What is the evidence that sound travels as a w+xntlhg f9.c 025py89 cc shn1.coumj ave?

What is the evidence that soundv q7*rv;2ijv xfmu.(6 xfa4kq is a form of energy?

Children sometimes play with a homemade “teleph 2tp89ii 7n f/ckxa*ldone” by attaching a string to the bottoms of two paper*xlac9i2p7fk8i / dtn 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 other.

When a sound wave passes from air into water, do you expect the frequency ob jj-18y4v+ u ut0 whrd/htsy3px)3mgr wavelength to changevrjtgyj+t-xy 4p/uh 3 8swbd)m 1u30h?

What evidence can you xiktj98p xu.t mn.;ak g,j:y8 give that the speed of sound in air does not depend significak kxp 9jigxujn,;ty.a m:8.t8ntly on frequency?

The voice of a person who has inhaled helium sounds very hi:0xx +olys7d xu 9q8r 3fft u3ofzeb1(gh-pitched. Why?

How will the air temperature in a room affect the pitch of organ sxngy4 0q ba21t plb/e63pd3l pipes?

Explain how a tube might be used as a fil p:.dkx)v ))u frvq;h/dn ky:rter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muv:dru)n) /;p vdykk. rxhf)q: ffler.)

Why are the frets on a guitar (Fig. 12–30) spakl++ qb 1,hgheced closer together as you move up h+ gelbh,+kq1 the fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear yf0d tkwm0f70 it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter”kmd0fw0t y70f — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said n3cm0f-r p 3aqto be due to “interference in space,” whereas beats can be said - 3rn 30cpfqamto be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lob 0bh2zyfgc d 5fq-vg)9j3 dpb qk/)5ewered, would the points D and C (where destructive and constructive interference occur)db5k q5f9vqp )g0ey-23 b hgf/)jbcdz move farther apart or closer together?

Traditional methods of protecting the5zjw60 .i wth ;*ozmww*bk.jo 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 r zi o.mwjz*ktb0ow; 5wj.w6*heduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a supw; b4rwu5.yx xvhss9 (erposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of thev. ;r4w9bwsyu(h xs5x waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the qpz9an+ u g*bn)r fdx;s4/o 2xsource and observer move in the same direction, with the samer *uxnz od4+2sxqn / f)a9;gpb velocity? Explain.

If a wind is blowing, will this alter the frequency ofidq2,9 l y3de/zmccl3 the sound heard by a person at rest with respect to the source? Is tyc ql9md zlc32d,ei /3he wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on any 6+c(8lop cgha cb9hr58 v/g swing. A monitor is blowing a whistle in front of p r+oya (68lchn g8b5gv9c/hcthe 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 h 4/zmdh.rv1tk5 bp919ph fxfi3*na oher shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimat549bx kh. ifpm3fh1 oa1dnt9*/ zv phre the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below thoa r5r/m5 (ywoe 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 doewmoo(5a r r/5ys not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 oofskwr9e.*qwu 01 g-$^{\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 foggy day.bz*ln1 v1 ,lae Without warning, an engine backfire occurs on ano 1n*b1vl, azelther 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 splash in;+mwg ks, +ux-y k(px(8peyysy o q::t makes when striking the water bey( w :+suxyn:-k(s +ymoe,8kyqpxpg; low is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pa+x6t,ck e4)xb7 fclazvement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. Hc)x+47fcklb 6 z,taexow far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of x,md4 q .q6b kg-6c zb;qy;ngldistance by the “5-second rule” for estimating the distance from a lin6;mcy dbg,.q-b4 6qqxz ;gklghtning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the paixd7s .maa02)xwvg0k sn level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity i halg9,+mt ro.s $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce ad5*tj/ v;kar.x*oo ql sound level of 95 dB when fired simultaneously at a certain place,*. 5or /oxva*qdjt;lk what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four e be:elw6 zo09b,r-ka fvn0e1vqually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level wo,zvlwa6 0kne r-0v9b oee1b:f uld 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 ram98o ;phw 2j.tl.bt qatio 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 devicemo 9bj.;l. ta 2h8wqpt? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pu *eb/t, phr9qerson speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a spherqbr9h*pe/u t, e centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose areaja8cc53ml 3e x a fezdsvr6.(* 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 modeisa)whyec 2xx,h+0t3 st amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a lot,xxyeca)0 w+hs hi3 2udspeaker 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 regizcnj o8 wvtcu u,4i 9o)/3-rvmb a6z5hstered 130 dB when placed 2.8 m in front of a loudspeaker on the stu )u6-zn8i4tr w3javc/ mc b, ohz9ov5age.
(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 detectnv 6;kf w/w.:02g tirw 0zfhxx 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? [Hint: See Section 11–9.x.t f2hwfigvk;:wxrwn 0 6z /0]$\approx$   

  If the amplitude of a sound ww * v/.xdmxr)bave is tripled, (a) by what factor will the intensity increaxr)b* /vw.d mxse? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but oz9xk9dlr4pt;9j c;wtne has twice the frequency of the other. What is the ratio of their i w; j9k;rctx tpzd9l94ntensities?   

  What would be the sound level (in dB) of a ; lgtw c;w8hrx;hki, h:)r( qksound wave in air that corresponds to a displacement amplitude of vibrating air molecules oi,lrhtw xw (c; qk8h;rgk )h:;f 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have wbbc hj+ d* +sp4v4 9arvkiij8 7wrus3,hat sound level to seem as loud as a 100-Hz tone that has a 50b i7 p39d rwjsui h,sjb4+ak8*4v r+cv-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that anbep desgkt--k +s5xm g2 .m4k(j( vg:c ear can detect when the sound level is 30 dB? (See Fig. kd5xv cm2j kg-+eg: me4 -t((ss.bkp g12–6.)

  Your auditory system can accommodate a huge range of so2nk2j:res/qqt ) mh9l und levels. What is the ratio of highest to lowest intensit9k)2 jr ql shq2me:t/ny 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 fr *w+tr 3-ef4wvcr-gtmequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mawrmrvc t gw+ft-4-e3*ss of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental ak6jvc5e*l j e0nd first three audible overtones if th 5vl6j*e0jc eke 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 an 7wa8pd:ud(u xempty su(wdaxp7 8u:doda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning qw.o*w ypf s44the range of human hearing (20 Hz to 20 kH wyo44wspf*. qz), 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 fre1 pm6 cj1arg/yquency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its opa1/mcgy r61j riginal length?   Hz

  An unfingered guitar string is 0.71 d::aac3msx1hg5f q h3 m long and is tuned to play E above middle C (330 H1xsc 1af:adg5h 3h:m qz).
(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 o,kj:b v 8pj:c1 vdagz4f an open organ pipe that emits middle C (262 Hz) when the temperature is k,z va1p :b 8g4d:jvjc21 $^{\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 /tuf6nx-,tlff 2x7z .l 9rhg s20 $^{\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 thubh-.e(n.g5f sr u*c fat must be uncove5bu* sf n.(ec-.gurf hred to play 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 resonate at 264 Hz,,( -j f-gh ,cqwvpsx ,3,hpnpv 440 Hz, and 616 Hz, but not at any other frequencies in between. (vfp,-phphs,,-v x,q ng( 3wcja) 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 fmz u6.vd)x8 h1.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz a)mxudh.vzf6 8nd 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 wdv) cu9qnh1urg79n9-*c1sm yekxun: fq5q7$^{\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 y2t f/d 7c4d 2avl((j5hact rs8*ha xlpresent within the audible range for a 2.14-m-long organ pipe at 20ctsa/5t a 7ac hr2yf48lxhd vd2*j(l( $^{\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 the outga qfm i4r9:hxl:uk: *side and is cl4lu:xg:i :hr mkqaf*9 osed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the 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 strings, onequg4twys4 -ob(x ;t(a of whico4 ;q(wbutx( 4sa-ty gh is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle atl6 fmpxdmle a1,6u( (/( ad msx+kpyx-c4b 4C (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 whistle operates at 23.5 kHzmf /r cw g.e4pnq,rf21xbry 06, while another (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 si rb4f0gmnpyxwr2 q1r.6 , fce/multaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning c *( +lf fklbla7hqj01fork and 9 beats/s when sounded with a 355-Hz tuning lf 7hlac f+kq (jb*l01fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned k )l5d9pgi9 *erc uum6f9rbn- to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Rec bn5-9rgk iul)pcu 9r ef6d9*mall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try tofub4xu:+(+lu1rl cet play middle C (262 Hz), but one is at 5.0°C au u(4:b+1fxt ulcer +lnd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a freqvv+,p :rvg73 xu9fayv uency 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 possiygv+ ,v9:3xp u arvfv7ble 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 one j+6bdy mvxv-6speaker and 3.50 m from the ot b+xjm6-vd y6vher.
(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 q5 oh*xd)u- 1q5ngcrvss m z.8tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what mu8v-.1q5os ucd)gm*zh qxn 5r sst 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 nzyv6+kl7 )r.+d b/qcftcc+u ,p(b hv 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assumerv) ,+.vpc6q7h n yu++bb(lk/dzf cct T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enex .z: iw:65e-ti9qdcbpp b:ygine’s siren is 1550 Hz when at rest. What frequxpyc zi:b6::w9t eq-pbi d5 .eency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine who7w3 zaxfx(ld x: wi0,qse siren emits7 3flxdz(x:0wqi x ,wa 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-Hz source is moving toward you at 1u 1xfpf+ft hw2k (*m;c5 m/s versus you moving toward it at 15 m/s Are the two frequencies fh wf tm *1+fc(up;xk2exactly 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 eb ff ahg3*qcc4xz3. )frequency horn. When one is at rest c hqg 3c.a)*xef3b4f zand 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? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receiv0d;xx khe69k31) . oyoezo ixkes them returned from an object moko6k3; 9 0hi)1xz odeye.kxxoving 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 speed of 5 m/s As it flies, the bat em m3h43izh.qknits an ultrakh3h34.i zqnm sonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubagv7al,:w5ffld3o8 3sq0tvg c was played on a moving flat train car at7fa5: 0fv ltso dcv,gwql38 g3 a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds.qk2z.bca;-e c Suppose the device emits sound ak.zc-cqeb; a2t 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wavezvdy/n ky h0 nx1)x: la3 k)mu7+sfs.as 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 Hz. W* vvu*m+) xexth4-kv u)bw nf(hen the wind velocity is 12 m/s from the north, what frequency will obs v)bkfhexvtu-4)+mx *vn* u(wervers 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 io2 72*z d cqg:slmrs4lf 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,uctq76h ny ;5f8 97 b *:baapzl rpy:sa*ambd the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the d:n b8al6abpsqcyz5 ,: apy79b hd*m;a *7t rufirection 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 sb2;,e eipfo4 upeed of sound is only abo4ie eb;2,f puout 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 travelinx7csp u3n.ybro h-3m 8g 8500 m/s strikes the ocean. Determine the shock wave angle it produu b8os.px7 3nhcr-y3 mces
(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 .o mi w21rcz,8gdi-n b$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhea5hwi8mp( il1xd l3i.x (b)kms d 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 hlx i3dl5(hsm )b(ii1kx. w8 mporizontal 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 sogjux5z:/uv st;m3v te6 pklf15xdu);nar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fr6 jx;vuvmx3g1:/el tt)p ku 5f;sdz5uesh water)?    s

  Approximately how many octaves are there in the human a2 h5n2or1hxp zvk5wcj0)- lt audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displayw5/h jj v ,qsozqqwf i5t0:/l9 called a sewer pipe symphony. It consists of many plastic ,ltioj9 v w50h:q qq/fz5j/wspipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound clos0j:(ie8pst cgbh p.s0e to the threshold of human hearing (0 dB). What will be t8 bj0si0gch(pt: s.pe he sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soundfn3;i- ejvfdn02jj0 :pmnle , and an 87-dB sound are hea jfin0l2jjpm,evd :3e 0nn-f;rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, plac do+mr2kr eaj/yt r.:a9 lvb25ed in the open, is 105 dB. What is the acoustic power outa9+j k .ra be2to2yrdrm :/l5vput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W ouhj :esxl.c ueum1 2(e.v /n)putput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output .mu el 2.xsj:ehe1u)uncv/(p in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over theiv61isx f7 .f-cvm/t4r o w;jbrr ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance o /v.-jwvbrrxs 7it 4mc6;f 1fof 30 m from a jet airplane engine?    W

  In audio and communications systems,y*36c ngx/2qgpbyjm 1 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 freye c/n;7m/tsbzf ,iz*u95pf h quency 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 by7v;j- 1xze4joo9r yq etween fixed points with a fundamental frequency of 440 Hz and a mass per unite xojyro- yzv19 q;j74 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 vert+ti3/q eq11ar2qnnld ical open tube filled with 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+1lan /te 2inq rqd3q1 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 mby.eegun fn(ll+/l-e- :eo;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 resonance (in its fund+fe m/nl-(bnylue:-g ;oe l.eamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observeht vr9 4 rtpicvo;:;ors(+y7sd to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1 53gs d5ca2tc5xd(b 5s b:mkmv000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly wcmbm av(s553d 25xsd 5:gktbchat 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 stationary. The conductor on g(sz he1s;q01( rbxqrthe stationary train hears a 3.0-Hz beat frequency when the other train approachesb 1hq0x z1rq(;sre(sg. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appme* h1; ze4ordroaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was ;z1ed4e m*hrothe train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just byo6f6reno qb :aa:.c*q listening to the difference infa.qa :r66qoen*b oc : 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 goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togethe,fl+e h35 udmnr, produce a beat frequency of 11 Hz. The shorter one is 2.40 md u 3nhfe,5+lm long. How long is the other?    m

Two loudspeakers are at op/l1 1pu p)3gk ,hjt)c;jbzwddposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown inwkl)ch)bg zd,pdjtp 11/ ;3uj Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about ke) t 4 lsgy5hdhoye,:fi3 l.-0.32 m/s what beat frequency would you expect if h3):k5i4e-h,fyoges td .lyl 5.50-MHz ultrasound waves 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 while the moth is flypy r8p::6ixo kj: nia7 p5wg9wing 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 wav5i gxanp9:wk:j ip oypr :67w8e reflects off the moth?    kHz

  A bat emits a series rz ,4zhozqo1c/ad(1 ck f t68eof high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each o a k ch4e6c8z ,tqfr1/zoz1d(is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wa6 ; ak/kmeyubk zy *az:.sw*,hs once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn 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 fre u:yem*;z ,y *.kb aa6kwkhz/squency 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 crx3 ulm ;fnc 2l,zz tll ro52j63*h)fban 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 wam3j; fz52n hc) 2l6r,oblxlulr tf*3z ves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” is6 a3 ddi3+jvqfr o+up2ju*a2nvolves 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 roq 2r+p6is v 3d+2 afduuoa*jj3d 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 thresha:k 1 lml+3gsr xke z8/g7vts*old of hearing for the human ear at a frequency of abv7lgzes 3l1:kx *skm8 +art/g out 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 Machdc;lx3 mii 78o r whbi/*.+lxlb)fj* s 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Wh*d rlhci73 *iw8jo+f/lxb. );mb xls iat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 5.cccm gk .+oz$^{\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