What is the evidence that sound travels a7(;nzie k mw;ru6b yk)yd g+4kp -0lljs a wave?

What is the evidence that sound is adgq2kw r 61o,(fqcj.h form of energy?

Children sometimes play with a homemade “telephone” by attaching a strqlz /n+j4y w;jing to the bottoms of two paper cups. When the string is stretched and a child speakyq4wz jj ;/l+ns 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 thn9+hfor uy; ctm7;v.o e frequency or wavelengt ; ; ov.7hconfr9tuym+h to change?

What evidence can you give that the speed of sound in air do9.y 3f:rnqmbd es not depend significantybm.:rfn3q9 dly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched.t:hhazie5 6 :v Why?

How will the air temperature in a room affect w)b+ceecx up g( nsw(y+n,rl* 4j*j l3the pitch of organ pipes?

Explain how a tube might bemr x+ v 3gab85b2swx7s used as a filter to reduce the amplitude of sounds in s 25 bwr3s+bvx x8m7agvarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig.y2m6(eck/ n ad 12–30) spaced closer together as you move up the fingerboard toward the bridm n(/6dc2aeky ge?

A noisy truck approaches you from behind a building. Initially you hear itd 1gm5qq 1xejx63rkbv a5o.v1 1u4hz s but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high- ex5s u 6k.vz ob1qj1q4r3dxv1g1ma5h frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spacea,yv fljj.(-z,” whereas beats can be said to be due to “interference in time.” Expljyla f(j.z-v, ain.

In Fig. 12–16, if the frequencysc0f0qczzk*nx r. 32yuf,q 2a of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer together202ck0fzxs n ,qa*u c.y3r fzq?

Traditional methods of prozc(wr pm1d+(vh o02tib +rw/s tecting the hearing of people who work in areas with very high noise levels have consisted mainc++ v2htr(m w(z10/si dbwporly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as ex m pzfwn.4v4,5wd) rz8cc kpcimn+cdg/ 8/4a superposition of two sound waves with slightly different f/48rzw/5v)4 +kpf4,znc 8eccd.pmgxw md ni crequencies, 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 hl( cvc*7g d:uif the source and observer move in the same direction, with ccuvhdg: l* (7the same velocity? Explain.

If a wind is blowing, will this*qhtgc l.4q:n 2 ofeu:wc 3pv5 alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chanc3wpfuo:q 2:nlq4*g v t5h.ceged?

Figure 12–32 shows various positions of a chiqnh+6 */w9vv,),co:hou/a)yuvsmnq r+slield in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At whcan munw/,r:os l+h uv )yqqoe/,vi)+69s* hvich 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 .m.v: ozy(emaz*ora )by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length (zmv* mzyaae:roo .. )of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears th9uj ekzw.ehkp tx ;40,e echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly ku;ejk09,th.4we pzx with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthu .xzgw9b)jf,( (amft s 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 3f8os 0 rdh ,dwe-ur.v72jg drschool of tuna on a foggy day. Without warnhr80-rj s3 d,eordg7vuwd 2f. ing, 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. Th7yncl (d a)u6 dnws9n)e splash it makes when striking the water below is heard 3.5 s later. How higunwns)a7dd6n y9c()lh is the cliff?    m

  A person, with his ear to the ground, hgwha)e; e+3p e,q*0u ylkde+sees a huge stone strike the concrete pavement. A mome ,)wldee+e*pgy0+ h3hk;uqea nt 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 the “5-secon :z3zu;guxuwibb)zr8 -i 8 nn3o /nrl.d rule” for estimating the distance from a lightning strike if the 8 izbnu3 : i l)wurxzuz3b8gno-/ ;.nrtemperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity ovt1z dai79ve-f a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose inte81dqm zjd1nv 7-8ulkal7 ;wocme hm7df(c56ansity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound le;*hui i1b, k:,f2tabqgv)w zuvel of 95 dB when fired simultaneously at a certain place, what will beh gabufq z )w,u2 ;:,*btik1vi the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance fromlis-dzmcm0v4ciq0qf . 7; r/o an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one enginefcisi 7.dvrz- q;mo/c40ml0q? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereaes7pv,f6ru6h8 ; f jvrs for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for 6sfuv h,6r ; 8vfjpre7each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speak b 8j-urj3kjdsn*/ c(fing in normal conversation. Use Table 12–sjnfj/cj(k -r*db8u3 2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardru5b;x zp:.jobbm whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplif99pfkk.v 5a ei/0;k.1kquk y(sggjko7s8 mbnier B is rated at 40 W. (a)k 99ne.osp/7u (0g1q kmk;5a jgki8vbf yks. k 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 registered 13 +hppl02*:rp8tsjd8z5 kxclw 0 dB when placed 2.8 m in front of a loudspea*j+d2 w8cprt hpl5:l0x 8kzpsker 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 lei; j k9/lv +-v+ ;8(v hnymggwbyyr(rr1jjw ;zvel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? v(br;wn;y1wy rj9jhr/( l+yz g8+gi-j ;vvmk [Hint: See Section 11–9.]$\approx$   

  If the amplitude of yvh5j(aalqv /kwfx* 3 / sn-:0a g(o a61kqvkna sound wave is tripled, (a) by what factor will the intensity increase? Increase by a factor ovwh aa6:g13 qof5 qk/yav/*v0l-n(a jn(xk ksf    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twi: sf1rtsy* 3vfo-x q.ace the frequency of the other. Wha.vq 3fa1:o*x styrf-s t is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that,n0ppbdvj 14gwiyxf 5 - 2rw8z corresponds to a displacement amplitude of vibrating air molecules o, 4dr-f2108n vw pzp 5xwygijbf 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soun+e l :p5/dgzijd level to seem as loud as a 100-Hz tone that ji5ldp/ +g:ezhas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frcaw;k)hkl 2my oa g-;(w2,0t6w xe aduequencies that an ear can detect when the soune2lw-ctw06( amkxahgdoy );,w2;ku a d level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What idqs: isy1i. ;:sv ks*ls the ratio of highest sis:;:yl1 v. isqd*skto 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 fundamental0el,omi qbkczja56s )1;w 4t u frequency 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 string be placed?j );,c0ozqbkuw51 si tl a6m4e    N

  An organ pipe is 112 cm long. What are the fundamental and fi.p /ni,qc0 dy)xid :tarst three audible overtones if thdqtp.id,0n)iya/x c: e 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 blozv8 .ilbq 2y rqp3pvdi ,dk-9xo)m 57awing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube dk8.l3pdr72qii-xpb5oqv z,v9)ma y?    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 spannin)8 aiozda o/) -u1gllng the range of human hearinl)gna o)i- ad1uoz8l/g (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as 6snn ld2v+;wg its third harmonic. What will be its fundamentnwndl 2s;v g+6al frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7 5co1 gjq )jo,0npf2lam6 w2jye k9*nb3 m long and is tuned to play E above middle C (3qfpj yj 2oe *m109aw)cjl5bk 6onng,230 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the lengc n8)irxtt 16cxue rb*v(r-s 6th of an open organ pipe that emits middle C (262 Hz) when the temperaturee8svnur 6-ric xc* t)61 (rbtx 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 20 . 5,hvgpus 2bar8ea1n $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute wo2-pk.5 aeznin Example 12–10 should the hole be that must be wn.ka-oe2pz 5uncovered 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 2fb-st/z*) zb ye-3+e zey8pw p64 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. ( w z8py+-e/z- fe3te *b)szpbya) 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 ends. It resonates xprz;t m cm00*at two successive harmonics of frequencies 275 Hz and 330 Hz. What is pt 00xz;*mcmr
(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 pozieu +u d93jm:z 5g1$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-lotf6 .wpb lx(4zng organ pi.pt bl (6zw4xfpe 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 lkwytz)r6 e)is q. a*7to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship ols7at6y.*zk )eq )r iwf 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 th+q5qdp(xx2.ut e1y drying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is t5(d.qxq21dph t uyx e+he other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and 5 ..y7v o:qt:+pi spomkdpup 2$C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz,921nzh , gwqcv while another (brand X) operates at an unknown frequency. If neither whistle can zh wqg9v,2 1ncbe 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 beats/s wh3z+oc ri5d iocv++ z4kg:gr;ben sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz r+4od+g:rizci3 b+o vc kgz;5 tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The 3 oci058thoqnp:g mf 7tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playe:qgct 5po7hf03 inm o8d together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if twftej.-(ku 7x io identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and thfe( j.tuk 7-xie other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks / mu/eca16m o;lyfvwl,,ih9p, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is o6y1piaehlm9 fu c,,; /v/wml 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. mbslmdwq59/- p3zv s xaqyhb2v 974/gA person stands 3.00 m from one speaker and 3.50 m fr3 -zqm2 myv9s d9 p/5lvg7a4/qsxb bhwom 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 a x 6fitnj34ntehc:j;4 t 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played6it4:3n;n x het fc4jj together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m inq,8uzxvr q efhj8+1w 2 air. How many beats per second will be heard? (8,j2qxv eh u8f1z+r wqAssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fiwbhm,gnf et :d93,mu: re engine’s siren is 1550 Hz when at rest. What fg9 hef ,nwbt :3d:u,mmrequency 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 iftf 8-zbuxj ww3byl7h6 2(r.c w a fire engine whose siren emits at 1550 Hz moves at a spee- 6b2u 3lj.8xrw7ctw (bzhfwyd of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourcacx/:kl b bn 24g5ai ycdgl4*-e is moving toward you at 15 m/s versus you moving/l4 4b-aiy cgc xlk5d2 n:b*ga toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same singl1 b, g+:ykc vz6udcsu:e frequency horn. 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 cg1k cz,bduy +:su6:vof 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 receives them j kb)hr . hnh9b)1fq/)eh vg-dreturned from an object moving directly away from it at 25 m/s What is the re/)q)9 1ebnvhg fb.d hhrkj -h)ceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a t1e+fv1m9sh an di04m speed of 5 m/s As it flies, the bat emits an ultrasonie1tfdvm+s4i m a1h 0n9c 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 n l irfm+i5)1aDoppler experiments, a tuba was played on a moving flat train car at a frequen) 1fmlnrii +5acy 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 ultrasoun: /i 5*heqbcd;5qhh hsiti3a,d waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from thet3 / hie5hqhiqi: h5ca;*dsb, sound source?   Hz

  The Doppler effect using ultrasonicmmrff0;,,:sxn)1xg g. r,jib xxom; b 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 frm25xopj n7ak:*( vzucaev/-j g - ;davequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who-/*7 v;jm -unzv5 a jxpagko( vc2:eda 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 movingycgq5it,53 fv on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What is 0*uu.pt t bkh vl0xq(wd2.dx.the angle the shock wave makes with the direction of the airplane’s motp tv.x( 0x.2*wuhtdl qu0dk.bion?    $^{\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 pla9j;1v)8ta azyltq2( hka8brenet where the speed of sound is only aboualy;k)(r hbq8 e t9t 2aja18zvt 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the oc (:..vqt3e1kfe/ffk q*ortq jio nl:7 ean. Determine the shock wave angle it ok.e / 7:ttiql(:f*v fj rqoq3f .nke1produces
(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 2 jwlp3ky0n+a $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the g+a.k c;/tj2bxac ao .wround flying faster than the speed of sound. By the ti+c 2k;tob.aacx awj /.me 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 pulseses5* h v( . (at(od2s:lezk q9auc:nas downward from the bottom of the boat, and then detects eche(nd*eua5:ltsqh c. a(o z(2k:s a9svoes. 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 the human audible raf(mhcg1) f8is- w vwem h9ay75nge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a bw)nc,vdu3l7c o 1e2wdisplay called a sewer pipe symphony. It consists of many plastic pipes w 71l2)cvdc u,b3woneof 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 m31t6 x uc b/2:fkycipq from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such q/kib6p :3ccytuf1x2 mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound 1 c ijx:favz8 l/d.*rbn6q8pw and an 87-dB sound are heard simu r: 1ciqf d*anwx8bj6z vlp/8.ltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is r8 d2blznn-yra :rp5rnh *y3j:ex*,c105 dB. What is the acoustic power output (W) of the speaker, assumi5rpn n-rdyr3:2zbr *c* ha,:l8yjxn eng it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops bn45ok.;thf uzy 10 dB at 15 kHz. What is the power output in watts at 15 kutohz. ;4 fn5kHz?    dB

  Workers around jet aircraft tyk r.ofe;j+ vrp:g,k-r pically wear protective devices over 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 the power interc .opg;-:rv, jrfr+ekk epted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the )6s-xn-a1sx rfym: o ogain, $\beta$ 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 frequency 1o8,k8 :sg yqjc$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with t6jo fhf s;90ta fundamental frequency of 440 Hz and a massf0;hf tsojt 96 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 vert -emk -9g/pvww d8hg+hical open tube filled with water (Fig. 12–35). Tm gd89+h- -hgk /vwpewhe 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 tuning fork?   Hz

  A 75-cm-long guitar string ofbdk k7tvg33+w mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the thirdb 73+3 vtwdgkk harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate a 4g7yt *skow-ks 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 cominw 8dk5x;vq8r ehf y: msu,y5;og from two sources. The sound is loudest a:yfur, 8ehd 5 5;mqok8swv ;yxt 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 stationary. The conductor on1*hmm8 1g*l6usr 9nwno*y akz the stationary train hears a 3.0-Hz bem rklg8ow6*n**1 z9ay1nuhms at frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you i0 xibwz e2+w4ps 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast 2 e0bx+iw wz4pwas the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the 7g)c5:op:d3sgec d e v +1hmeyspeed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cas+1) e ce gdg5p7oev:: hd3mycrs. 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, soundinrx26uo3j44n*u u; nz g6mgnim g together, produce a beat frequency of 11 Hz. The shorter one is6oz4uj4gu3x*n2 g n u; 6irmmn 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves ps764k xofsp6cast 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 the speakers, at B, and (c) he hears the speakers after they havx76c4oskps 6fe passed him, at C?

  If the velocity of blood flow in the aorta is normally aboux,+ 2c8mm1hz;nh o+m 10jbdq2wxi m hut 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? Assume that the waves travel wit1mhjnh1++;0u8d2cx2x hi zw m ,mqm boh 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 to g:urxyxsm fdj)*91 -tward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off t j-duxgxr 1y)*mfts9:he moth?    kHz

  A bat emits a series of high frequency sound pulses as it appr8xl0gob( s 4htoaches 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 sobh 4txls( 8g0o that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vilm zrqhnni24f 5a)s76x lage 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 (on5 qx) a fmi62n4s7hrzr G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromib+d yyq25s56 3ptzwacsed by the presence of standing waves, wh3+bw5 dcqyz t5 yasp62ich can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involveb w9nslh6 liwc,6 4sy6s 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. For a 90-cm-long csw nll64i,h6w9by6 s rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at.,d.t d yn;srj a frequency of abou.tns;ydr d j.,t 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 hears the sonkj-.egtmh0un5f2 hwua9*1at ic boom 1.5 min after the plane passes directly overhead. What is the pla9t5 e-0nh1gku*.fh wu ta2a mjne’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1- *7iyle zoku;5 $^{\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