What is the evidence that sound trav ca8b .tn jmu/;0cop7zels as a wave?

What is the evidence thatm6d xc :k3v6nj;av5 rm sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a stridrvt) * ln.*zqy n(s,w7tssl/ q 4z0ewng to the bottoms of two paper cups. When the string is stretched and a child speaks i s lqz ed,lyw/)(wn .t40rvqst*7zns*nto 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 or w )9a7b 1oe0qf*4q aqrbt+lqpvavelength to chang 7aatevqf90 bo4l*q1rpq) bq+e?

What evidence can you give that then 6.bm s4pu5qp1g1q lr/abkobe(8jq; speed of sound in air does not depend signif8(b;m sj46bpq.g q1kp5rquloebna /1icantly on frequency?

The voice of a person who has inha2eh/ggmo++wj+a: r0e lo wjr1led helium sounds very high-pitched. Why?

How will the air temperature in a room 1dldq:6(feimaffect the pitch of organ pipes?

Explain how a tube might be used) wex :v8p0bkp as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car mu0x :vwp)8e kbpffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as y4y+kt cr6lw0 cou move up the fingerboard tok64 t yccwrl0+ward the bridge?

A noisy truck approach(e8,v 7p7szr3h g8isv9v dry ies you from behind a building. Initially you hear it but cannot see it. When ves3z(r 8p 7v8r,sg7 yihdvi9 it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats o8.eoenkw g89fb+by - can be said to be due to “interference in tinb -gfe 8.w9+obeyo8 kme.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woulk-aty )9v :omaf,1v5fa3bsnhd the points D and C (where destructive and constructive interference occur) move farther apart or ctf:sy) f an1ha,o9 v5m va-kb3loser together?

Traditional methods of pr+d zq mb0+y1kxotecting 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 +dx01 yqbkmz +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 thoughtjpp;rhi1.2ptw. x 2v flso( o8 of as a superposition of two sound o(o1phfp2. l.xsr8v itjw p;2waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source x-jz hrlqz7;b ;x i2z21. mnqaand observer move in the same direction, with the same velocita12 .hqznx 2b-r q;xz7i;z jmly? Explain.

If a wind is blowing, will this alter the frequency of tbcdin 1.vg9*p ;fauhkh / l7.qhe sound heard by a person at rest with respect to the source? Is the wavelength or velocity chan/l9* gf hac p. .nbk;vh1d7uqiged?

Figure 12–32 shows various positions of a child in motion on a swing.ia vpux()+( 1ly+q aic A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest freq viqc)uip+xa(1 l+y a(uency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by lisoosqbz(c4j d..7a h *stening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 4scdshz oojq7*.ab(. s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterliak0 ;h 6j,hwb/ v35znjst,soine. 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? Assabv,swsj6honi;3jk z,t h50/ume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 )pna p5g+:kds$^{\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 sv:,z8, (rdr tp g):9ngp twbyechool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fi ,,9n:ybtdggprt)r 8:epv z( wg. 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 ckv4 reuzs-u v, kk,*y4dyw:7tliff. The splash it makes when striking the water below is heard 3.5 s later. How hi,-kruy7sk*yezdv:utv4, w4k gh is the cliff?    m

  A person, with his ear to the ground, sees a hu5y yxd*;ne. yj 7baa;zge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apab;.xye ;z 5aa7*ny djyrt. 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-second rulevk;ch ;)*fy jd7et gz4” for estimating the distance from a lightning strike if tzkecgdh;4y 7jfv;)*the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 12cfaj; x*xcm*(0 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 inten0 8dog g;uc5bcsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pabf lss96 o+nwi,g.( rroduce a sound level of 95 dB when fired simultaneously at a certain place, what wilw+9 srnlbi g.f,o(6sal be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain d7gnnyi3cjh,6 9j ubncb, c,:ristance from an airplane with four equally noisy jet engines is experien39cjy rn7,icnjcb gnu,h6b:, cing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas yxor0 a7bb..hfor a CD player it is 95 dB. What is hbay7 x0b..o rthe ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output oftls(wv lpf;vv-:cu 4; sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth(-:tlf v vlcvps;4u ;w. $\approx$    $ \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 r.y(s g2 -i 2v04lge4obim5p+o pwi lyarea 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 modestz6zup d.nw5;ipp17,6 xak ta j 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 loudspeaker connected in turn to each amp. 6t judxpnkwia1.,;azz 75 6pp$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a cj5lz sw(g17fj fvr10dB meter registered 130 dB when placed 2.8 m in front of a loudspeakers7lz0gjffw1 v(j rc15 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 /e6x :e 928bbgypaykj)fqrt,level of 2.0 dB. What is the ratio of teyj )2tqfy/gb,:ke p69 a8rbx he amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the 9u88m3 (;hke5 )cr vsetcuwppintensity increase? Increase by a factor ofchvp8ect5u w 3urs(9;8m)k ep    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampllr9mfkd 7 r3d(3cze 1zc+9arxw *n -skitudes, but one has twice the frequency of the other. What is the ratio of their intensities?*1c9ldwkaz crnf- mx(9 3+z7 rde3rks   

  What would be the sound level (in dB) of a sound wave in air ts 3ki zat(;/cw z 9tj4fr0k8hghat corresponds to a displacement amplitude of vibrating air molecules of kkzshi8;(j9zr3 t4w a0 cf/tg 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level t 8petq992 xzmxow n8.so seem as loud as a 100-Hz tone that has a 50-dB soun9xm2wptxne.q 8 9sz o8d level? (See Fig. 12–6.)    dB

What are the lowest and highest freumj94zn8fgpk ;)j)iu ( hmkp1 quencies that an ear can detect when the sound level is hupu49gp kzj;)8(m)mi 1fjk n30 dB? (See Fig. 12–6.)

  Your auditory system can accommow5w*:6,vz xjot7 cm-u y(h;q0ccg yyjdate a huge range of sound levels. What is the ratio of highest to lowest i(zc 7juq;xc0c*tw5y6gjvm- wy,yh:o ntensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length of se p.+p8.5 7 bal)cmolb(wteuthe vibratel.+e)mab uwp l7st op 58.cb(ing portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Wwpf 7)- :un77pirl1upm5fx xe hat are the fundamental and first three audible overtones i pp7wf-ri5e1xlf7 :n7u ux)mpf the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across t+utt (5tbvy+q e)avr(vg0s0hb/*uq)ukr ha-he top of an empty soda bottle that is 18 cm deep, if you u((sgur+ hbqb*ea5tv r)0kq atth)y+/v-uv0assumed 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/doeh3 q : )ttealyo8t7tn *x. 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 lengths of . o /t:dy3t t8)noqhe*ax e7tlpipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequenz,iwnu(i pl.+c- w4rsy) 8 vwscy of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of-)l i wwvu (.w8prnsczy+si4, its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abo xysp*6+kg51 t f-fuhdn4oy*n ve middle C (3f4fo-1hy ks 6x+t*y*upnd 5 gn30 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 length of an open organ pipe th8 m+yrji)hhjgwd s t k6-166wjat emits middle C (262 Hz) when the tj6-jhykgi 6m1 + wth68sdjw )remperature 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 f xh9ahp2ly pw,7kympm ( ,zv(vw.3 3eat 20 $^{\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 t;t 1g7 fd1kd.stt -fa i ;tce8llqgh93p( hij7hat must be uncovered to ple3 hjtt;9.1(i;lt qi gf 77dsctghlk 1-apdf8ay 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 aia6i. mko(k2qt 264 Hz, 440 Hz, and 616 Hz, but not at any imk.2aq(koi 6other frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two sucf3mmcm)4x a-h cessive harmonics of freq-a3mh mcmfx )4uencies 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 h/vr5qr n/q(u $^{\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 presentkw4y .dwb2eb8 within the audible range for a 2.14-m-long organ pipwb .b2y8dk4e we 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 to the outside hfd:kt 4e8b sw9k1v-/ypes)gve+x k4 dffl//and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear ca/ef d /ewgvhfk4bk-/8ls:4y+v9td) 1s ek xpfnal. 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 .kdq i+sl y,1lp lddw53yfu6,jz6 w ;sone beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is3 jkfsyul1l5ddw . 66z+spw;d ,,ylq i the other string? ±    Hz

  What is the beat frequency if middle C (2s, vu*gqztkor,a8ix:h1 / 5ya62 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while anoth6yd0i) 3ieo /ebkzeal b/kp /0er (brand X) operates at an unknown frequency. If neither wi/3lk6 ipea/0 bd0 bzeeoy/ k)histle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 .l:yj;) e;szespl hk*.cm 6mf 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 vibrationalyjsl6 .h cp;kzm:;fs*m le).e frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the gu8 +gwsh* rayid, 20wsame frequency, 294 Hz. The tension in one string is then decreased b+ga02srw8uih, w dg y*y 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fluf fz94kz85cbxe* )bkates each try to play middle C (262 Hz), but 8 zfkbace9xb4zk f)*5 one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, Ak3ev nq3m vwy p8: gyr/in67j7, 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 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and7p/: y jkvrm8e7n3 vyg 63wqni 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 o :by +3fm3s ekjejl)a9ne speaker and 3.50 m from thee 9k+)j mbyal3:jes3f 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 Hv1j)- n ul bqv;z:g si,/sta1xz, but a piano tuner hears three beats every 2.0 s wh1 :q;g1,ui/)z sxv-s jlanvb ten they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.fg njb3f+mtj,8- xl a664 m and 2.76 m in air. How many beats per second wil lxngb-fma+t 3f6jj8,l be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren0:y 0t qnw,nlf is 1550 Hz when at rest. What frequency do you deq0tl0ny,w f:ntect 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 detectq6isr2v8k c.aj t;hckqgf(+e-wbb i/ :(ul o- if a fire engine whose siren emits at 1550 Hz moves at a speeqs q(r2j+g- wbcea/:ct;fibu-i l( o8. kk6 hvd of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency ifeucbsrh6vkzzt84 be2 f2 qf8 i,62 xw0.*fsvy a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are w 66y*v,hr88t2qxs z. f2b iebfzf2 u 4vskce0they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency h je86(5+c-(e c ffplu3s,lkm. znj2yppobu: horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hekhbfm enly -ocpl56c:uz( + u(38, f.epjs2jpars 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.mr)fgvn u/5w4jtwjryo3ev (3k;k n 6 )0 kHz and receives them returned from an object moving directly away from it at 25 m/s What 3v(/y3ronj4 vm);jkwn) gtw65krf e u is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wal y f-zyju4;c49wmha)d l at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wa hyzw u9y-fm4) jdc4;ave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopp3d az8)rphl94 tcm ue3ler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a s4 l9 ua)8mzp 3e3dchrtecond 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-b)ixs3;cpf;mf ber aonc ,g 9y l,i-77flow 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 f; xna )e ,gcof3ibmy7r, 7s;ci9l-bpin large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect ut v7x1q 35lqtbet l3s*sing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570v4tps6:mpnhoa k 4wj :ir2w00 Hz. When the wind velocity is 12 m/s from the north, what n6jhtm2iv4rk p w: wsa40op: 0frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at kc+a353xpr: kuq q vxy:s84kr 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) Whao7w-833s-p 8 tqwwshwwufw+ dt is the angle the shock wo hw-tw3d3s8u w wp7s wf8-qw+ave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sound i0,)s9xylbv- h;kcg sds only about 35 m0g kd)h bs lsy,xv-;9c/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 ocean. Determinek2dri h,d v68s81 t)odtyrn*i the shock wave angle it pr2yn8,dt6r rhii dots)d *8v1koduces
(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 i ), 2.y6rx4xjrz brmep;hh0t $/theta$ 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 ground flyfzja: o 8,1uss +(: iqjwb+cfxing faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Deter( ocixjfw:u1: jazfsq,+s+ 8bmine
(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 rezb mma6au13 n;t )i4sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is design;atu ez)i1m4m b63raned 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 rangexayajz6(fc 2vgg( n83 r ;x3ax? $\approx$    octaves (Round to the nearest integer)

  A science museum has r2.ak)wy4 s*dil;asvha6q 1w a display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, w4kl )viw;qa*wy 6ad12 .hsasrhich 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 / dk bb cm+ztg1gl).j.u(2qrkfrom a person makes a sound close to the threshold of humum2l .1g+r j/t. zkkcbdb()gq an hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when a nf 5h.*agl(5bfd l/nnet;g8cn 82-dB sound and an 87-dB sound are heard simultaneously?tgl;ge(ncd* na5f fn.8/ hl 5b    dB

  The sound level 12.0 m from an y kd ya1-z2nw1y*5ka loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, as1awy y d k*nkyazn1-52suming it radiates equally in all directions?    W

  A stereo amplifier is rated at (1h r9bqf l;d5 cru;sc150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outpr;s 9h(rqf 5bc dul1;cut in watts at 15 kHz?    dB

  Workers around jet airx++myuw0ov3p craft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 14v x+o 3ymwp+u00 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gaz7/ zjnbwlt*k a0 98apin, $\beta$ 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 vioaju.l3 9oo,4 j )twyyxlin is tuned to a frequency 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 between fixed points n nl 4xyg-jcxqreowf23 /*j0k 5 1h.otwith a fundamental frequenc.-x/o h*rnke cf5wojxn0 4q3 l1tg yj2y of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a verg rm e7kn 5c/w kyo8:kw1igj,l5w1p:a tical open tube filled with water (Fig. 12–35). The water leki :1w/kpogkww57 rge nm yaj1l:c5,8vel 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 of mass k3k0c5ejqz ypcp 0() r2.10 g is near a tube that is open at one end and also 75 cm long. How much tensc5k0p) 3(ck0jpz y erqion 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 observjiekw3dm v m;j80v a ,.i1c/lbed 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 coming+dlh7g pu.7 ll from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is min+7h .l lupgdl7imal 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 tra)h/ /r9q;a v:mh . r gqw6lmcx;ug5iahin is stationary. The conductor on the stationary train hears a 3.0-Hz beatw;mg;mxh9ai):r l.ra/quq /6h v h5 gc 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 is 538 Hz. Afterg:nd1r /)a6)nl kylie it passes you, igi1ak: )enl)6/yrdln ts frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening m j54fp6vm o,gto the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as i,5o6mp4vmfj gt goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, v/l1fx.p,xss obnma2+t w-x0 produce a beat frequency of 11 Hz. The shorter one is 2.40 m long+ns xt of/s ,wvp xx.-mla02b1. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as3 a/r/qnk8ryj it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identicarq/rn j3yka/8l 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 0.32 m/s what beaf:g: dw3r qkh5nu/ ;:kpb*eqqt frequency would you expect if 5.50-MHz ultrasound wavgd:uqq/f3k:* w5 enqk;rbhp: es 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 mothh62s8mn ad :)s 22bqdutx:taf at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wa2muas6sfqt82b dt :hxd :a2)nve of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequencjcd)q*k 4:azly sound pulses as it approaches a moth. The pulses are4) kc*j qzl:da approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. l4zir ez+j 8,a12–38) 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 onlz8,aj+ zi er4ly one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence 1z i1a.jlp+ulo52zjkof 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 theklj2pal 1.j5oiu+z 1z fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstratihrq.m k+5) pso *;dfwhon, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. sq)h*r fpkd+;.5mwhoWith 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 threshold of hearing for fpoq46c gsn 5b+ n d(/eblr,,pthe human ear at a frequency of abouto 6+prq5 4/ bnn ,bf(lgdpce,s 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. 5xx(/jwu 0pw/pg 9aosAn observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitus(axu9p op 0wj5/g/wx de?    $ \times10^{4 }$ m

  The wake of a speedbosh ft+0ddy sz3 q35i5gat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h