sr.8q6djnto .requency ranges. (An example is a car muffler.)

Why are the frets on a guitch. s5qs(mr/lz+e c v7o kvm)(ar (Fig. 12–30) spaced closer together as you move up the fm/ vs c 7+5l )h(ozqekvcs(.mringerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear,fju2,;fb7lo -v b tu oe5myw/ it but 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 Sectiobvjt b5yu/l,fwf;72 eou o,m- n 11–15 on diffraction.]

Standing waves can be said to)ylzl g+ wg-)w be due to “interference in space,” whereas beats can be said to be due to “interfewg w)+-gzy)ll rence in time.” Explain.

In Fig. 12–16, if the fre/ 98 ;ccg7yx vpjeia,mquency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer t7c j axycm89i;pev ,g/ogether?

Traditional methods of protecting the hearing of people who work in areas witho r y**fn:b2zea1hxjg-1ff.i 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 devic *f fg*h1:r1fyaixb oej.-zn2e 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 shopbhq imxrks 3qr7q1;n-)su28 wn in Fig. 12–31. Each wave can be thought of as a superposition s)h1 -ki; bm rqr2n7x3p8qsuqof two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sou:cryj+ 2zp 5vslb1r9 lrce and observer move in the same direction, with the same velocity? Expr:5 l19r+jlcs yvb z2plain.

If a wind is blowing, will thdx blnj+,(d0ew t)a1iis alter the frequency of the sound heard by a person at rest with respect to the sourc(jxd) dlei1 +nb ,t0awe? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitorur *5f8j4v3.gn 9awmkj -wty(h aj- pg is blowing a whistle in front of the child on the 8w-*v(5hjry3ju g4anjag t f-p.w9 k mground. 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 bym*1 5lvjhqcc;g3 0sdy listening for the echo of her shout reflected by a cliff at the far end of the01gjh*d sc;m 5vlcyq 3 lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline.* ivi i qyt0b -osqglr-x9*)xv6ao9;l He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the )q -b-t*xo;os9vglai6 qi xri*vy l90ocean 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 at 20 . g i gb/4y,-r)svhtir$^{\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 juum x6jaul1(;xaowm 6pbxy .5: st above a school of tuna on a foggy day. Without warning, an engine backfire la 16;x5.mwam oyj uxx6ub(p :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 sp63 v3 jzaudky.lash it makes when striking the water below is heard 3.5 s late3 a3d.kz yvuj6r. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strikg r09g+)1m s7lhxjdxj xyl5cl9g99qre the concrete pavement. A moment later two sounds are heard from the impact: one tram+hgrx yc9xl0gj99s95g )x qd rjll17vels 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 d k,cj) 2o0sgktistance by the “5-second rule” for estimating the distance f) s,k2g c0ktjorom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain le/((jt;lw:devjz3tafm /t xc /vel 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 intensyw:3 . ,bei*w sjfu/izity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lotfk mo2/kcj qlckx87 0fm* kv;/ 1)haevel of 95 dB when fired simultaneously at a certain place, what will be the sound level if only ok k0am ; of xfv7t*8cm)hjkqkc1 ol/2/ne is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from zlf 7-ka )ucy mz0tyct6h;m/ -an airplane with four equally noisy jet engines is experiencing a sound levealzfc0 tyct u y;) 7-km-/m6zhl 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 of 58 dB, whereas for h0 oid9f8tev5v u,e)zj(oq )5pf 5luwa CD player it is 95 dB. What is the ratio of intensities of the signal and the b))uq5 ojep t9v, vodf05z 58(fh eiuwlackground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power drwc k,e,4 jzqw0s78e output of sound from a person speaking in normal conversation. Use Table 12–2. Assume t,0 e zdcjw4,w8ek7sr qhe sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum wh4h1 * r/udv+0jh 6ihl-qoioieose 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 the more modes.j yod.j.yb/1 m2s jtuis7k u3t amplifier B is rated at 40 W. (a) E.u1i .djbym2t u js.7/oksj y3stimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB met zv(8.zi u 5kwi qyn0-hrpd6i;er registered 130 dB when placed 2.8 m in front of a loudspeaker on the stq0wykd8ii n6r hziv z- .u(;p5age.
(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 d/e d - qd)4pmnz -o12jg+bktqjetect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hin4qd)dpz- j/bmk qt1+ -ngjeo 2t: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is mp9/)z fh,fh7so. dgh.c ozn4tripled, (a) by what factor will the intensity increase? Increase by a foz4)p.sgf9,mh h odh cn.7 z/factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twivxt*ip3g20 2 x o kshruw2ci7-ce the frequency of the other. What is the ratio of their intenswt0 c*op2hkx27s 2ruxi-3gviities?   

  What would be the sound level (in dB7i2. jan g r-(1(fbokkt:pfpz) of a sound wave in air that corresponds to a displabrt 2k(zf7i1ga jpo -:fnk.( pcement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must 9cf6 b0nr3gbtfifzr *l n* -h0have what sound level to seem as loud as a 100-Hz tone that has a rnf 9*3-bc*i f 0gf0btlh6nz r50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencie6 .e/ 2pfutg0fhwumy 4 z(x9rzs that an ear can detect when the sound level is 30 dB? (See Fig. 1 uyz/0fz( 9hxepwf4r 6u.2mg t2–6.)

  Your auditory system can accommodate a huge range of sound levels. What is tha 9ic,pgn m dvggj(04yhe,64be ratio of hi6vi4ngac0,g,jdy4 mh9 p e(gb ghest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. u 4jgnk2y6v ytbnn6/9The length of the vibrating portion is 32 cm, and it has a mass of 0.35n kbv/2n6ny6g 94jyut g. Under what tension must the string be placed?    N

  An organ pipe is 112.)is *.ar ycp;a2:/+oer dpbab;qrf o cm long. What are the fundamental and first three audible ov:*qci or; ./es d. p2 brpfbr);+ayoaaertones 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 you expect from blowing across the top of anv0t(r5(ybab-d 9pz (b2 7em7 cr uwbvz empty soda bottlz eub9t bb( r7ry(zw2bad0 cvm-(7pv5e that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tveta g: u/a2:,fbd5jj ube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range tevg,a b :ad:ju 25jf/of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third hari:wd0ba. mobzh)i(lqpew5/v, qr 4s(monic. What will be its fundamental frequency if it is fingered at a leneavsh, 5blb(40pdq : . w/ozw)(iqi mrgth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle ox.tt9xko2 lb,k1r1 hC (330 Hz). 2tlo b.1h19xtk ro,xk
(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 op2;yi zl olw3nsfc0;p )u;9i ksen organ pipe that emits middle C (262 Hz) when the temperatuyspk nl)i;fl;s 3o9c0u;iz w 2re is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at g5ovq 0 z+-vwm20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute innhnpu3s8 v e3a4,zb9 wy-s wo/ Example 12–10 should the hole be that must be uncovered to pln- 39 wy/pe shnw4zb8vs a,uo3ay D above middle C at 294 Hz?    m

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

  A particular organ pipe can rrb-k-(q ;uu4 6gqh0g wey/rsresonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betkgbr r;uw6/q h -e0urg( yqs-4ween. (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 open at both e y:o1ifs*mvq0 iwf f;.nds. It resonates at two successive harmonics:oq f yf0 ifsi.;1vwm* of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 c m67the52 .f7 qpovkk$^{\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 hooqw qn/;,e e7v fq2l-/uf;ha 2.14-m-long organ pipe at 2w -fl,n 7eou2/ ;qefhovh/q;q0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to thevz.d6x1 d,q fxqf y(+e 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 thed1 .xf,zyq6qv fxd+e ( 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 i1tc9 o)j l tp2g3zaujbs)3.a adjust two strings, one of which is sounding 440 Hz. How far off in frequency is i.z9231galt )u tp)acj3bos jthe other string? ±    Hz

  What is the beat frequency ifn.ne1lxe9z1 yg: n hb/ middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistllnx*m,l. (vije operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If n.n(xiv,ll *j meither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 pu8aa5x. cs fgs0 x3;abeats/s when sounded with a 350-Hz tuning fork and 9 beats/s when so3cspax;.fsg8 5ax0ua unded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 29;p c2q2 fef;ix4 Hz. The tension in one si;ff q exp2c;2tring is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if g22ok /o0bfnk 2 pls6-s q*9onb7 kkoztwo identical flutes each try to play middle C (262 Hz)ng9 s zlnob20* foo oqpsk622/ b7kk-k, 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. Fork B has aus/ 2vr/c ycf1 frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible2u vc/1sr c/fy 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 standsv8d, ,m spiq5q,g4 zii 3.00 m from one speaker and 3.50 m from the othezp,q4gmidii vq,, s85r.
(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 enz huiau8j8l ) 6*oo) )nuk+wsupposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, whaw + luu)una6z o)ni8j oeh*8k)t 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 2.3vgq.m 9f t tlz6f3,fj64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20ff6 t339gtv,f jq. mzl $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz gbk tyjq:d 046when at rest. What frequency do you detect if you move wit g:b4jktqyd06h 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 sire t l0lp9h;k+ozn emits at 1550 Hz moves at +pltko hl z90;a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward pr, k;h+gt jyw(3ncy- you at 15 m/s versus you moving toward y -y p;,3kwnhjcr(gt+ 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 same single frequency ho)zw 2)ftto+w arn. 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? As+w )z2f )wtatosume T = 20 $^{\circ} $C    Hz

  A bat at rest sends outu+m ku ,y( pdm.g,b0voloql/( ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it av, +,lo(blgy.0u ud/qmo kp( mt 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/dlpog++ ki(i 1s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat heario+p k il1(+dg in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, al,x( u0 5o ak+ygl1eou 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 statioku,uaye(ol x5lo0 1 g+n. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter usd7w)a(l:yv go b7fr2kes ultrasound 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 )7wf(:v2 dg7aoblryk beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect uska 2ex0k 0 zdpi7-mfm +3bdn.bing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hzbz vzkk6h91b/ jf(h,u9n kj0k. When the wind velocity is 12 m/s from the north, what frequency wzz (9uvf/h bkn9bhk0j 6,jkk1ill 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 ifq4k u pnqj b0/s48* /kg)k:mzngn0nio 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 310 m/s (a) What isb97 - rdgphufy(buk69 the angle the shock (9b-f9b ud6h7ugkrpy wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sound isggw vf8u13 pj: only about 35 vg: gw1uf 3jp8m/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 travelinz-1+s)jz qmrb g 8500 m/s strikes the ocean. Determine the shock wave angle it produce +zqzrsbjm1)- s
(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 b3t s0h /06f zp*cym9juf ejt+$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead r hs z1u1w/yf-fgcb1.and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. u/.wgsh1f - 1yrz1cfbDetermine
(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 downward f niq;(d(h;cqt tbs55jrom the bottom of the boat, and then detects ec ;tb id5t;j(qqc5s (nhhoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in(.if f78 ye a9iklm2yr the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It con f 3g0+ovvkwassivh 4/;w.;iv,hac4zsists of many plastic pipes of various lengths, w;4,v0 o saa i.+3 ikvvswwvhg h/;c4zfhich are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sjy2 cwk8dj.v:ound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoe.2 :jck wvdj8ys?    dB

  What is the resultant sound level when an 82-dB sound and an,cf hw w i*4+/gzzf6ybqrh8:z +rj1hm 87-dB sound are heard siqj:zw4 8h+y+r1zfbwc*g6 /hfhi , zmrmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open/xe ii5;bslil; a743er8 ug0wakhuusg 11 9z h, is 105 dB. What is the acos0ii9i ewzgk1ax85 e u;g;br1ul3hs4uh 7/alustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output :.sysf+tow ed p19i1iat 1000 Hz. The power output drops by 10 dB at 15 kHz. What is t9w1+s if:1.op yditse he power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devic7eig s88;m awyio8fx-es over their ears. Assume that the sound level ofyemxa;88o7 8gfs- wii 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 communications systems, par ed1584 4gqu9i,is w1xriz 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 frequs*difwag16 ;5eq e4 fsency 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 be 5,jzxzub(,oq k4 qie8tween fixed points with a fundamental freqeju,8qi5z(k4z bo,x quency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled wt vl;u* ;wllm,ith water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tltl;*v; w ,umluning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at (oo k;)/(hnfzjsmsg6 2 rr-v none end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode)om 2fk;j/ z norss(6-h rnvg() with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatejp5kmbqyqx-d v0br k gw 9xa vup 6f01(*6*h0r 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 range3 w-t.cl5c9 pwu 07;x iobch-zumi 0nb coming from two sources. The sound is loudest at points equidistant from the two sources. Toc- 7cpwuc9m35-nwb xii0blto0 h. u ;z 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 is stationa w/h1a;zgq ;gary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train qhggwa ;za1;/approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 t7tr t1nut1*v zhg*6fHz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constan1nr hgu v *ft67*ztt1tt velocity)?    m/s

  At a race track, you can estimate the speed of car n93fly1pltt/ s just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goel ylt n9p/t3f1s by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat xqsaz(3v; ow4.wn: j:-c ucbdfrequency of 11 Hz. The shorter one is 2.40 m long. How long is the other? 3q:b(ux; jwnac 4c-so wvz.:d   m

Two loudspeakers are at opposite ends of a railroad car as it movr d i8il).i+v4uo:fnzes past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakervlf irn4z+i:u)do 8i.s have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta isbm/w)ys7 5mh d normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assm7 )sywm/bh5 dume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward o , 5+b /0+e0rtxjlm- nhkzedibf;ja1the 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 refljm ,nke + bztdb5fxio1/jr00lhea- +;ects off the moth?    kHz

  A bat emits a series of high frequency sound p9qhhd e w(1+khulses 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 detected by the bat so that the echo from one chirpkhhed+1h(9 wq returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Ajfh0 q*6ly2hmlpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is 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 whichm0fjy6 hqh *l2 overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be29bg 9 z8,pp x -eme90nqao5kiwzwh1a compromised by the presence of standing waves, which can cause acoustic “dead spots” at the nz 1,0 eo aqxipkm5-hb2p9za9we 98gwlocations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, call5bsc)2ta8(v ir crk(3o mqut6ed “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. Fr3v5c(2 ark )t(ocsuq ibmt86or 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 huma*z z6+ p2fzu -fkzoh3en ear at a frequency of aboouk fz3fe* 6z-2z+zh put 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hearrj)8e+ n*7w+ml3huso8 r o2dmyy48i wd n.sur s the sonic boom 1.5 min afte*+ sylydro4m8.+s7mih w)8ju2nnu ow 83rdr er the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1e+sus m:;tl3d5 $^{\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