What is the evidence that sound try 7t, 2i7d4*eu ujlakwavels as a wave?

What is the evidence that sound is a forpnc /7hpz() :2 etkheqm of energy?

Children sometimes playza5wtb p;:pgie4lk; .x+y t) x with a homemade “telephone” 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 g5 )4tb.xw :xetzpa;il+py; k can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do youwzki,qo1vs4l 8;o b 4k expect the frequency or wavelengk1k8iol z4 w;bsq4 ov,th to change?

What evidence can you give thahq ydioxx.g(f :38/ zbt the speed of sound in air does not depend significantly on freq fx hx3dy bz8:.q/iog(uency?

The voice of a person who has inhaled helium sounds verg*iew+9 tfi0ggld kmt;v w5; ,y high-pitched. Why?

How will the air temperature in a room affect the pitch oi( m4b4,/pyrnp1ne pxf organ pipes?

Explain how a tube might be used as a filter to reduce the oq5gh 3p(w0eef,h f7ramplitude of sounds in various frequency ranges. (Agqp(r ,hfo3w5f ee0h 7n example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer td7clj bmb;8p 4 2drgz:ogether as you move up thegcdml ;pdj4 b:b7 8r2z fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you flwo2sdfc,/zj 139eq3 vzye( b8cdm9 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 11–15 on diffraction.]q,9/ cecs 92b(mdvz3fefljz1 83yod w

Standing waves can be said to be due to “interference in space,” whero7v,rj*sb*y2 qdwcy 1 eas beats can be said to be due t*yws vocbyr,j 2q1*d7o “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poin ;bhh4 *fdji7c*, xtrmts D and C (where destructive and constructive interference occur) move farther apart or closer togeth 4c ;t,bm*h7jr *dxihfer?

Traditional methods of protecting the hearing of:9nl) uj 8/b:fzzblvb 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 to the ambient noise. How could 8 )nuzj/:9l: f bbbvlzadding more noise reduce the sound levels reaching the ears?

Consider the two waves s 1m.hm)odlm0hi-/i hmhown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which o m)i m li0mh.o/h-h1dmf 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 lq-2ocoq;n y,and observer move in the same direction, with the same velocity? Expl n2 ,qo;yqcol-ain.

If a wind is blowing, will this acxhdyi,j84 6fycgs :. lter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelengthxi.4h cdysg:f,6jcy8 or velocity changed?

Figure 12–32 shows various positions of a child in motlp*ibkw.k-8 e)2jtn)to(y+r dczfb*ehi 2 u 5ion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasdhobb8)rfpy- u 5i2j.( wz enc*i+ktekl* )2 toning.

  A hiker determines the length of a lake by listening for t -q,iux 3zs3/ae3nxrghe echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.rnxa3u,x gi 3qsz3e- /0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shiduqb enotx.) 8yu48npx 5a 4t*p 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 e4qtad54np* y. 88xxbo tun)u 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: rct9flt zf :f72nd: pkoubz,xq;gvq./r2.dvelengths 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 drifting just above a school of /r1qcs( jcz6*ck, kdjtuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elar6cq * d,jzc/k(1cj skpses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The spl. sju2xto0jr( ash it makes when striking the water below is hea2 o(xju 0jst.rrd 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concretez/ww,r1o-zdak8+ h js pavement. A moment later two sounds are heard from the impact: one travels in the ai r,d1 zw- k/owsj8+hzar 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 err xgrv4; 1oj9hy1 8qeib dfp+g,or made over one mile of distance by the “5-second rule” for estimating ;xhpv,r9d8jb 41 go1 e+ qyifgthe distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensit0t;tkazyvhgng. * ,m gb x80/ty of a sound 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 ofd9qa4n/nqrw 2mp zjg3)4a si79 u-hwx a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB +m j uadpv31a4when fired simultaneously at a certain place, what will be the sound l 4au1dmj+av3pevel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four e:tn ufrq9 :.ciqually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the :q:9ntru ci.fcaptain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio pr9 8xvro-kj:e:/ mexof 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the bk ro9: x8mrp/:-jveexackground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outputh 4ye;kjr q47q of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads rougehy q;kq47jr4 hly 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 eardrum whose areayo0tveq 16.qm 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 2 6v r de*4f3gccpq7od050 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in4o3gc7pv* fc0e6rd dq 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 dB meter ry(pkf-t6/r mf cbon -+egistered 130 dB when placed 2.8 m in front of a loudspeaker on the stfy-(m-f nck p+rb/6 otage.
(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 g+2jdl dyj.m(m8;y(+;ef fjlei/iny sound level of 2.0 dB. What is the ratio of the amplitudes jlji emg 2yd(/m;j8+lff ;e.n(yd +yiof two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled*19t7m5 tnhjhzobfr8 r3 ;zxz, (a) by what factor will the intensity increase? Increan8o ;z57xrtzrt93bjhm * f h1zse by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one3.kbcm x2g8br has twice the frequency of thebxgrc3 km 2.b8 other. What is the ratio of their intensities?   

  What would be the souw3fe (e/k/zwe nd level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of e 3 k(/wefz/we0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lev6m ip-6 09diwxh/abq pel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (qp6i i/h axbpw960-d mSee Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when thentyr:i o9(2xfws c2d g i6.a.4cwzxh9 sound level is 30 dB? (See Fig.r xc:hoz 9f ng( 4.s.wi 2td96wai2cyx 12–6.)

  Your auditory system can accommodate a huge ranal c-,*cioayoco,og*/gcfk4/2q (u dge of sound levels. What is the ratio of highest to lowest intens,g*cuq*(/ao/dyg24oo ccfo,i-cl akity 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 fundamentju 4g*zjvh8m+al frequency of 440 Hz. The length of the vibrating portion imj4gu v+8hz* js 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 lq7kal1 izqg.( a4x/gfong. What are the fundamental and first three audible o 4iq7(g/ zfax.lk 1gqavertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from 7bk 0s)mf8khxblowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a bhf0)m 8kxk7sclosed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe org4fl6 tt vwf.(qmm: qo-an with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pip-fo:lw tmm 6q.t v4(fqes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz asl*p 1wo xdty.x-ru-o6 its third harmonic. What will be its fundamental frequenc- ud61r - .pwtoox*xyly 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 tune 4uswto 1uh72pd to play E above middle C (330 7ht 1s24wuou pHz).
(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 pipsfsw; 0 6u (guqe.7kfjt6vh3ke that emits middle C (262 Hz) when the temperature is 21 . qjeu7whf30;tkvsku gsf6(6 $^{\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 20 h r*0bztl(2ds 2:t/jhm+arkw)*yihyg 0 xa/u$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpie qvt1dszeg:k310 5lqece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C ad:13 5eeqq skv0tlg z1t 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 264o:w5bj2mj yx4ve 2kj; Hz, 440 Hz, and 616 Hz, but not at any other frequencies o2ykx 2me5j b4w;j:vjin 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. Itufx 9quws9j d1 q2cr)*a: dwze:orj/7 resonates at two succee92 dj/adw9*rcw)1: qqo 7:urs fjzuxssive harmonics of 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 p9hen gf-*xe ssigprtf0x+ic, + 1n60 $^{\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 within the audible range for a 7yj.z y 7e1tymi;c. va6.q qa1mv+ hqipvso/*2.14-m-long organ pipe at 2+.q;mt a vmae1yvc7 .p/qjyi.* qzi17shy o6v0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 c7r)6 es.;niji:db hpxm long. It is open to the outside and is closed at the oth e)drhj7 si:b6n;ipx.er 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 adjust tw22jfwdn ,pxlq8y*l 8lo strings, one of which is sounding 440 Hz. How far off in frequency is txn, yj82dqp l wl8fl2*he other string? ±    Hz

  What is the beat frequen2dva0(nhao4fhdv2e* fiz5 h,/ z ap4fcy 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 (brand X) operaq1:kbjv u6-r:qb . gaites at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when the16:bq ujiqbav-r:.gk y are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whhlik gskc92*ki7h8) h en sounded with a 350-Hz tuning fork and 9 beats/s when so9i higk *khlh ck7)28sunded 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 freq h - jt sw/oq6j26-:ubvdl*rrz, ob)ocuency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat f:v6j/z uobqs)td,o jrlh-2*or -6bcwrequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each 7tq d* l)jzm;ntry to play middle C (262 Hz), but one is at 5.0°C and nq;t*j)7md zlthe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, bsayg6h2lm5 /x(j e7cA, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beal/b2y6 5e(jcxgham 7st frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A per,w.ushjfxwg(su/l (f 9dba 6i4tt9 i1son stands 3.00 m from one speaker and 3.50 m from the j(w.6/g bu49x tw l fsisa,h(tfu9id1other.
(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 vl/r5:c2qhxc vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibracq52cr /hv :lxting 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 myv*g c2a8nv9s in air. How many beats per second will benva9 cgs82 yv* heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’i6qls/ 1eq-q..9vvhee5sk w vs siren is 1550 Hz when at rest. Whe i.v96v/.wseq-eq lsqk 51hvat frequency 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. What frequency do you detect if a fire/81lk b r w8/plewras, t11ggi engine whose siren emits at 1550 Hz moves at a spe8r/bl8/grg 11wswp1ti e,lka ed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz snyp5 a;rt) /cj0k0 oobource is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two freba; y0c5rok)nt p0j/ oquencies 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(l 2mrx n*9nkj one is at rest and the other is moving toward the first at 15 m/s the driverj2r(*l9n kmn x 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 and receives them iokj6(p .yk1q m1,:ppmmxd;treturned from an object moving directly away from it at 25 m/s What is the rmk ipjtpy1 kpm.(1,d6q; om: xeceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a spbhi:9pf,yum;s* acy/ eed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat heafyhms:/ aycpui ,* ;b9r in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originaf(ypq k s9n7m;l Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played thqpfns ky(79m;e same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Su:5dh)w rn rzp/nzlnt--nf1i : ppose the device emits sound at 3.5 MHz, and the speed of so1)-pnrnf:wt / i:rzzndn5lh -und 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 ultrasonic p46dd+b1,h ad;iyw j,ir) qsgwaves 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 fre 45nyl32kdx urquency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency wil3l und2k yrx45l 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 movp7pur4h1ot4s 2c,g5r;ddal z ing on land if 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*...1a8h whuv2+ lj pl jseo:nqcy+xn) What is the angle the shock wave makes with the direction of the airpps . qvh8y:x*c. +a.nlelw h21nuj+ojlane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sounu0risuhg y58l6nc(q(n )i2xc s1iru. d is only a xr.2uilusscq) 6y rg5in uc(i1n80h( bout 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. Determineudz)pg1ps,y je;- u 6u the shock wave angle i;)sz ed 1- ,juuyg6pupt 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 .8si c-a2x x bpc/tzn/$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overheadhn(;+ ,lkzm 2:h vtpgc and see a plane exactly 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. D:z,(h mp+g;ntlhv2 kcetermine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses dowk9)2yq/:e k.ia tjcllnward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum t:2j )i9/a.kyelq kcltime between pulses (in fresh water)?    s

  Approximately how many octav-tcjn vof/a)p+ cs)s1es are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It cons.e /iqj8v u d(gta3z6pists of many plastic pipes /eujv6 3 (iqgz t.d8paof various 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 makes a sound close tovy3(svlsfko j3 .z9zkel-b9 8 the threshold of human hearing (s9 ksz. ok bv398-l jef3ylz(v0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound le+rq segw37r)hvel when an 82-dB sound and an 87-dB sound are heard simultaneouslwsrg )7+rheq3 y?    dB

  The sound level 12.0 m from a loudspeaker, placed in the j+p9ly mbm+,b open, is 105 dB. What ispmy9m++b ljb, the acoustic power output (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 power out*qt (vqr9btw; put drops by 10 dB at 15 kHz. What is the power output in watts at 15 kbt( qr;wvt9q *Hz?    dB

  Workers around jet aircraft typically wear protective devicvex/o.ny ph c:v51u9c, ji;uaes over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine? 9v/. 1iycjxu,e: cuvapn ho5;   W

  In audio and communicaei p 5qdxkl pmb/5()e,b 3sc2tt *+movtions 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 violiq:5l oluk ys/dmx( 5l6n is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a vi92s- w7q41 +emrjiig yyi xzt;olin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit wm sziij7r2yyext+ 4q9;ig- 1length 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 tuku) mgip-t,q. be 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 dist,pg tqkmi-) u.ance 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 24blvly q. w5a/tve+1y.10 g is near a tube that is open at one end a evyy4/t1v5wl.aqb+l nd also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obonfqsf)kif-v p fq+s0 6,:,uw served 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 t:jigfici (gr n:l. ,w qh(kc()one 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 leve iijrg:ki:w cl(qn ,g(h.(fc) l 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 sepqkk -q5 qm0,tationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when te0qm, k5qkp-q he other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam )2m ;qqwvmi.s train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (as2qsmm)w. v;iq sume constant velocity)?    m/s

  At a race track, you can estimate the spea fze;1 i6iv d yv:*kje-g;9qbed 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 1;vv*g9 fy a z-iedqjek6;: ibby on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 ;ck/s5+ww; bq 2vkfmvzl*w 6gHz. The shorter one is 2.40 m;v g kk65w f qsw*cmv2bl+;w/z long. How long is the other?    m

Two loudspeakers are at oppm8d0b kn :ie8qosite 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 obser: nkbqd8i08 mever 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 aoiqw*7b.z mw2vz q98cgrta is normally 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 cells? Assume that the waves travelz9v wqm g. i8wb7c*qz2 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 flyuus;7 l,r:f cifz*zivggs 484ing toward the bat at speed 5 m/s The bat emits zic74s;f u8:gusr ,ilf zv 4*ga 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 pua -w6oe69r)xmh sj+vcej, n4olses 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 returno+j-js ,h a4ewv6c )9ernom6xs before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signa -h+gtt 0jzsnl;kj -3bls 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 musicazg-sn0jb-tj hk 3 +tl;l 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 listening can be compromised by tho7 4lmo+/muyry( fbq 6e 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 fundamr+q y b 7uoo4mfl6y/(mental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,”, du37 v3nhiqgpgv/-hn5t 2q u involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. Witp7v3iqut/-g5,h gvhn nqdu 32h a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ea8 0 c d3ocw/1p2gfjwhvr at a frequency of about 1000 Hz ic1pv02owwcdg38 h /jf s $I_0$ = $1 \times10^{12 } W / m^2$ 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 thewnf u.i oft)3w6t;fe6lipg -( ground hears the sonic boom 1.5 min after the planewl6e;wipo36t fn)t(fg-f iu . passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ismhw35ciob0m ,ej j0z. 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