What is the evidence that sound travels assrs ;t/rb.3i phv) dzy9k;;se a wave?

What is the evidence that sound is a form of energyuza73 bl)x8 fioei +2q?

Children sometimes play with sipw8*s p0ng: 2/rgaga homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a childspprw*8:n/gs i2a0g g 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,v43w u;hx0mr en s,y:0zrw0+ wdwy 4tv do you expect the frequency or wavelength to c :, +rw4dw4wxe tzv3u0y;rvny0 h ws0mhange?

What evidence can you give that the speed of sound in air does no(udq)co tj5cby bw m1677 eoi9t depend signif yuo6 d9 oweb j7bcq(mict)751icantly on frequency?

The voice of a person who has inhaled helium sounds vec -0,j(jspk, mm d*vinry high-pitched. Why?

How will the air temperature in a room affect thhenmhlk w /psn ;j-io+d)y.0+6/wrb le pitch of organ pipes?

Explain how a tube m 5eiqzs 81k jcsiay+f7zs1c3z,9j* gkight be used as a filter to reduce the amplitude of sounds in variouyazqi z s csf1k+3e87kz59cjg,j* 1iss frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move .z5:- ejs;bm3gbyql .z cenm(up the fing e;yl:z5.gc(3nzq .eb m-bsmjerboard toward the bridge?

A noisy truck approaches you from behin4h-pee3gn1sm r8 6kqqenh/5v d a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Secti/hnpeh 5m61q 4n-eqsr3g8e kvon 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas bz jjgz60/7n,ezdae /heats can be said to be due to “interference in timeng6zze7 h/ ,0de/zjj a.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points)* x)rhxvgkkid 0 )ejo+4* yrt D and C (where destructive antgorv kkhx4**x) y)i rj e+d)0d constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas withz cgm 0i be 0,chaa;:4rkyt/w0 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. Ie kc0gb,:;0i hzyar 4mt cw/0anstead, 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 ofiayh9dqs7 o3;t mf0n6 as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (;0tym9sq d7 ia3o n6hfa) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obhh6qk:48//va si c-saiffq7albekt 7yc ;e02 server move in the same direction, with the i;h is:7saf-akq6ec42y7kq atv80h/e/bcfl same velocity? Explain.

If a wind is blowing, will th.+g,f +7qhd niwx8- jdom; kla:efi d+is alter the frequency of the sound heard by a person at rest with respect to the source? Is the wav. f;qdgfj, lam+- :xe dwn8k7 doh+i+ielength or velocity changed?

Figure 12–32 shows various positions of a child in motiu k4m+idit fs) q40*f4slqu;won on a swing. 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 frequency for*iu +twi4 ;)0df ks4qquf sl4m the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her smq:gkcf-yt mn2ov -j ,g/ f(j5hout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting.ym2fcvm t/gn-kj:qj(- 5o f,g Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He ,ezpkxa2in9 ( hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and (pikx,29naz edoes not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in as u ak1bto2mgj c;920dir 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 ot ux( 3w6vgy)a4,ixbk6eyjh: n a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elaps y,4 e h):ikt6(bxjy36a wgvuxes 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 m;s3g f:rl0 ejt:3qtitakes when striking the water below is heard 3.5 s later. How high is the cliff?3eir ;gt3 qf:0st:jlt    m

  A person, with his ear to the ground, sees a huge stone strike tyc:d wl;l od.8he concrete pavement. A wc.dl;o8yld :moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. 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 rnqx :mi6:ac f) 7hxs9rule” for estimating the distance from a lightning strike if the temperature is (6hsqx )9c in7x :rm:afa) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thej;wn hl 2e3s7p 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 intensity . mg6/,l8+sgldwemmnr 6km o 1is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaned e2m2/-vhu uvously at a certain place, what will be the sound level if only one is exploded?eu -2dvhm 2uv/ [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wrk,cts, *quq1bn* +a a8rj2h pith 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 engine? [Hint: Add intensij+u q2snc1kaphq8**ar ,tb ,rties, not dB’s.]    dB

  A cassette player is said to have a signalb o)vdvhw4xz+ .l l01bl ;o3xh*zc+ fb-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the o+ vx)z0;vb lbxhzd.4 1w 3*c+lbhfolratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person 8 gix*iw,jwn*speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mout*g, jni *iw8xwh. $\approx$    $ \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 s+m1mrwfjlyg :ol4t j .;jf q4,trikes an eardrum 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 amplifier Bh)pfq;-wfm* m,guq .- gwfyg5 is rated at 40 W. (a) Estimate the sound level in decibels you would expect atuf)- fg *h5pqg ;-yf ,mgwmwq. 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 130n* z wu d6:wy8iq*co1u dB when placed 2.8 m in front of a locou1 yd8q6 wu :z*w*niudspeaker 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 d c0p hr 7rfntjfr50k7-B. What is the0jr 50k h-f cp77nfrtr ratio of the 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 theg d0-2mzubuj7 intensity increase? Incrd7 20j ugbzmu-ease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement axz ,t/vxk;w b)mplitudes, but one has twice the frequency of the other. What is the ratio of their intensities? w;tv,/x kxb)z   

  What would be the sound level (in dB) of a sound wave in air that correspondispug(ehn5h8h- s3d yt0+g m2s to a displ-0y2i58gduems 3( sgn+ hp hthacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have w10 v k 27;,hdi.qxlip7c ,plwusnw8jnhat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound levvk u.7n ldw0,w7 j8p;,1nxlciq 2i pshel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that zf*f4u ) g,g3r q2qecean ear can detect when the sound level is 30 g)qu42*ergff 3zqec, dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge r(uk3ho -0 sp osadwm2ul)6oxp ioy;1 )ange of sound levels. What is the ratio of highest to lowest intensity3o ly;io6ps2 o(kh-wpu0)smu1) d o ax 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 (d4vx gxx2zr(0fymj 4(avmb)of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what t( yfmm(xa )4dj42z r(vv0 xgbxension must the string be placed?    N

  An organ pipe is 112 cm losej3wa: *qc a(ic2;dbng. What are the fundamental and first three audible ov abjq(*:3sdcc;e2a i wertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expec6b2rbv +lyz9z.)ve fot from blowing across the top of an empty soda bottle that is 18 cm deep, if you ass+v62evl 9)f bozb zry.umed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pip3hprf y9-ok7 ) 1c3cwf1ktvj res spanning the range of human hearing (20 Hz to 20 kHz), what would be3 jkfhkr- f7rco wvt13y1)9cp 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 v w kx823g qyeg4x-fckdue;,,Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 604,de, g;3 yxcqk x2u-8fvegkw% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middj63w)yy 7)hsov,asm ule C h,va6uo7 s3y )jwym)s(330 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 that emits middle C (262 Ht()f3.edz (n; kluu vez) when the temperk;dl .en)ut u(3(fev zature 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 d.q;.fo t6:vx* ycx xr8t;a8q9okmp i20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the f) o+ppe a32/1osun qj bz/9tknlute in Example 12–10 should the hole be that must an)+b/nko 1up z/eq j93tosp2be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 61,lykwa* rk t x2tl88y.o- ;.visv:koj6 Hz, but not at any other frequencies in between. (a) Show why this i; i8tklx, s.jvoya:yrw-2 ot*vk8k. ls 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 9eb qqdz4tqgu2 20-(baki0w htwo successive harmonics of frequencies 275 Hz and g(b2uzb 4 -0we0dtqaik9 2hqq330 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 18u/4 uy23 sy3 mraqdp qsbi+b$^{\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 preselb+nz.fhp g 038hcik* nt within the audible range for a 2.14-m-long organ pippk c* +ngh iz3fh8lb.0e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm loy,deet4pe:p/ ng. It is open to 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 eep:dy4/, pte 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 evrd/l5 w zqz4n8ery 2.0 s when trying to adjust two strings, one of whizzlw 8d/5nq4rch is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz twrwciyl9,c-f: :x0d5vn ee*) 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 another (brand X) opert urng o: h1yrum k6ljpp3071:ates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 r07jkl3utrn:hp m :yp6 ogu11 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produe1jcvh1* s e v:zb6:chces 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 vibrational frequ b: hj*sc61 h1evcz:veency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the so + ;udo5k6 +tbbwuw8mt 2re(kj6pnp; ame frequency, 294 Hz. The tension in one string is then decreasedw pn; k6p5rowetotd bkbum (+8;u +j62 by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle3 w*7*mm50 vzv 4njagkb 4emre C (262mkbw jm*0a4m5*nevzrg7v e34 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a .laz8 / ek4fp e6nawy/frequency of 441 Hz; when A and B are sounded together,8ew/kn4az lp fae6y./ 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 and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.xgd4fij m33izm 2 8bi-w .fjy*ipqg/200 m from one speaker and 3.50 mfd fw8qm 34-yjbg2ji2mp*i.zig3xi/ from 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 t5( kq(,l;klm;c 1nimxzi da1 supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the f(z,mqkk (d 1 15nlt;;lixiamc requency 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 )z jlk mp6)wur.hgn*2f ioq z)q;-p42 mxx8kpof wavelengths 2.64 m and 2.76 m in air. How many beats per second will be hezk 4) )o8 pmqi gkp)m*-.qn; xwh6x2 ulz2frjpard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 15/l7fjzvp9x3 y 50 Hz when at rest. What frequency do you detect if yo/ 7fv9 zlyx3jpu move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sireqj 0x(e(5f3rxm*ja8kc* rjpjn emits at 1550 jp(0kr x(j8aj* f c5rxmeq3j*Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source isbti ru*)3i4ml: o23hqadiwuei9u)f * moving toward you at 15 m/s versus you moving toward it at 15 bri *qdfl)4ui iut3wu2hi em:o3a *)9m/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 equippn(gr 5b ,7 lpu2pz3.sp ystsu1ed with the same single 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 of 5.5 Hz. tnlpg ,y1bs2735 u spp.zsur( What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wavesp4gs(z,zjv t7b1 d p8a at 50.0 kHz and receives them returned from an object moving 8 b4pvg,dp(tj s1z 7zadirectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wj9y *r(kr;a poall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wavr9yjr(pao*;k e?    $ \times10^{4}$ Hz

  In one of the original Doppler expe3jwm;.p7ds 1co cq2fj riments, 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 10 mqf1o ;. 3ms j2cdcj7pw/s ?   Hz

  A Doppler flow meter uses ultrasound waves tutbfh m3r 8-9majv/4 3u;qzny9a. eayo 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 the9am3ht94aa/ qzu 8yu vbmf -3e;ryn.j expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of freqg 864ombzyy6vt3pgd 2uency $2.25 \times10^{ 6}$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 sw fdwr8ti,)/lqs xl 86i9; nvmound of frequency 570 Hz. When the wind velocity is 12 m/s from the north,l/r;8i ,lxmi wqdf9) wv86t ns what frequency 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 ij6c--bl 2(wyglwsmr. r +-wl p(fa4 hif 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 sounb* m h xo;0;kmlvqo(2cd is 310 m/s (a) What is the angle the shock wave makes w; qb o*lomk20 ;hx(vmcith 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 thn faktlp0k5, /, 5/w-.hqlufw v3w auye speed of sound is onlykyaaw/5,w tf.uv lf,wq-p 5 l0nk/3hu about 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 ocean. Determine the shock d/l1ms,,fox )mf , sehwave angle it proe/ ,, lms)fhs1,fm oxdduces
(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 ejt4s dc ye4n74 yd3v9f3 clr/lha q;6$/theta$ 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 ao3ldzxwe6 xp355x s9ubove the ground flying faster than the speed of sound. By the time you hear the 55x u3lpx6zw ed93o sxsonic 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 pulseso /;u6f bz*fid downward from the bottom of the boat, and then detects echoes. If the maximuff i u/z6bod*;m depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how macj-y1uq y8zt .ny octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called ybwk vc 3k754 /zx,kt k7zv( q6oje-lxa sewer pipe symphony. It consists of many plastic pipes of various lengths, which kt o5 x7bv3v6lewjck,(4y-z 7kk/zqxare 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 m3 sry*igb03 3ue;fu wd from a person makes a sound close to the threshold of human hearing (0 dB). What will b3d0u su f; *w3gerbyi3e the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound 3 bx77z;ixlop and an 87-dB sound are heard biz3p l;x7o7x simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed i0 o7a7)+ (on xci+qvdh.mw izkn the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directionx.hn)v7 0qk+dzc o iw7o+iam(s?    W

  A stereo amplifier is rated at 150 W output at 10.i tfi1c)jc5b 00 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts a.it cj )f51bcit 15 kHz?    dB

  Workers around jet aircraft tupw 9rciq 4zco6g q3z7x;et/;ypically 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 intq;reo39zp7w6zgx ;tqcuic 4/ercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatio f)sl q9fg-oyhy+1* sins systems, 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 frequency usf .q ,yc*/cl7qnbl51$\frac{1}{2}$ 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 w6l 8bj2ji a//obt(jciith a fundamental frequency of 440 Hz an2 jiai8tb (/cjbl/jo6 d 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 vertdk3r e5v+7xp( m6 hzdcical 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 thz3m(hredxvck5 p+ 6 d7e 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 c2d,vjl8+ d6 iamhv *aqt6 7qu2.10 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 third harmonic in the tdhj6vc26*umqaiqv8 d l+ a,7 tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatez,mu 1gkik5 8 z0kx:k)wpf qd2 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 from two sources.e.tu //z)x6r/ i3a 6nck tm8;jevdx .cqun:mt The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds tharc63 niu/kc .8)m evq;jtzuen dmt /6ax. t/:xt 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 wh5j 3tmcn bk vl:q(y0d0istles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when tb0 nc3q ml: tv0(ydj5khe other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam trai2kv (34tg -pvsbj ..yzih)jlbn whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocijbp( z- tyv32b).hlvgkij4.sty)?    m/s

  At a race track, you can estimate the speed of cars just by listening t /lg o;;u0nmgpo the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of anmg ogl0/u p;; certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency owtqcel wf p826i,f, ;df 11 Hz. The shorter one is 2.40 m long. q t6dpcwfel,iw2,8;f How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past (/, cmhmwjc4wgl q;.qa 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 qlj 4qm,(/.cww;mg c hwhen (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 8rnp3lcqnguus+6h2 5rm) 5 zz0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the redps3+guu8 2cr znnqh5)rzlm65 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 g(,y t6c dc2s6qur)9 w7)yj6plqqntl at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. 2gwj lysqqc6nu6q69c()dt, tplry7 ) 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 frequency sound pulses as t5sl ii s71w4abniq)9 it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emits n7 i b9)5a1i4lwiqstted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villasy9kp hsk 3sg; rbnyrg3g 1nzu*/k:dj4,z 4*jge to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12ny*/b;3zsk g3jry kd*g uhjgspz4 sk ,9:n 14r–3.) Model as an open tube.

  Room acoustics for stereo lqqypy w ac+rd-v45h1wi/ j; h7istening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4. h;+j w5c7/r-v4qd qph1yawiy 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 “she4p3c4cnf( ea +)xdg3) ei-(qw snq uinging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. Witci(+eehqg-x 4(w3us3) qn pna4)df ceh 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 the human ed19z7qakvr+c/nl , vw *;c s2i5gomq far at a frequency of about 10s2,q9k7daonwi/vqrc ;z* f5cg1 +vm l00 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 o df i5m(o*tm3l fde38hears the sonic boom 1.5 min after th3d(i ftod3eom8 5l m*fe plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat kz2)nfvf 12kz6sp. t2sz gvw;q8x( lxis 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