What is the evidence that sound *fcxd b-(o2j hqhogneb*4 ,pce-ql. /-vish ; travels as a wave?

What is the evidence that soulg+2o(fmjp- 3yu1 tj hnd is a form of energy?

Children sometimes play with a hoar5gx ;g9-o7f tl4mmd memade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a chif9gr74o; am-tg dx5mlld 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 th .2aswuw3a.om e frequency or wavels2mw uo wa.a.3ength to change?

What evidence can you give that the speed q3x r)xjhy.+ :9f21kt ylqak yof sound in air does not depend significantly on frequency)3jlq 9r x 2ktqx+:hy.yfa1yk?

The voice of a person who has inhaled helium w5 thk qz0)0gwsounds very high-pitched. Why?

How will the air temperature in a roomhwp.l9mmdcf: f 4/e7g affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soun2l*ja g:jui0n3 :enwc ds in various frequency ranges.0w2nngujacel j:*i3 : (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethosodmwva,chy(3w1d m0b b )+(er as you move up the fi0 +,yam(w m 3vdhwcd (oo)b1bsngerboard toward the bridge?

A noisy truck approaches you from behind a buillu s6b.3uin sdxr 50, evnyipad+j,:4ding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is sud4d6y,usn:ejrxiv3 d+p5.ainl,bs 0u denly “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 “int j -cvy,717xyczd57z suddxj (erference in space,” whereas beats can be said to be due to “interference in time.” Explainx 1sd-udd(xvzc jc,77yj7z5y .

In Fig. 12–16, if the frequency of the speakers were lowered, wouldt4 t1;8b :yrpzq6s6lww( wlzw +.xnp o the points D and C (where xw 1p:p;6(l 6 n8wyswbrlztzt4oq+. w destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting hjk2 (.z5m lq88pxskx 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 headphon 258(lqx kpkh8.msx zjes in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of 2loh6apx(l )i b5*b* kdf pe5fas a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the twoopk)i( 6*h alefxdb5lp 5f*b2 component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the souni3ajb x t.amda7b *y uo5d. or5b*.h2rce and observer move in the same direction, with the same velocity? Ex .j5 oo*7dbty*n5bu.xair3h b 2.amadplain.

If a wind is blowing, will this alter the frequency of the sound heard tw/nmo ;-0:emdq3 rm xby a person at rest with respect to the source? Inrm0m ewx/:m3t -q d;os the wavelength or velocity changed?

Figure 12–32 shows various positions of a /d 1 ba0x(/tbp7kth,.v de eebchild in motion on a swing. A monitor is blowing a whistle in front of the child on the(e d7 a,btbdk 0v.x /t/1ebphe 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 lg,2x. ug(bribm/(1eqxh2+, lfaahrof her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after ,xg,/lb+ .xf2r(almq1iea r(uhh b 2gshouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side o0gsf/mtq6 4ea mknbl qx+b h-x3:1w h;f his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Atn1f b+ m-whl/;s x6ma qg :30h4kqexbssume 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 wav f/walsvh zhn). i :( n1lcn/rb6*q6eselengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy dhsl13/ ff3 q1euq;-cwz r-jcv ay. Without warninczhw3/ u q1fc;srej1-lqfv 3-g, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makx(iwz-w a-n4*3xiuvft1u d wi4 ic+zq;q0ny0 es when striking the water below is heard 3.5 s later. How high i4u0w3 uq1y;i(4qvn-+wxitni ifzd 0zw*- xcas the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concuw9r;9(lu8 g 7jbqphfrete pavement. A mq9bp(wu f lhr8g79;ju oment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by h r+( lj5ta4wi;8bd*phnq 75sha1t,x ydsyg2 the “5-second rule” for estimatin,sdqh(btxa w52n ij gp1a75yd; t*y hsl4hr+8g the distance from 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 paih3 2n-khse ob8 v0n5mmn 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 intta a 3qn1l5jyios *r,(ensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produc r7es:. sxg8)ilq,n g8uf7 x2ezqv t4de a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, notxir s.lxt8g 2q,dzngf4qv 7 e8es )u:7 dB’s.]    dB

  A person standing a certain distance from a/iw52ogqkex1a5 0 dhjva x,;q0itd ;l n 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 the capt0a/oi de; davqxq i0j2g;x5wk5, tl 1hain 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, where9qmrfmde: d.i r.7i/tzf1 *vfas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 d7 .1tmv9mrdz fie q/rffd*:i.B =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in nobrp ex28 eke-iwr) *n2y. 8vxcrmal conversation. Use Table 12–2. Assume th cy2)x-evwr *be2x pr8n.ke8i e 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 whose arex; 4ed csho vy:3nuip2fwc57)a 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 abm bgv hm;p :na765rg*t 250 W, while the more modest amplifier B is rateg *m6bgb5mhp nr;:av7 d at 40 W. (a) Estimate 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 meter registeredf6j s .p2qw c4fz*hh6flqq.*ahg:c;z 130 dB when placed 2.8 m in front of a h*a6qqqc 4z2wh.f;:*hf zf jpcgs .6l loudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Wha,(ac6uxi/y v g6b q8kgt is the ratio of the amplitudes of two sounds whose levels differ by this amountq,kigb/ y(v66au 8c xg? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wil-44c wxah4//jj ybr)ztsmox) l the intensity ij4a 4c4 )/ws/h-xjz)yoxr tmbncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal disg1qzlg1+l 7: s 0c9l nncrhxs,placement amplitudes, but one has twice the frequency of the othe q0 l1l sgzg, :cns17r+hxl9ncr. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspond62 hp dat1uwqh -v14q-mdh3iys to a displacement amplitude of vibratinh2h -tw3dh146-dy1 m piqqu avg air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level toa(6j :3zax maq seem as loud as a 100-Hz tone that has a 50-dB sound levea3:x(z amqaj6l? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detd4nzhyf/)fx-cp gqn .9ek- +kect when the sound level is 30 dB? (See Fig. 12–6.) kk4e-nnf/xg.p z c9qdy)h- +f

  Your auditory system can accommodate a huge range of sound2 .o ./icm,ifnpyrf:q levels. What is the ratio of highe i. o2rpc.f,nfm:i/yqst 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 ypf,)d+k. q m1la)u zsfrequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the stri ,1 ))daml.puykz+qsf ng be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible nwon9+oep 8 .-6bvk ukovertones if the pipe is nuk-o+ow98vp.e bk6n
(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 freo0k - jmoqzt09 1cztrw0 baf8m2g7xw8 quency would you expect from blowing across the top of an em70tb0w9gr 8xmkw8ozfz1oq a-ct2 mj0 pty soda 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.p2 /rhp:glt )9xn xsd a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengthsp n:srxl2d9./xph) tg of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar strinucoo e 2bzeg 2 9(wy870m/0tvp,o yqjtg has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency2to,zpwm90g70y vce(y2/ te ujoob q8 if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar/b :v97u7 nd)ug uxitj string is 0.73 m long and is tuned to play E above middle C (330 Htu)d7u i7g/xb: nv ju9z).
(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 anrt4ft0/ ko7xfy.qauny28n7k zh 9hk0 open organ pipe that emits middle C (262 Hz) when the temperatuu4 nfktk z9x0khn2af77 try /hy8.q0ore 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 7a tk pc3c0lz0d4:b)my7vsw v at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiec:qb+a ;hlmtnpd( 9mlm8+ckr- e of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 2n-mc+9+h :pqk ;bmrda mllt(894 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 Hzov3jau( ,xsbl jlt*fo+;dg * 0, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why thij ftj;*dav xl,bl o(s3o0g*u+s 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 re2 )tifc u/1poru/ :/6lgmeoopen at both ends. It resonates at two successive harmonics of freqe1f6e:rtum )2/p/ /louoc rig uencies 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 tbv 4o5ell;ay-g0q(p $^{\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 fog cducn /5jad+0(rjx;r a 2.14-m-long organ pipe ajr xg/(cd5+d;c uj0n at 20 $^{\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 to6mwmc/ gna9okxm32r/ the outside and is closed at the other end by the eardrum. Estimate the frequencies (r a2g/k mxom/n93 wmc6in 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 tryingd+: e) qq1zlde to adjust two strings, one of which is sounding 440 Hz. How far offdzq1e:q el )d+ in frequency is the other string? ±    Hz

  What is the beat frequency if middle;1 xa z,tzbxyxxxl3 4jg1h73r 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 whistle operates at 23.5 kHzzz jzm)5rc*y7, 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 simultaneously, ezy *)7m5zr jzcstimate the operating frequency of brand X.    kHz

  A guitar string producv r220 hfp rqs-xa*m2des 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrsvr02ad*rq p2 -xfh2mational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensi hnntd26: :wnax-dhizm7 ,iu5yl *t5gon in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Rehw mgnl2n7 naut*ht,-:id 6 d y5zx5i:call Eq. 11–13.]    Hz

  How many beats will be hearmf wti47en.-z d if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and 7f-imztn 4we .the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency 0 xzqhm0n2md8of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are soundenmx00qdm82 zhd together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m ap+qoq5 q2pqtu nkm++*zart. A person stands 3.00 m from one speaker and 3.50 m frn+up5qkqt2zmq*++ oq om the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuc z0x5+ /lozkjner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the f+kc/ x0 zzojl5requency 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 wavenwi7py7) z :y)epdh;i lengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume y;nizpy hei ):77 wd)pT = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 0i2:3 jqou 3srq m;ucwHz when at rest. What frequency do you detect if you move mcu3 0qujqoi:rw3 s2;with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What 61 xicx*b; kj7a4 o,wren ojd)frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 346kijxx ,jnda)ore1w*o c; 7 b2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source wk9rk. -roj/l is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two jl -/k9.o rrkwfrequencies 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 equipped9g7 f1*wiigq 7kc pd+b with the same single frequency horn. When one is at rest and the 7c f1gig 9*k7bdiwp+q 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 ultra-l3-l) p+ltu,jpdpfz sonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound fre-uf3plz)lpp +jtl d ,-quency?    $ \times10^{ 4}$ Hz

  A bat flies toward a w dv15d/ee 1zidall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequee11ed5d z/d ivncy does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler exper es rbdln4074iiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of b 0e4rdl7sn 4i10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wavp-ex)zd ;a ku,+rhcjm :; .gsres 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 expectj c mk-;:re s+.gdx)z, raphu;ed 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 ur38bm1s* w*ee3 mtq*b; hsdjp)ugma .ltrasonic 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 Hz. When gzp 4-)epqk(* h; wtytthe wind velocity is 12 m/s from the north, what frequency will observet- wk tpz;qgpey(h4 )*rs 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 laibrj/s .lp2 vxx691u ind if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 w *z(hf6c uuia yr7/ne-here the speed of sound is 310 m/s (a) What is the angle the shi u*yfn7 au -c6ehr(/zock 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 atzs v3 3-:nzufuqv- ;jsmosphere of a planet where the speed of sound is only about 35 :3jvsf--zsuzq;v n3um/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 850) o. 4rc-+w dda.vbnqm0 m/s strikes the ocean. Determine the shock wave angle it produces .w4nma.d )droqcv+-b
(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 0xpm3grz)j)(ii t t8o$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km ( judatzg(f0j*d y,h7 above the ground flying faster than td(f*(7,j agt jy0hzu dhe 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. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses dowwg o3nn)4:: jpigtq v2nward 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 t2gn :pj4n tv3w:qgoi)he minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in 5ipw.olk2ru,; xxo d2the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphd /rrj ;/jdxpbibc105-l4l k fony. It consists of many plastic pipes of various lengths, which are open ; lx1-bkj0fr5bi cdplr/d 4/jon 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 close to the threshold of5)v :n: :hurp2 uf m+kwj/xsoh huma)/hp2nmjuo:wsx:v:fh+r u5 kn hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87l+lkwe fdg)s y r4.c(1-dB sound are heard simultarsdyegl(cfw1 l4. +k)neously?    dB

  The sound level 12.0 m from a lo 6g(mvijq a0c0udspeaker, placed in the open, is 105 dB. What is the acoustic powegmv(0iq6jca0 r output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at -bfty d2h, (qyop ,s8c1000 Hz. The power output drops by 10 dB at 15 kHqfso b8,,hp y-2tdyc( z. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ov+o*k vc6 hy; i bmbq9wh25jz;ver their 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 vbh+; 9jvh ;biqyck6z25om*w the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sc.ulcmv6.7ba38b a w7ufe ;o f(uz 2gtystems, 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 frequjt2-s5 kw1 k-b-ir s9g0yqcofency 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 vix-i (jgea0hr;mo1-y 9na *c58q zvxf oolin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass pei r* myn81xao; 9-j0-zoh gax5f(qcevr 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 verb6+w 2srzzwxksy 2 43htical 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 to the water level is 0.125 m and again at 0.395 m.+2yb sww zk36hxr4 sz2 What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10( s0cjcp ,bvd4f+t7cj g is near a tube that is open at one end and also 75 cm long. How much te(pbcjv t j7f+,cc4d0snsion 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 obsbp*llgz pr,.n lyn;))erved 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 500–1000-Hz range cocw 1pyk *h7:1j4/l x ypuz ue0txx8+qaa(;wngming from two sources. The sound is loudest ag4xkcax /ju+8e nwzya (l*t171wqhp 0u; pxy:t points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is s aam6r3y7e4hp 5db,*ljg2e q ltationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is hla pejdby*ae4 gm,57rlq326the speed of the moving train?   m/s

  The frequency of a steam train whistle as it ap- lgc rxhd/wsc( xv8;)proaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume)-/ ld vw(8gxchrcs;x constant velocity)?    m/s

  At a race track, you can esti2m,84w2x og*2pl(v dm n1wyxm olos4jmate the speed of cars 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 octavwx lo84o12ygwnm s m(v*l, xmj224dp oe (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11: :v*p5u6 v 3: v:ndvpycyuqegq+t*ge Hz. The shortergvycev du6 :3g y:*pn+uev5 qt*::vpq one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it e4hh)*zjebn lnm u00ov6s0h3a ;l* fk moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between t elnnzk43mo 0*hh)j0*s; u bhf0e6vlahe 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 * u6nmx4v9p7ylw ajhq y9c3gb4 2i,zjnormally about 0.32 m/s what beat frequency would you ex by34ijwnyu7 axp glhv26m zj*94,q9 cpect if 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 3;-e7uc1 h ixh0yzmx(aywf zoq 65)qo is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that waxx1zm (0f5u7yeao3 qo-; icw 6zqhyh)ve reflects off the moth?    kHz

  A bat emits a series of (v(h5+nk,ysvf5 5nb o 3c fo8na*rqthhigh frequency sound pulses as it approaches a moth. The pulses are approxima,8oh nqovys*(53+ a5vbrhc5nt fnk(f tely 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 chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. nyb/y .0hxw+e12–38) was 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 fundamennwx/0h +e.byytal frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence et3wc vl.uee n6 p*c/6of 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. Calculle3.n* w e6ccv p/te6uate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” i cslu1bg 8b;,znvolves a long, slender aluminum rod held in the hand near the rlu; 1czsb, 8gbod’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. 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 thresd wp2z4te)x;.q n+ +dsz 8obmvhold of hearing for the human ear at a frequency of about 1000 Hzm be d;otsn)q2zzpv+ .w4d+8x 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 2qn).i* gu8/tx*4uq w9sppf ri .0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? ts* pi/9u4qwgifnu x p.r*)8q   $ \times10^{4 }$ m

  The wake of a speedboat ip7lew.)da;/a e es,/ sx5jtmes 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