What is the evidence that sound travels as a wa kirwrj0v :o-wqd,cbb+),2 otve?

What is the evidence that sound is a form o1;pbxy6g),nfhjv 0 ot f energy?

Children sometimes play with a homemade “telemheg*w +tr+28 z*kil wphone” by attaching a string 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 cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the oth 8wg+h+z2irmtklw*e * er.

When a sound wave passes from air xwla 6agn9e9;fg.x1ep9+uls m :hl x 0into water, do you expect the frequency or wavelength to changusea nghx09le+.lf;6 ml9a x1 9pw:gxe?

What evidence can you give that the speu;za9 qd- .t z)9zei+il9yc + tzb4piked of sound in air does not depend significiyz+i-b)tep 49t 9zd.kz ;z+c aqu l9iantly on frequency?

The voice of a person who has inhaled helium sou39p(fvrx nn(yo wi)s sreco)9( yq/l+nds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipeckb1xq nhd10+s?

Explain how a tube might be used asqxp( r.xdb hft 29zcr2bx4e:/ a filter to reduce the amplitude of sounds in vari4b22r9cx h/dezfb.pt:r q x (xous frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togetmbf 8ewd5jjw/u0 t*6 xher as you move up the fingerdj u ft8wb6 /j50*emwxboard toward the bridge?

A noisy truck approaches you from behind a builrpit,.ow- b/ cg:df.yding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is sudd:,.d .ircwfoyt/ bgp-enly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said nn*7cagxsx8-0z pp0o to be due to “interference in space,” whereas beats can be said to be due to “inopa*xx7gn8s0-0 zc pnterference in time.” Explain.

In Fig. 12–16, if the frequency of the sp8 geu4zbuvfo7ti6 . k4eakers were lowered, would the points D and C (where destructive and constructive interferenc8 itob .vf6gu4e 7ku4ze occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who wor.fzx6j1 di-z ck 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 to the ambient noise. How could adding more noise reduce the sound levels6x d 1-izf.zcj reaching the ears?

Consider the two waves s/1ohznfmw -8 q2l,hik2q x fx+hown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves withwm, +/kqx8 nlihq21zohf -x 2f 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 ando 8yj q2 s3;t+nrqr(lr observer move in the same direction, with the same velocity? E r jsn8lr3 o+2qr(q;tyxplain.

If a wind is blowing, will this 2) pozmtz2(3qgtw7hh 2/n ru halter the frequency of the sound heard by a person at res 7m h2w2orht(zzu)h/2npqgt3t with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitort7y8 l** uup, )beurud is blowing a whistle in front of the child o b ,7*)t 8uyuudp*urlen 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( 4x *fxfe y6wsohxt61xg5( hx her shout reflected by a clify*sxeg6(1x(h6 oh wxtx 5 x4fff at the far end of the 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 below the wouv 26 pt63o r7bcn-zdaterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep 66c 23orut7nzdop-bv 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 wa+ hsjq 8o3exz.+ylz4hvelengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is driftinw b6sqktm .a35g just above a school of tuna 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)k5 ma qb3.ws6t by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The spla pxh8l v7c0uohff16+ 9g .dphpsh it makes when striking the water below is heard 3.5pd60.v h7x1p 9chughp+l ffo8 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge4h4/-ofadv -ey9m ruvw6g ab+)d qa4g 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, a4)e6v ua/49brda g vw a m4qy-hdgof+-nd 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 b y91 xt9xv+sznnp/-h“5-second rule” for estimating the distance from a-bs p9nxxn9 1zvh+/ty lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soundxl/c63ial stb*m/cmrg 4 n-f, at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of t7ga 820onk 37iqxlgip)8i qf a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound2f b9unpsrbj-w-/g t, level of 95 dB when fired simultaneously at a certain place, what will b-,-u/bfpts2j 9b nrg we the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from a6wr8 1b 1*ircm3gzzpdn airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience m1 1gw*r3zdpib r z68cif the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a k9zev q+9ics-signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensit9szevc 9-+ki qies of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power os2a* nw7;mn 5 2t*q fwym4wratutput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered4a2;y5w2 smra7wn* mw fnt*tq on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum wb7dlh ej)ud) n .412oqzufc2tji0+ s mhose 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 B is rae0hz27s;jwd*q be( b oted 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 ampsbo2w *(e bqj7e hz0d;.$I_{250}$ =    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 130 dB when placed 2.8 mha-e ,7nw7xg n2c4k9tzzg 3nr in front of a loudspztgk hex 3r 7 2nwgnz-4,9a7nceaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Wq ohc 4*g qrgv1y(6(lmthg*59 9dttwrhat is the ratio of the amplitudes of two so*y (6 lrq wt1gq4 tmr9vt*d9c gh5(oghunds 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 y /5z/lxbjjl(0p ma0z intensity increase?0l/ jp/jzl5m x(za y0b Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplit xh1xfeyeayfde3ma9+.bh ;g/.,x jn ng. ir/ 1udes, but one has twice the frequency of t1jxfhr.,y 1mh/n/exgg yad+ee . ibf 9 x;a3.nhe other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in v 1f+k ywn*dm4gl1 jb8air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?f1v + *nm4kg8bwj yd1l    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tonad5dgr:(s4sy e that has a 50-dB sound level?(gd sas5yd4r : (See Fig. 12–6.)    dB

What are the lowest jr9p3+a)sgu6ke hh1k and highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.) kh kg9aer1+3) su jhp6

  Your auditory system can accommodate a huge range of sound levels. What isp; 8,twnhn nnnhiiwe0418p-e the ratio of highest to lowesnnp;ew4e1h p-inn 0ihn8, w 8tt intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz-sr;*u .s zc4t -rlosk. The length of the vibratingtls;rco 4.s-s* rku-z 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. What are thgit(q5.daz dag:n 5du zo;-bt:n.ir8e fundamental and first three audible overtones if the pipe ii nb58azdit.od- rqnug z(d: at g;.5:s
(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 enqpl 1poinf +1)c mc-7xpect from blowing across the top of an empty soda bottle that is 18 cm deep, if+cpnl 71)1 ofmq-icp n you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning thelm w,o*ov fs*s-p2w;7zw w3xb range of human hearing (20 Hz to 20 kHz), what would be the range of ;xf-z mop*swvw2sb o, w73l*wthe 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 z6ni, bu dzovdn//z3*ku n:f+its third harmonic. What will be its fundamental frequency if it+3zz:oku,unv znd6i* nb/ d/f is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string p rnw tm 685/lgnjdi; e0c/hk5is 0.73 m long and is tuned to play E above middle C (330 ;0hjtni/p8gm/d56l rkc 5n weHz).
(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 m+v+ ,ivwc3ieng2w0urr0h4d d iddle C (262 Hz) when the temperature rv ni+ vc2+ ,hue040wr dgi3wdis 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 e1tr0,r-yzs 6k;gwpx z0sd6s 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–whto)ea, pc3q wy)g ti78 6e:x10 should the hole be that must be uhoeac:p 7x)ei) t, y8w3wq6 gtncovered 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 264a(z hnf2zuw- 7:coz)v Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show ow : u-z)n7v(chzz fa2why 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 en +rd8nprw4i(c ds. It resonates at two successive harmonics of frequencr c (ir4pnd+8wies 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 n upi2l/9 r8e57jwd8m z-znqly,d c2i$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present wdvh d-x ao5(o+ t++- 7daeopsqithin the audible range for a 2.14-m-long organ pipe at 2do t xe+ dqoav h-dpas+o+(7-50 $^{\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 -7*ad: qqlrw ezmvz ;2zu;id-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 reu-wdd z;l :r*eva;-qz7 im2zq lationship 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 adjust two stringsu3.ua+ kwpf 5r r(utu0, one of which is sounding 440 Hz. How far off in frequenct uf05uu.r 3ru(wp+ kay is the other string? ±    Hz

  What is the beat freqhj wtm8x);7afu psqqzq9 ;w.1uency 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, while another (brand8dfughe+8n/)4.1 ivfisakh r X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of freque)4nre ku s.ig8ff/+ahi1 hd8v ncy 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fksw-kx:vs-i1q4kn x 4ork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning. sx1-qk4-is:n4 wkk xv    Hz

  Two violin strings are tuned to the same frequenyqv)+*xe:d (a5dqzi: b5tgdr cy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequencyq5ddtxygb : r5d)v +e: i(q*az heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes + *9jasbke7rib1 f g4 z4mos8beach try to play middle C (262 Hz), but oneig8 k944msajef*sbbb1rzo +7 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 frequency o lf9y40ju06bg8 o pdpbf 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 fpd8y0j069guob 4blp 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 p*m g.e3jou0;*uxxmnl2cm5 ny erson stands 3.00 m from one speaker and 3.50 xj*2 xuo3nmg 0ycuml 5*ne;.mm 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 supposed to vmndp k(.b59iv3iir x+*z;,tzs er/bbe vibrating at 132 Hz, but a piano tuner hears three beats every 2.(vz;/n53+rkb ieit zr9i . bdm xsv,p*0 s when 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 2.64 m and 2.76 m in air9ki9jdmc8 h: h. How many beats per se9h8idkc9j :hmcond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engbpexzz 3.b) 36u.kbeline’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/s z .u3bbx 6k3b) ze.ple
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engil bmt) l2g)6vmba: i(tne whose siren emits at 1550 Hz moves at a spalt b :i mgbmtv)l)26(eed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source ifs w)gt.(s5r f1eltvk: w2t c3s moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two f)(twslvs 53t fw c 12etkg.:rfrequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is aw( -snq. q4 :aak dum92b2f/sa 9jibrxt rest and the other fqrawn a 9x/24. (usba b qmki:-s2dj9is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sox mnn6s)/jjr)pxp gv71w // axund waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound freque/jpn sn)jga)/7 xpm1rwx 6/xvncy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an nsnu *t7zj )7cultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wa)tus zj*7c nn7ve?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a m uj(z 3d0bs1ppe6hqc2;rf5w aoving 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 m1zwu6 psa(fbjd5h2c;p3e 0q r/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure b 5t2/ +a n-j6vzhkmjijlh; y,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 frequez2 jl+,nh bav 5/;kh-j 6itjmyncy if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultradau m)yxx+*u0l2 e8ow sonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velrg;qgo/ uk2s7,g t6x bocity is 12 m/s from the north, what frequency will obsers; /b q6,ugt r2oxgg7kvers 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 ctk e -9 2 s:-3/utg*wurh.3b ubi)ah9nezmrmat 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 (2tb m/u kj*jk;8 (twg.tto hzthe speed of sound is 310 m/s (a) What is the angle the shock wave makes with(8t* . k kw; (bgtm2jj/utztho 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 ohb)2 ak 8s ce-xq) t1yzpyyyw+6tj m*5f a planet where the speed of sound is only about 35 my5axetb k 1-s 8)t2c*6hyp+mwzyjqy ) /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 3ibgu*d 40iygnn-p4ez oa (c+ the shock wave angle it po*-ca +4 niyegb(3ug40dzi n produces
(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 (gux5/kn -u2cn-eb odiyd/6wnc3 do / $/theta$ 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 exact 8h;vi :4ola3-is8ji/u txuculy 1.5 km above the ground flying 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. Determ-8 sxcv3loi;/uta u ui4:h8 ijine
(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 d/xbmr/ d+s;w kevice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echd s+k b/mrw/x;oes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the85f9p jn;qf8z oqp7ur human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Its1g;encurw u:4 ,ps9l consists of many plastic pipes of various lengths, which a1p:,s9;ncw suur4lgere 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 from a person m(svdas8-/cy:i dnu 7 qakes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 su7cqdy8 ais:sdn u/( -vch mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound ;ad 7z-c(5t4rf2cki (e gmrbc and an 87-dB sound are heard simultaneously57rbcgridte-c ( m;fk2 cza4( ?    dB

  The sound level 12.0 au)y4d/kn*o-nj hcqm)48l vxm from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equa))* xayjl n4cnq4uk8 -o /hdmvlly in all directions?    W

  A stereo amplifier is rated ajj,ph+ x;)wohost z;l).3nj at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? .h)ts3;;l+)hxpjo, j zw jona   dB

  Workers around jet aircraft typically wear prote l uz7: h*mdwco(n.hm2ctive devices over their ears. Assume that the sound level of a jet airplane engine, at a d mdzc7(*:mn uw2 ho.lhistance 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 intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicai9pevyr-2t m3; vp3m7dr fh6x tions 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 tunedvy3dszb /:b d; 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 with a fundament (*vmc) k3( gkg+djpnfal frequency of 440 Hz andkfmpk n( jvg*)(g3 c+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 vertical open tube filled w gtef +y- .rz j-)g0u slnn1ov1)lfxc4ith water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in thu1f nrxn zsgjel 0-. gf l)4to+vc-1)ye 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 2.10 g is near a tube that is open at onuqdc(8ju 6z 5iux,esk4yp6 8o e end and also 75 cm long. How much tension should be in the string if it is to produce resonau8 ucu86osj5 ,pdiqe4 (x 6zkynce (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loo7 kz97h4yfiq cr) qmm7c7h v9rp ($\frac{1}{2}\lambda$) 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 fr(x/rj x r(iqti(yb:u(om 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 minimal at a point 0.34 m far(ir(ib qy( /:rjx(xu tther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statiohw*821hp; n-le veykm d9nka.nary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the otv 2n8yla9mk*nh- e1.dh k p;ewher 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. Afkxxto 7g8.jmby2jr:p+8l ( ijter it passes y7xkml8.jyrp(t xj2 o 8i gjb+:ou, its 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 to theussv7gmur-j9k ; t*2c difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full oct r-s*mkj9 ct72ugs;v uave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together;v01k m9vplpwrs+xg n;0 c kt3, produce a beat frequency of 11 Hz. The sp;p9k3w gns+r c0kx v1 ;lmt0vhorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past /l ku aur7kuhlh29qqg1wb m : k /p1)3o6qu;ora stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) k7m qh;lrkwup1r /u2hg)k: 169boluaq oqu3 /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 0.32ysny cv g4p0.+ m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected fr0v. scnyg4+pyom the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flc nzxke3r-:;c+4s do tying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects3 +4odsn:t c;ezrck -x off the moth?    kHz

  A bat emits a series of high frequenb,. 2d nignx4 99xpqwlv,7e ypcy sound pulses as 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 retu9 7ib d,x9 qpwy,2pnlx4.evgnrns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vcwfo4g)8/gb(d9 ed2k hrhl 0rillage 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 dh0 4bg92kf(/8e rwd rlco hg)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 sted,eweg: 8xk,wreo listening 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, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this roomxweed kwg:,,8 .
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, d3)o*a01 tnvft(ue1 y 5 ejeqaslender 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 emitef *j10 ao3)uedt (yqtva 1en5 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 fdp00 .jlsk+zc or the human ear at a frequency of aboutl0kj +sp zd.0c 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the -grw t2 r lk*pfn6y f36m)8vjhsonic boom 1.5 min after the plane passes directly overhead. What iv 8)*6rgrt f6ky-2lfp3j hmnws the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatp ,i.4udsk:wcc.n e kix v022gt1t ce* 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