What is the evidence that sound travels a8* fsmai 8oc(ws a wave?

What is the evidence that sound is a fo4/hh)0 rhpc 1zrl /eqerm of energy?

Children sometimes play with a homemade “telephone” by attaching a s)fp 7kjci -oux.zlm49tring to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other lk)- 9zi.4fj7xm ucopcup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes w m6gquidd uqa ).z:;hm*u 79kfrom air into water, do you expect the frequency or wavele)a;id uzq6:7uhmu*dgmq 9.w kngth to change?

What evidence can you give that the speed of sound in airb-jq,,l -k3ncrwxqb m,mv3 qt-s li*cd5 lt5 + does not depend significantly on frequen,kbn3l-bv, d3irj-tqm5q , +xst-c5wml* cl qcy?

The voice of a person who has inhaled helium sounds vejp; gj1xh23 4m8jk xrkry high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipes? :8 8xqan6cpshl,d( rq

Explain how a tube might be used as a filt,sz.ps)u b6 sfer to reduce the amplitude of sounds in various. )upsf6 sbz,s frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spao) bvk:ohas89 ced closer together as you move up the fingsv)9o ab :o8kherboard toward the bridge?

A noisy truck approa clj)y91 ex3fo hdh67uches you from behind 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 ny93dhefl )uc617xoj hoise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,kyb y9:x*cg*hjx/tf/” whereas beats can 9jcxy b /hx:y*k* /gftbe said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woew/l1u 7/xjxct(i-7 ajpxt- t uld the points D and C (where destructive and constructive interference occur) move farther apj x/a -xc1u/t-jtpl7ei w7x(tart or closer together?

Traditional methods of 8 tf-la:w 6us3;ygyu9zxhy,3xbs *i kprotecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition 6btyxx*fy 3h,isk -;gyuwl9a83 su: zto 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 a7d3mjiov9 -jlh 8+dg h)4z pgus a superposition of two sound waves with slightly different frequencieslm3ij48ghz+g 9 -7) dpdhvouj, 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 sourv.l0a.yl zr 9hce and observer move in the same direction, with the same velocityv0lyr9ha .lz .? Explain.

If a wind is blowing, wingv 43c krcdp6al:, a(ll this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocitgncpral6,k 3a(d cv4:y changed?

Figure 12–32 shows various positions of a child in motion on a dd e )/7zltr-b9l4fqgswing. A monitor is blte-)lr4 /7 zb dlgd9qfowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her 4g,ykly 6ks 0h. lfa.b(pb di2shout reflected by a cliff at the far end of kp,al4iy. (0bkd2g ls bf .6yhthe lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just bebd4ga8qm ty4;ne s3 9vlow the waterline. He hears the echo of the sound reflected from the ocean floor ddqe4g t 34bs 9m;yan8virectly 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 with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths intd8cdh5uv(v6 xc l 1e( air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of ta+zao1r v- - +linras/una on a foggy day. Without warning, 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 -avr 1oan/-++zi slarthe fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makuoif pk-k7 a8:el,2 dies when striking the water below is heard 3.5 s later. How high is the cliff? il eiu2k,7daf-o: kp8    m

  A person, with his ear to the ground, sees a huge 31njf0rb3ry - p8mzfaf s,h0x stone strike the concrete pavement. A moment later two sounds are heard from tfmp,j-a38r3 b0x0 nrhysfz1fhe 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 y;t0e wo9a kok(c -+oidistance by the “5-second rule” for estimating the distance from a ligh(ykt cwk-oo ai e;+9o0tning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at xybe(d m/ww*7k s3cd 1the 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 soundaai shp950el7 tgi)in- w/yn+ whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pro 4c7ij/s +96p mbf*zfpyym gu;duce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only ongymmy /i ff4c7*s zp6+u p9j;be is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distancele g ;-axbwi5fj9 ms0; from an airplane with four equally noisy jet engines is experiencing a sound level bordex5 bls;g-f0wjmi 9; earing 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 havean1j z vfgid/e:w x;o +zfc(;, a signal-to-noise ratio of 58 dB, whereas for a CD player cxa;d:;ni (/vfz zow1,+ egfjit is 95 dB. What is the 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 of sound from a person speaking in normc9t .sd or:le2bij59mr)vk1 vxq5r, nal conversation. Use Table 12–2. Assume the sound spreads roughlr)qts vlx5:,2d mkce n 9vroib5j.9r1y 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 eardrr jrgx. +hk9s5a,uv5 dum 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 moda3qe+/-/r 7uzk4( d iojhgqsd w9iwp3 est amplifier B is rated a d-gp3 kideq auwrzwo9/hj is 4(/3q+7t 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a d/btfkxhzwd; 0- -.o ,8t0hij3 ahcz ziv o0j6dB meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stag3c vfj8 o00t hta6 i z.i/j-oz,-0;hxzhkddw be.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Whby;v:1z+ wbrsat is the r1vwsb; y:r+z batio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a snw pz4/m)md 5pound wave is tripled, (a) by what factor will the intensity increase? Inz4dw mm)5 npp/crease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has tw 7lt,o01i *azgm3p vleice the frequency of the other. What is th ,io0lmv7ap1 3elzgt *e ratio of their intensities?   

  What would be the sound level (in dB) oi:u)3 ; jud)vq;izv gmf a sound wave in air that corresponds to a;md;q)v:3 ujuv giz)i displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone thatc ub;p o+ppgbzcn q4j4dq l 393o*46ue has a 50-dB sound level? (See ebcluo*;pjqp pn 4boq9z + 63u34c4gdFig. 12–6.)    dB

What are the lowest and highest fres:sqn )j7wfn1wr-nl , quencies that an ear can detect when the sound level is 30 l7, 1ssw -jn fn)nqr:wdB? (See Fig. 12–6.)

  Your auditory system can accox/q u.yj8 r/nlmmodate a huge range of sound levels. What is the ratio of highest to ./qxlyujnr8/ 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 fundamentah9j yk2piy54v;zbt; xl frequency of 440 Hz. The length of the vibrating portion is 32 cm, avz94t;5pijy xhy ;2 bknd it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm s*uod )a t6kykpjpwk1 wgg9m0)p3 16 j1o ,osilong. What are the fundamental and first three audible overtones if the pipe is 9kj1gs6opd61o),akw m3 )p1 *yp 0js uk tiwog
(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 acz-)rh okajxvh*/ x wx 13tkp/d-8-denross the top of an empty soda bottle that is 18 cm dee3 te/odhkx-d -k )/rvxn8h xp w1jza*-p, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build06v cevwfa)xewvfj/1 *il3 j xz 9l-k; a pipe organ with open-tube pipes spanning the range of human hearing f-wwjleak)ifv0z36j *;1xe xc / vl9v (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 its third harmonic. What win7 m)yzxr.g3yr3 vg5i0jlvccndehm592* m 3 n ll be its fundamental frequency if it is fine3.dvgyyh0m)ml cn3gm z529rrjxn nciv35 * 7gered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to xk/,3n*krl1bk -ag9el/dy .hw t7 mxoplay E above middle C (330 Hz). 3l7 whn*ao9,mgld-e/ kt.kk / 1xxryb
(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 Hzb +(:, nrvev. zg6lxfq) when the temper:xv gq6,fl(b +ev z.rnature 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 ataf/h4 : hvyz-4ij4uq a 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 holfh) w+o1vs5pqe be that must be uncovered to play D above middle Cvqw )1hfo5+ ps 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 26 /c+h s 8vc0gcgio9b1w4 Hz, 440 Hz, and 616 Hz, but not at any+ cbhc918gocwi s /gv0 other 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 ion p88k:cj we)s open at both ends. It resonates at two successive harmonics of frequencies 275 Hz an)jec88nk ow: pd 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 p,219f7agv7 qpc73bodhw 3zfxg pbk m+w af)1$^{\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 presenk9,dce9m*v n qt within the audible range for a 2.14-m-long organ pipe an* e,9 dkqmcv9t 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 ooipf n6w)r2fon xt ,cp*e5(sf6/ssp0pen to the outside and is closed sp*pc5 ss fne)6nif tr2, (foxpw/60o at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjhfm)7k80wn m * sncm-un9e 0gcust two strings, one of which is sounding 440 Hz. How far off in n nkmcchnm0seufw)9-m87 g 0* frequency is the other string? ±    Hz

  What is the beat fre(i)3adocrl 1fh7 c.kuquency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz,s zt3/iv d4yft+p (v 2+duepa*3in.in while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a ui2( 3d .4dinnvfvstzi*3ty/ep++p 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 when gtryn 54nuh0-sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vihng n40yu-t5rbrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequenc2kjlm:ae5+a l ppds+x1vxp -e 8 kzz0-y, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Red-5jsx+a plkpv8 e1pl kz+-xem a20z:call Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to6gpv ds pf*/ 2ww)o,bp play middle C (262 Hz), but one is at 5.0,wwg)pob p2s/*6fdpv °C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A,fwh co7 +8bw+ 85uxthh 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 Cbt7 wch o58w8ufx+h h+? 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 stands3qk xwmyvfn20p qf97*d (yyu3 3.00 m from one speaker and 3.50 m from the other. q02*wf3k(du9x7 y 3pvqmyynf
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piank-, /cmm sg8ag/xoz6v o 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 frequency ofagxm /mgsoc/k,-8 z v6 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 2.74 nv:xzefq0v.6 m in air. How many beats per second will be heard?n.fevx:0 zvq 4 (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s scl3xp *(ai/ v:09x(t7w/ lycjf yw atsiren is 1550 Hz when at rest. What frequency p9ivx(/ac0s wtw3f : al/(yl7cy* jxt 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:j)* tuh8bi -hfl fno:. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a spe jh:in8 f:ulb)t-h fo*ed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sources0w n:fyl9 4uo is moving toward you at 15 m/s versus you : ols4y9w0unfmoving 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 equip3ibq 6k 7my9r9gb oyr9ped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 mbq9o my3gi7yr9b9r 6k/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz anv +u2av 8/gkkcgr:*dud receives them returned from gdkak +ugc:u2*8rv/van object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As ii1/9 r q8fyz.ecmvyn 8t flies, the bat emits an ultrasonic sound wa vf8cr1n/.9 yi8qemyz ve with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playex86xizx;xoca.+jnqwpb r (jw + c96m;d 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 statixj qp9 rx66cwb.nio+w( jc;+8mzxxa ;on at a speed of 10 m/s ?   Hz

  A Doppler flow meter u cj 9 jg0u;l mg(4s/nqzqtu.a0ses ultrasound 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 the soun jlsnzmj ;/gc0t0 4quug(9aq.d source?   Hz

  The Doppler effect using ultrasonic waves ofn,d+fef4si ,slsug p0j-dp4) 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 o75mzo)b+ n)5:nx gimkuvo x u4f frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are loci5 zxbvno )4mg5 uon7k:m ux+)ated, 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 h/p3ipc /q79jlwz w.cits 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 ip i7ua*.h4frxx m:by;s the angle hu *fx 4bx:.par7yim; the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the tfor 1diql2+/3j2hn2+ ucawtte,pe d; hin atmosphere of a planet where the speed of sound is only about 35 m/s2,jq2+fp1 o iat /ehu3r wnltce2d ;+d
(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 strikesv gl;29ofc.le the ocean. Determine the shock wave angle it produ.o2c ge9vllf; ces
(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 na 2bx77fslidzc y i/ 4,r.3cgssd5w .$/theta$ 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 a,+/qc9n0h qk uydgr6( z fp6nabove the ground flying 6 fa/(+u,d zyqgk9pchrn qn6 0faster 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. 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 deviceoxwyojl /0jcb8rkxv. q:4 a99 that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to worxq4 .woljvx:9jr9b k cy /08oak is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are thyzndq 2h/*)fuej ,k+q ere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer p5 *n(q,jgerdbipe symphony. It consists of many plastic pipes of various lengths, which are open on both e gb(,qerj*5 ndnds.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a personlu.3smpb yt 3/ makes a sound close to the threshold of human hearing (0 dB). What will be the soun. b3lsty/u mp3d level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound arev( gwtip0k4a7)v 6djhi u.n1 k heard simg p0akd)k.tvn7 6ih uw j4(1ivultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed e9t;l ec7ppy570-qliv v cb)(f vwko)in the open, is 105 dB. What is the acoustic power oubcovl ()p7cp;7 w-t 59kvfy0i qvee)ltput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powerp k0bxgq 9 6q,z, tw.ip+ux7g4g,rox h output drops by 10 dB at 15 kHz. What i67bo ,. 0 rgp4igp9,,z txxwkqguhx+qs the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective de 7q*+./ke ed(gvz*f na m:ighyvices 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 (g 7nd*e:q .vkaeh ymzi*+fg/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 syste )+ujja + ekgf/5kuvx1ms, 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 x1v)i4mx.p hl h1 et*ais 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 violi j3,tqcifbv cnp7t0)i i c3a75n is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length of ip,cc)f jcbt7 3qii 3705tvn a$6.1 \times10^{-4 }$ 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 vertical open tube filled withx70anxp3 a2n +sxfdi- water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork whxf+n ni3xsx- da02pa7en 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 striyz9g ix 7)tm p;,yqg3ang of mass 2.10 g is near a tube that is open at one end and g7pm; txy3qzy9,) gi aalso 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 tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loopr:qwb;d(i*k ;q g +y;z3kxb nf ($\frac{1}{2}\lambda$) 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 sourqslz7*39x ght 6 jwa 7+w0jasoces. The sound is loudest at points equidistant from the two sources. To determine exactly what the zo3s a q96sjwxahwtg+j0*l77frequency 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 condz*dzgks(r5t- p mg 9uc z0);yluctor on the stationary train hears a 3.0-Hz beat 0 gyz(u5dp*c;st9 ) m klzgz-rfrequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whisvi))g/tiq ra6ugwdn -.y7ylk. a m1t5tle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 H7-/ yaimtd.vl1 qn)g aryw ik5)g u.t6z. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can ejz w5sw6u620 w fol0sestimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. 0506owew sw6 2zjslfu How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat gwjz z(*nf m9 g,;h55d 9citlsfrequency of 11 Hz. The shorter one is 2.40 m long. How long is thmc;z5dinl9j*g z tgsf, hw 59(e other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past vab l;8c;0mk+ s9oga ma 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 thsavm c 08 a;lmob+;kg9e 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 normallyv4jo: 9:a)n.xnnlm)pa bkpp4 about 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 anp)pln bnmx .4):po:kv aj49cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward wab17f*9m kk.zi y 3kythe bat at speed 5 m/s The bat emits a sound wave of 51wf .7y*ym zi3ka1kb9 k.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 frequency sound pulses as it ap,m*ky..nm,h 6ja- wy ewbrk 3hproaches 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 cky..mk*, hebah6 yw-nwmr 3j,hirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once usicp u7v( im.;med 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 muu7(mimp. i c;vst 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 12–3.) Model as an open tube.

  Room acoustics for stereo listening ca pidn+i: +/ *+idutltwn be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. w++t+li:n/ipdtdi * u 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.qi,4vfa5jz mux g /w2 “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. With a little practice, the rod can be made to “sing,” or emit a clear, lo w2ma.i,xjgu4 vzq 5f/ud, 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 fe1;u3z* 3d kz 7hq tfccee(pv-or the human ear at a frequency of about 10vct7uz-e(ke3 1 cf*; hp qdze300 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 hea+g g-,a6 sayrars the sonic boom 1.5 min aftgag6+a,s a- yrer the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb4q-lsvt jb 6 a1(tkp;+o *mjisoat 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