What is the evidence that sound tra-oft8xp-f3u a2+njx fvels as a wave?

What is the evidence3 :f9g mhqtag7 that sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string oeksb zt* 315l9g1 fhoto the bottoms of two paper cups. When the string is stretched and a child speaks into one cup,kos l 3* fozbh91e1tg5 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 pat blo+*6 8ktayiqbb; 9sses from air into water, do you expect the frequency or wavelength to chany*k b;8oa qbtt96+ lbige?

What evidence can you give that the speed of sound i)bd :sn n 3-zu 0q+yyk62pekvqn air does not depend signif:ebsqpkv n6q nu) y+z-20y 3kdicantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why?dir99r2 ian3hkf 6 e)1 ckfwc:

How will the air temperature iz pg, )ai /*hxumj))qz mh/,9oblyhe)n a room affect the pitch of organ pipes?

Explain how a tube might be uso)a ;( cd lu1ci19incted as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car c1d(na1ctli) c; i o9umuffler.)

Why are the frets on a guitar (Fig. 12–30) spaced cl k(ldd;h7qogel2l7-kc2dj6tx:bh+ uoser together as you move up the fingerglk: d(h27j -u2dcol7 6bdex htq+kl; board toward the bridge?

A noisy truck approaches you from behind a building. Initially y p* 0jpsxd,x3pou 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 Section 11–1 dxj3xs,ppp0*5 on diffraction.]

Standing waves can be said to be due to “interference in space,”2ohvp o2qp4 7 y.n3cra whereas beats can be said to be due to 3hyvap.rono274q c2 p “interference in time.” Explain.

In Fig. 12–16, if the *db+)x ni8yb6wgzgh4 frequency of the speakers were lowered, would the points D and C (where destructive and constructive interferencegn+y)6b *hx z8gd4biw occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in arejbm5 *6-q8te2tan amo as 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 nm2j -o b5t aqa*8m6teblock the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two wav9pul -oe5, +n,vbd mares shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different freq,ep vun9rd5mb,-+a oluencies, 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 and observer movz3 ynihd1l(;f*up9 up e in the same direction, with the same velocity? Exp*ynf1 i 9l(;zuphd3p ulain.

If a wind is blowing, w8a y/ 9xagh6t1qn w6tkf 9wuq0. nuas(ill this alter the frequency of the sound heard by a person at rest with resp6n s9uqtfa6xa0/ay9(whug.n1 wk8t q ect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motiono/f/; c-v kaoxddz u rk5o5u-, on a swing. A monitor is blowing a whistle in front of the child on the ground. At which positioxc; uuv,kork/d 5-f/azo-o5 dn, 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 echooay5m;k17z j5 lrkp-4)ds s-rt q s1tg of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. p-sg j5-kr 4z517q;1r)madyssktto l$\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of i-47ldk.5+mm kpn lgpr wc50*( tvwmjhis ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume th*t 0mwgc5 i(.kl v+-pkr 7ldpwmj n4m5e speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2dl8/mz lwtt530 $^{\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 drifti1h8,qh3 tpujc/ti+ph .k5cwda8exa )ng 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) by the h+t.hhca8,d1 3 / eiuw8 qtcp5j)xpak fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking (nd 7z/9b5 flnjs5gvpyuw0q9 the water below is heard 3.5 s l q5y dl9 buzp/50fn9w7vn(jgs ater. How high is the cliff?    m

  A person, with his e1. gwwg 1gie0 n5f (hhftjg;5j. 5zljpar to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are hear jihtg 5hjj1wg 01fp.w5 ef;g(5.gnlzd 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-sec z.h y-acpq+.xxp s1w6ond rule” for estimating the distance from a lightning strike if the temperature is (.s +xa-p c.p6wyh1 zqxa) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1 ybm3*4hwu ( ;duvyc+a20 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 intensit1ej.98a rzpyky is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sojtr m2l :cm3 yyl92(bkund level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is explodedclyj9ly( b trkm:23m 2? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally n-zq zblbn.t4/*urg7 n oisy jet engines is experiencing a sound level bordb z/r7ubnqz 4glt.n *-ering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal(7 b1c( p;imlr i,ivqqibnp70-to-noise ratio of 58 dB, whereas for a CD player it is b,i;bpnicp (mvqr70q( li 71i 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 normal conver *m.oxjs* epsm nw65u.sation. Use Table 12–2. Assume the sound spreads roughly unifx*.np6.*s 5wje mu omsormly 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 eardrum whose aree x 91dj:c,mjwa 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 rl;xjh xfpns0 ae,7n/w0/bk)cated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a;/xcewk /)l 00ajx,np7hs nbf 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 130 dB when placed 2kp(ofje +6pt ;.8 m in front of a loudspeaker tj6 ;(fk p+peoon 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. Wha3l8t48wp yg xucyat :2t is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectiotwx8u 3la:tpc8y2g y4 n 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what l+z )jz pzr z,y+28aiw fg1gh-factor will the intensial8w yjgh++ rz-fg zi1z 2)p,zty increase? Increase 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 twice the 8 by;fk+ .w 2s*tv rksnu5w-utfrequency of theks*8.u5fy n-trkbw+ vt;s2u w other. What is the ratio of their intensities?   

  What would be the sound i,tsg vc4 0hw).sp waji81t2o level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.1i)s vo.iw sja401 w2pt, 8tgch3 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud uzh (6lux3 .aras a 100-Hz tone that has a al x(. uuhr36z50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highix6y)a/ 6mgwr1f g6 nxycr*i-est frequencies that an ear can detect when the sounx6w*1 gigmnfxr)/ y y6cia- 6rd level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge ranf7d*clr(7rr x ge of sound levels. What is the ratio of highest to lowest int lr(d7xrfc* r7ensity 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. pp,vywi; 1c)h The length of the vibratiwiv ph ),1ypc;ng 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 the fundamental 1m2d1 .jl /yx -cuwebhand first three audible overtones if the ph2bxuy. c/ ml-j w11edipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across t:o 6i7z2 y.futa ,jjjtap8lxu+4nc y2he top of an emp ujpxto6l caj,ufyaz2i427 :n .j8y +tty soda bottle that is 18 cm deep, 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 build a pipe organ with open-tube pipes spanning the rangf ah5t1k-ld 7cxx41yle of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required5- h c1 7x1ldatxkyfl4? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540u*th dl* u+w7jf7)ejf+ 0legp25ebxs Hz as its third harmonic. What will be its fundamental freqeghe5+ p julj s0f2be*u7 txdf+wl*)7uency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mrj9kg9 e/;k/w *njsaliddle C (wj/;nglr99akjkse */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 -9mv-) um2b.*c1eg ubxd rpxm emits middle C (262 Hz) when the temperu1dmbvpm.xb- e)*mc- 2u 9xrg ature 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 sjlc6 s s2 d(yi:zo(thy+b57o 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 Exaez8+ o-bg hi)yo,jxy )mple 12–10 should the hole be that mu-+y o)xyjebz)ig 8ho ,st be 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 6 tul:nsgo( 3sgc ,rb,7y9rh( 3tae 9z2s(afcy16 Hz, but not at any otl3s aacyner bt9s2 ((: rgf9uo7, ,hct(zy3sgher frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It *9l6fezaq -dgresonates at two successive harmonics off z9e*qga-d 6l frequencies 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 k/j 4feo:gr: pnsifqf485;p tftaz2 6t2 qo5v$^{\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 wigjy,,3xk/4tygia- rcthin the audible range for a 2.14-m-long organ pipe at 20g,iyxja 4c-t3gr,k/y $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm p :ay,nl sn+*e0eo nq-long. It is open to the outside and is closed at the other end by the eonn0q s:*y nal,p-e +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 adjust twos.pa d y4t p+v0p.p3li strings, one of which is sounding 440 Hz. How far off in i4dp3pys. 0l+p.vp atfrequency is the other string? ±    Hz

  What is the beat frequency if middle C (7o gn l*jf.d0qc ee8j0262 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 anotba(:uk/nuax8:dfx7e95qpbfou: m 5 nher (brand X) operates at an unknown frequency. If neither whist9xbeuf(/58unx7 : mk f:b:o5 adq apnule can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sou;h,l4r pm sxq7nded with a 350-Hz tuning fork and 9 beatqspmr;4h lx,7 s/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hudbwgnsakm ;4p7 -4:dvr2c8vz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard wh4dv w 2r:g84n va cmps-;dkb7uen 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 middle C2gqz-d) ai b/w (262 Hz), but one is at 5.0°C and the other at i wg qdb-/)z2a25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency o.0+kfywd(7u0 dcat 6fsjhq *tf 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. f w60qyc.st0+*atduk f(hjd7 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 3.00 m from one sp x:ri 4s8 fvkqd(3i*6qf7 hfwf qp;0maeaker and 3.54fd;kwaqf f(ri qx:msi8qvfh6 3p*7 00 m 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 be vibrating at 132 Hz, but a pianm ihr* r)spjb,fk46jxfo :)7z o tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrr, z :i rs7o6f)bjk fjp*x)4mhating 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 aq d r4fx61x9 ;omb(s3rgqoe6a ir. How many beats per second will be heard? (Assume T q6g9o6x qboe (d xrmf;s1r4a3 = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is k (ay+ o4f*l,lckl4ht1550 Hz when at rest. What frequency do you detect if you move with a speek4l f(o+*ht kaly,4lcd 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 rim +z-nbu,z9 whose siren emits atmr b-u,nz+9z i 1550 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 is moving te7,yp dbe,u 3doward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactlybe,py3d7ue d, 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 sinc4v3 + apf2zywgle 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. What is the frequency th acy+f3 pvw24ze horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends oial3pd-ctj p,+ 5x.tvu zq 24vzc4p8zut ultrasonic sound waves at 50.0 kHz and receives them returned from tzi4v2-a,zdujpxct3 5vzqp8 4.p c+ lan 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 it flies, the ziqv+m2mug)g66ci ci-vdq 7 ows )*a+bat emits an ultrasonic sound wavu7ii+c6w6v-2*g qvo)zmd c +i)sm agqe with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopp2:8pj xh, ,j*+s kmn3lzrse juler experiments, a tuba was played on a moving flat trjm+rjnsejsz: *,k 823h,l u xpain 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 m/s ?   Hz

  A Doppler flow meter ucb k v twj5rf/tv8 cn7ao73k;4.vo6tvses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 Movvn; c6 7k3bw/torft 8a v7jvtc5k.4 Hz, 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 sound source?   Hz

  The Doppler effect using c5 4 kd*bntra2/rtiz+ ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits syav -g5e)2kmy ound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequengk m)yy5-vae2 cy 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 t ;,3ti5toh obxmwq)a;s/p 1gif its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What is p 7bls92 .mf /y6dgscfc f/wx.the angle the shock wave makes with the direction of .s p9ygl 7 sxcbc.fwmf2 //f6dthe 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 atmoszrswv-mro1j1 ,9p w/y9ect 2vphere of a planet where the speed of sound is only ab /1wr1ws9 -tcy v,m2poje9vzr out 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 wave aa+kdj)xj+-br 6 o- qe1; vfgkwngle j -ebkgwdv ;oxq-16a)f +rj+kit 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 t:h / e04;uwbjtg kr2y$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and o8spvd0s97(j,t rifjrl4gr 2 see a plane exactly 1.5 km above the ground flying fa8op, 7trsj 2lv09rs(4drij gfster 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 device that sensab *t2ey:pm;ds 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which:pt2masby* ;e it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible13e24) oijpttyaonq9 g,x ja . range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a x,skhhp 7ip,0sewer pipe symphony. It consists of many plastic pipes of variousxip,0 s,pkhh7 lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makb t;;.k-iuka gi.-b,ne9e:i pahlqs( es a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquit - . ,klt ai;bia-nebepu.sigq(9:k;h oes?    dB

  What is the resultant sound level when an 82-dB sound and an 87 h8fpjn4ju. wj h px43kt:ry20-dB sound are heard simultaneoujfh2k . wjpr8: 4ujy0tn34xhp sly?    dB

  The sound level 12.0 m from a loudspeaker, placed in th)8hy uh+,lxy1wt 8uhw 7btn7ie open, is 105 dB. What is the acoustic power output (W) of the speaker, ass8 htuhwb x8ly, 1) nw7htiy7+uuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dropas c 4jjs1fpd; pv06/js by 10 dB at 15 kHz. What is the power pcja1dp; /vfj 40j6s soutput in watts at 15 kHz?    dB

  Workers around jet aircraft typically we* dh8k. lx yn57w 4pwxmrw9e2kar 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.d * hk wxyexmkw9l847wp5r n2 average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sh*fz+vop +v x8r gx-myx:sc*/ystems, 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 frequewe.9ti y;i wr-1yaau( ncy 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 viol7x :1e xnx2hifin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length of x:n ie xf12h7x$6.1 \times10^{-4 }$ 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 iecj h;2j1 hwp5w )no2anto vibration above a vertical 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 the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level isn ejcwh w2ohp2)a ;j51 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 t)hg,z px)gdt n- wya c/*b:p(dhat 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 funtgx/p)w bad:(pn hyd),*zg-c damental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed l24qad ccx8u3m4na0f to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tn90j /e0sojlwone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 l wes090j/nojm farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statio7xdxmb;.6g 8zsp6ley nary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train app z x b.e67d;smly6x8gproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you)up ():1 yqa-otazaf i is 538 Hz. After it passes y:qafzyi p(a1 a-)otu )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 estimated*d0a 2 4 llisu*iy9m )8cmgtv the speed of cars just by listening to the difference in pitch of the engine noise between9*slym8ti igl*vm cd 0)4ud2a 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. How fast is it going?    m/s

  Two open organ pipes, sounding togelj,efl;5pweq l 3vp(r(1tl7r cw0bv(ther, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is theeel(rbrl7 pw(flp05v,3tc; v (w1lqj other?    m

Two loudspeakers are at opb0 g(b5j-pp pzposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) (b5p -zb gjpp0he 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 0.3,gwa:- p qmes62 m/s what beat frequency woul-g,e: amp6swq d you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at scup8o)lsup 7c l7pu),r 5 0ghen:)aeh peed 6.5 m/s while the moth is flying toward the bat at speed 5 hlhpe:)agp,)c n)0u 5s ucr7ou8le7pm/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it ap8rnloi jdm4v c6kp kw.5)ak 0so9cj -8proaches 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 okk -ocmc5dj v688 ksp .)w94rlja0nichirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals (83kxag lsocy5z1(4)yj myl gfrom one Alpine village to another. Since lower frequencyya4j zlyx(c s5( ym8g3)kg1lo 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 12–3.) Model as an open tube.

  Room acoustics for stereo list o +ct* a(st vlp-u3eu-an(av,ening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of t(-3tuena+va-(tpo u*cvs l,ahe pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singinge iz3ety 4f 84we*brrv xw*vcx1lp05, 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 p3i,fzber 44xx1 twlyv8e * ce5 wv0*rpractice, 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 ear at a frequency of 8,uxedxms w: 4:vyp5yabout 10m:x548 y,:puxe d vwsy00 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.;iu4prs ew 7y0o.xn9m0. An observer on the ground hears the sonic boom 1.5 min after the plane pas9ep;4yxru0ion.m7w s ses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbovff)0c8n ubte ; knl:2at 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