What is the evidence tkdu-n7r0vurd , ;zw w,hat sound travels as a wave?

What is the evidence that sbu;w eqz 978:4jr 03 k(zje vfme6ckapound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to4 waj51 j7 mh;eq+zmmi the bo+z i;jhjam5 me17w 4qmttoms 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 other.

When a sound wave passt. -xfcmj+i;3si4 sovju; 7wcme-- wjes from air into water, do you expect the frequency or wavelength to changcm3misjs -;o -w jfvt+e;7uxc -.wij 4e?

What evidence can you give that the speed of qh9x;qw,d6a ,n m(-k,rb +d al.hsmzosound in air does not depend significantrho zk6d xm h,q,b,d9n.as-l+ w(aqm;ly on frequency?

The voice of a person px g(0 cx3ky8ybcx) 0dk6 0b0uxei::5daaugwwho has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch ii/5.jtpv0y 3o dx me7of organ pipes?

Explain how a tube might be used as a filter to redu4 h7c8g-g doxace the amplitude of sounds in various fr8xahc 7gd -o4gequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clo - mw02vi5zvgaser together as you move up the fingerboard toward mv2g wvzi-a50 the bridge?

A noisy truck approaches you from behind a building. Initially youw8/j1(g qb0 m5ywpaul hear it but cannot see it. When it emerges and you do see it, b(0p81 am5lyg /jwwuqits sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas bgbe2vdj(7 6;2i :a1-at;iq eynbmc bufi :s2heats can be:; eaj 2uh7 nb:vfyseim6;i2 ca-b1tg 2dqi(b said to be due to “interference in time.” Explain.

In Fig. 12–16, if the fre 3:9f*eg2zldsp-/vhd s.etm ae p*u* vquency of the speakers were lowered, would the points D an*- .vehsuze psge 9t mdf:dp*a3v2l/ *d C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hear+s )-px)ylw zting of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?x p+-s)wy)ltz

Consider the two waves shown in Fig. 12–31. Each wave can be though kbcy ,bqhi)/k:3dyz wh*x0p;p1 .npst of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two cosb,c1kn)ppzy3 :*bwd hqhki ;p/y .0xmponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shbd, td90l ro02jo /k/cm/xk cmift if the source and observer move in the same direction, with the 0co//t9k2 cxmbr,dko/l0 dj msame velocity? Explain.

If a wind is blowing, will this altajg3 +cio:) o6 yp /ls8ztdr*xer the frequency of the sound heard by a person at rest with respect sxtly6:)p+oarjdgcz* i8 o /3 to the source? Is the wavelength or velocity changed?

Figure 12–32 shows var5hw1gfuu )js4 q)gj;(r )g l lk:jyk2iious positions of a child in motion 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 thjhy) 2jk4q;gw figuk5gjlr)s ) :lu1( e highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines t6l6)i,cbbv( xv 3q y;swfm.hzhe length of a lake by listening for the echo 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 of3xz,; (b flqvsbw6)i vmych6. the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shipqlb7 71xwlic9 just below the waterline. He hears the echo of the sound reflected from the ocean floor directly7x1 b llicw9q7 below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air atqt3, 5+ 3r(pxas+b.; fmoetkxwzboh: 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy,huzgdzp6 u) n;t2qb8 4h0jzz day. Without warning, an engine backfire occurs on another boat 1.0 khh 64gupu ,t2)qnz ;b80zdzjzm away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it mak061te zg hsb(qdyn an91z ,v+des when striking the water below is heard 3. b1qdh,1nn zdestay z0 9+gv6(5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pexh:(r l fv,4bavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How fa:hvlrbex ,4 (fr away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made t a4i2m3o6fuz over one mile of distance by the “5-second rule” for estima32ima zo t4fu6ting the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound *i*thqa/ fagesun-0 -a,agu3 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 levef/au/g) ya/oy;l4 jh,gff g g*:igy(ll of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lev:mxmmp iz:w 51el of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’m xiwz:5mmp: 1s.]    dB

  A person standing a certain distance e;o*sr. eldx/)hwmy2from an airplane with four equally noisy jet engines is exowm)eh ;l drs.2ye*x/periencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB,;uptak : tu77a whereas for a CD player it is 95 dB. What is the ratitp takuu7:; 7ao of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the poweso9 q 8khpn,-nr output of sound from a person speaking in normal conversation. Use hos,q9 npn8-kTable 12–2. Assume the sound spreads roughly 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 strildnt)px( le oq:)8f3lkes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more lr.kt1*;kdv lmodest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from tlv ;1dkk.*lr a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front oyc..6thfvvm+ f a loudspeaker on the stage..hv y.vf6cmt+
(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 :vty: cdwf4 c4dB. What is the ratio of the amplitudesf4t::4wy dc cv of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a souny j:ifjac* y1.18uhc qd wave is tripled, (a) by what factor will the intensitfcy:* 1ia. jjc18uqy hy increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudyi y( x1c0q nk(2xzd6tes, but one has twice the frequency of the other. What is the r6 (y0n1xtkdz i(xqc y2atio of their intensities?   

  What would be the sound level (in dB) of a sound wave h09,y 8wqplc i6rfz9din air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz fhy q89rp9d06il,wcz?    dB

  A 6000-Hz tone must have what sound level w h*;d3r k*mqfj+iem,1w s 5rito seem as loud as a 100-Hz tone that has a 50-dB sound level? (See msf*w1rdwi;himer,j5 3*k q +Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can d xtq9hquywo 2ntno8((ej52 dp32bc* yetect when the sound lw 9(8d 3tu*qoto2eyc5hn(yxn 22qbjp evel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodaa f *mqptl292hte a huge range of sound levels. What is the r2fpqta2* lmh 9atio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violinyxpiz5 jgds045,5 lko has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tens5s5ld z j4,op 5i0xykgion must the string be placed?    N

  An organ pipe is 112 cm long. What are the9q uek6kv7nhj2c cm+ 7 fundamental and first three audible overck7 +6 cqjvh ue72k9mntones 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 w(x+su 7wwsw u2 i* h,x, phkdk)hxw;;zould you expect from blowing across the top of an empty soda bottle ;z)7hx uuwid2(wh,kw+ s hk s*xp;,xwthat 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 span;lzg4u*b h3vrning the range of human hearigzu lb 4;v3*rhng (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has , j;,hgnu 9zujz k4ve*-ttzo lv4s4 :xa frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its originu t9 zztxzv4; :ej,ngj44-k*uohsvl,al length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E ,1dkno7m qqv6wx 0ris; +7lst above middle C (3kq1l7 r wo6x ivq07m+d,s;tsn30 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 an4h 3sql+ul9nbkx ic53 open organ pipe that emits middle C (262 Hz) when the tempech49+i5k n s3l xubl3qrature 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 2 sa xpb677b-gm0 $^{\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 1tk9y6y 2*,f rt2asrj0ut us4t2–10 should the hole be that must be uncovered to playry2t2 k0 tu*t9rf sstu4aj,6 y 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 616 Hz, but nlkz,t)z 7(7 nmjm el0jot at any other frequencies in between. (a) Show wlz7) e m,nzltjm70jk (hy 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 resonates at two s7lmo8lnim. .m y8wwaw9b-m eniz55x ) uccessive harmonics of frequencies 275 zy)blemwn7.8 il 5. mo i-manw9x 5w8mHz 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 te. -coaz835n0 hvouy $^{\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 presenighzq;lc,+9t j2v s .wt within the audible range for a 2.14-m-long organ ;z+q92i chv.tgsw l,jpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately age3 (;zlt ks94/fnpu2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate thu k g(9atl ef3nsp4z/;e 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 wh /hv ,;-acdqrt(fa g xmf0h,j/en trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the oq r,dm 0jhfa xh/c/va-f g,;(tther string? ±    Hz

  What is the beat frequen3s e1hjh7nxz2v cb/.fcy 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 (brandtzf jhsg) .u.a;y*+f r X) operates 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 they are played simultaneously, estimate the operating frequency of brand X. ).fa tu;j.fr h g*ysz+   kHz

  A guitar string produces 4 beats/s when sounded wm a.st/pxwvqy2.7 -lm qw13 wp tuy);yith a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of thea u 2wxpsp1 3 qq.lmwvw.myt) -yyt7/; string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one 6 pf7dcty1p f,0yu8r6sn iq/kstring is then decreased by 2.0%. What will be the beat frequency heard when the twrpciff8n q uytds ,6ky70 p6/1o strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to p h)o qafzmu;kw g/v728e0rj+klay middle C (262fk) g eq 8mzhjo0wv+/kur 2a;7 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequen lk1.nr*q ys26 c0lakwcy of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possibleknl s1.02wykr*6 lac q 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 apapv / boomjx(q3-y7e9 lrt. A person stands 3.00 m from one speaker and 3.5oo-e/l7yv9pj x(3qm b0 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 ay jw9b:8tl / l9cxoub.t 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) It9xc/bwub yl: 9l8.ojf 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 air. Hihbf017je3 x.cna ki 1ow many beats per seconka n07cbih.j11ei fx3 d will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a 37l gxsbzp8+r certain fire engine’s siren is 1550 Hz when at rest. What frequency do ygbl8 +p7rx3s zou 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 engine w )m1 xczan/+kdhose siren emits at 1550 Hz moves at a1kdn+/ ca)mx z speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in f-l/)p*+ld*xc 1aohlsan/flbc ( 8aqwrequency if a 2000-Hz source is moving toward you at 15 m/s s/ )w/bax8*oqal( nlcfd-pll1h* ac+ versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with k2 b)mrsoqj(j2 r)6 vithe same single frequency horn. When one is at rest and the other is moving toward t oj)(22ikr )rm6jqs bvhe 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 souno g74dt0a e2v o9,kk+orn:5sljd ycp4d waves at 50.0 kHz and receives them returned from an object moving directly awcondsey,+d9 pkg07 o2vrjt 54l a4k:oay 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 (cu qf;81sqfn3g+ww/l nd9- fv2waen 5 m/s As it flies, the bat emits an ultra nwf1n(wn3-8wq; sf2u q9l+ca d/fgevsonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, sbd 1eyfbm)nw5 bxzn,x q,,i;aj--)xa tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What n ,jd1fbsb iwz ;-xb5y)-a xenm),,qxbeat 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 mea:ui6cz lzeh ..sure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to c z.u:zlih e6.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 waves o:uig vz8 .(rpo(i bk)ef 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 wi)tw uc9+nn1 en)- btxhnj:pv5nd velocity is 12 m/s from the north, what frequency will observers hear who are located, at ren )+-cnte wb5pt) nu h91x:jnvst,
(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 rx2zaft2,0u h 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 spe* h *xva (a :va.mwxz.iee87uyed of sound is 310 m/s (a) What is the angle the shock wave makes with the dawi*zxv .vea*.x8 a7:u hme(yirection 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 t:gzm 2svdqzk4 *x33 cwhin atmosphere of a planet where the speed of sound is only aboz2 *v 4gdsqwc33kx zm:ut 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. Detewk*c:w ir)l/rjr ul*d y 93)m,ztkfx9 rmine the shock wave angle it pr)9i):w urlk/xry jzt*,fkdm*lwc 9r3 oduces
(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 js 2jy:b+kbc($/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a pla jt : vfk-9auv3 9wle+wj-yl z7p/cmayz6 y*6ine exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the son 6f: l9zw/ 9wyivaza7lu*k-ec-jtyv +6pj3 y mic 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 sendtmq;iu;aom,* n +m)kss 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is thei;ko qusn)ma; *m t,+m minimum time between pulses (in fresh water)?    s

  Approximately how many oz02u wbmp-ox 9ctaves 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 ,4 6avpz7k)ibm1p zpy. It consists of many plastic pipes of various lengths, which ar,az 6i)1 zpykpv7b 4mpe 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 to the threshotn- g:tvtid8b e: z4r5ld of human hearing (0 dB). What will be the sound level of 1000 such 5 :-8tb dgveti:tz4nrmosquitoes?    dB

  What is the resultant sound level when an 82-dB soun- m7cvkdd yk;cke6- i1d and an 87-dB sound are heardky1-v cmkidke 6d c7;- simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, pl8c1bgfc- x3ys)iqwm +n.f7y /;udcd vaced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assw+8u 13nc7vcdqi.s /x )fc- ymd b;gfyuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Ha 0x1hgf4ykjt (1qo :fz. The power output drops by 10 y 0q1hfx1jtf(k 4:ao gdB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typ mb:*pwuy+ndx5 00cow ically wear protective devices over their ears. Assumy5+bpwonuw0m* dcx:0e 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?    W

  In audio and communications systems, the gainy f fohf7udk*8sd8)(l7zdv x* qnvp37, $\beta$ 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 frequendpp8: u-)8 q cen.izrbcy 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 fh;vo psw b**q,2u.uudixed points with a fundamental frequs;q po u wudh.*b,*2uvency of 440 Hz and 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 tub+fprcl es0*/ rbosg4) xpst;8/rt k5q e 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 f+t0ssetk; o /)gx4 rrs8* pp5crb/ lqto 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 2.1u77bf 25vrfikk9)ihk0 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to prodkki5 i7rff729)vu khbuce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed t/2(tg o(ori l(pr; lz +iq+vwvo 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 tone in the 500–1000-Hz range coming from tw7wz,yhq ,kd-qt 2(diwo 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 farther from one source than the otherytwz, dwd72 hq(ikq -,. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is sthombne 7(dd i2p22 v5w .)dgndationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other traii5dp2dvb2mo)nd2dh 7w(e.n g n 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. Agy:kpiwy 50t ++iwvf7fter it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant vel:i0 p+kvw+fit y57 gwyocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the /s*+ s. 9ne81 zksqz ugrm3wuyt jgq71difference in pitch of the engine noise between approaching and receding cars. Suppose the sus3z+jz/9gnqmysu7.w1 qk se*1tg8 r ound 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 together, produce a beat frequency of 11 Hz.a+f 3aarl/o4 19ng a. 8 xarenkbt;-mi The shorter one is 2.409olb+aa 4 mi3r knxat/rf ;1g aae8-.n m long. How long is the other?    m

Two loudspeakers are qat(zm zr;e65at opposite 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 me5z(r tz a;q6have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of ba1*c9 *v h0ml05iq ipqtc/n q26tnsdjlood flow in the aorta 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 l9j/15ipc6q hcq0*smt2 a *vnit0nqd 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 j1cdrx1dko +y6z5l1u moth is flying 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 reflk 6 ud1l d151rc+xojyzects off the moth?    kHz

  A bat emits a series of high frequency sound pvg;5 u 8dp)wnlr /ov p3ezib)3ulses as it approaches a moth. The pulses are approximately 70.0)n bv5zr u3v )8;p pg/le3wdoi ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38)dbyk;g -r ecd r,oaawq,un-;yu7x7 /) was once used to send signals from one Alpine village to another. Since lower frequency soungwe- ox;d -7qy,;/bk ,7 )nrrcudayua ds 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 listening can be co,-. 33wz shukqc qv1qwmpromised 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 fuq.v,s3 3h-1wqcz kuwqndamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender azo5 e(ktke3 ljk 5,oh;luminum 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 bkhz t5j3el o,;5k( oeke 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 thr)psbcuv; w)5kk1q9h ycrgw9qfmr 2hrto3 * +7 eshold of hearing for the human ear at a frequency of about 100v 9mb) hqr975c r+kfy*2; 13)uqtwgo rhcspwk0 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 2.0isyl, ghzyehoy/o.g v jz0*88u( /v6m . An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Whe (omz 8s,yghi0./l6gy h8uy z *j/vvoat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 +9fxi9+,mqt-6 1y mz e rsriswyrj,p.$^{\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