What is the evidence that sound travels as a wave?q qh*;w ,fdf ;d8qdw/ 7j9boqs4a.jdh

What is the evidence that sound is a form o+ost il2;g)h of energy?

Children sometimes playop-6w xnx* d3e with a homemade “telephone” by attaching a string to the bottoms of two paper cups. d63-p*ox xnew 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 passes from air into water, dozaj v,c.z;x by2..x vw you expect the frequency or wavelength to chvwy;x2czja x.z ,bv ..ange?

What evidence can you give that the speed of sound in air does not den.8(rq yeq/m apend significantly onm( qe/rn8.qy a frequency?

The voice of a person who hgd;jl-byhi4 4ec g vj11p*eo8as inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the xtg1 :;90k7kgmx xev gpitch of organ pipes?

Explain how a tube might be used as a fiy 5hhsx7,ts;f)ae- 1 ij -iwrllter to reduce the amplitude of sounds in various frequency ranges. (Ah5fh, t )j-1-i;xwsse lri7 yan example is a car muffler.)

Why are the frets on a guitar (Fig. 5 q9znyh/ uoi)12–30) spaced closer together as you move up the fingerboard toward the bridge? ) zih9ynuo/q5

A noisy truck approaches you from behind a building. Initially*x) z:x2 z1em;b nvmrf you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of 1znf *2vx;erx:b)zm m the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be du v8c3k- uqtt/ve to “interference in space,” whereas beats can be said to be due to “interference in timequ8ttk3c v/- v.” Explain.

In Fig. 12–16, if the freqrsw7*jfo4o/buc8 n4(pe. d epuency of the speakers were lowered, would the points D an 7pen8e4fo ps dwj ru*4b(.co/d C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who wom7:mb nd,d d5 igxll.8rk 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 headphl m,:dndm5 8i 7.gxbldones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31,x jz2 eokh+ a8i8p2fd. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in 2dxa 8+k8o f2jezhp, iFig. 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 move in the saynx o63 jj+x-a1j;te kme direction, with the same veljjat- xnejo6 x+y3k ;1ocity? Explain.

If a wind is blowing, will this aanx16harm o4r2, hmh*.74t jaqicu3whd8io8 lter the frequency of the sound heard by a pers dh7i3h.ano c8x*,rjqiorm64m4h2tauw 1a 8hon at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in moti5g37uy vg1ak*y jgqx 64l- szbon on a swing. A monitor is blowing a whistle in f 6 k3v4z -ygagqs1x*uj y5bg7lront of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her sh0)1jbsf4*mgq khqn a;t f5fmwudp:08out reflected by a cliff at the far end 4p dhnqf0f0*mkj:b)qg 8 5;awm1u f tsof the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the ( qx(xu2wtbip)-ibjvonz ;-. 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 the speed of sound in seaiqo w2)vut pjxxz.;i(b-n( -bwater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 paagyx-uvvc1f 2f 705$^{\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 fog sv4pk: g+vy9un;es b)gy day. Without warning, anv n+sk;v4: p9usy) ebg 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 fish,    s (b) by the fishermen?    s

  A stone is dropped from the tonki )qe+xqz49 p of a cliff. The splash it makes when striking the water below is heq 94 zke+)xinqard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a h.sndcc8ycq l;4 zgj)o, p2 o:juge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occurqco,8yco2jcp s gd z:4n j;).l? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mileo9kfjl1s( y mntj lyhl)56/ q2 of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperat/6fjl j1sy qylmn(o9h 52kl)ture is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain levrfo9,o c jcj,3/q* hp3iw 9fryel 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 oits .n2;cp8vw 62 xgxlvs(y1uf a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sounh csd:vlyk s0*y 7iplsq2h 19+d level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is h2ip:vd 7l9 csk1 hys q+ly0s*exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance +,t vku m-g ;zpm;e-gpfrom an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experien ;;m-t-kmpeu+ vgp,zgce if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hz/ltg1y +0 hrsave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for ear t0l/g szyh+1ch device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power 4jf3khuc:m ;z output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the : j;zuhm4 3kfcsound 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 strikes an w cnzzy8h*clz 8)k.srbt2hl (3a3k *meardrum 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 the6: gnrecz a7t2 more modest amplifier B is rated at 40 W. (a) Estimate the sound l2tan7rc6 z :geevel in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dBry 28uj va* rhndr q1yosj2:-ucz)w(4 when placed 2.8 m in front of a loudspeaker on ther-y r)1 8j4c*(z v njdu2as:u2yrwhoq 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 typicx fgni 0g m92 .wkirff5(wqo;l(;uka :ally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of twq rf i k;f:(kwui 9f gn5x(lo.a;m0g2wo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor as5s z+ qq7ca 8b/c/zawill the intensity increase? Increase b 5c/az +qzq7 bac8ss/ay a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one 1h)q ouv4b6zw fzo t5;has twice the frequency of tbozvzuqt) 641; fwh5ohe other. What is the ratio of their intensities?   

  What would be the sound level (in dB) igzdq4rk6r8jhqbib76+)a /n of a sound wave in air that corresponds to a displacement ampl+rh) 6bgqi76nj rka/dzi 4b8q itude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100 kpo*/vjur c-t13p.px -Hz tone that has a 50-dB sound level? (See Fig. 12–6.r 1/-*xvutk p3j.oppc )    dB

What are the lowest and highest frequencies that an ear can detect when thez+c /xjcywh 4sw29vr ;q l*l0s sound level ic clqjwrs* ysx29 v04+z;l hw/s 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hug38 bkt5(r xv- py(tcxhe range of sound levels. What is the rabt 3yv (tx5-k ph(cr8xtio 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 violin has a fundamental frequency of 440 Hz. The length of: kr9/; nzjs7eue9 fp8m eve1o the vibrating portion is 3fvp9e j z ;n oe17e8sekr9:/mu2 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 funda koj( 8adw*h(3hw,j ramental and first three audible overtones if the jkaw h(j ,ha(o3*r8wdpipe 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 the)ir0b+ l up7tj top of an empty soda bottle that is 18 cm deep, if you assumed i+ 7l ru0jtbi)pt 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 tht: 4dz,ncz:,gs v-gscub,x0 9znt8lie range of human hearing (20 Hz to 20 kHz), what woud-,9gtc:zngi b: v szcx8,4 ns0,zt luld be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thicw(/eh8rnf ,cpdbf0t k (3w+ lrd harmonic. What will be its fundamental frequency if it is fingered at a length of only p n,k((fr+wfdl0bc/e8h c t 3w60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to playm 1hjkc)9 aj(daw1; hd E above middle C (330 Hz).ac )dadj9hmh;(k1w 1 j
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits midj dog0fc 46bi-dle C (262 Hz) when the temperaturibfc0go d46-je 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 2am/j j) k-- io*jjgu4k0 $^{\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 123aa gc5c82sfh –10 should the hole be that must be uncovered to play D above middle s haf3g 5cc28aC 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 re ) vrfp14,-noekf8*ex;wlzy d sonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why f,nx* f; yv)kwel -18doze 4rpthis 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 resona9 p+;a2xe u- xjvk.pog +qyxm2tes at two successive harmonics of frequencies 275 Hz and ;v-+jpxy+e 9a km2xpx.q2guo330 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 g ld0(tk.f xgwzh+63k$^{\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 with* ke)o 1/scwgein the audible range for a 2.14-m-long organ p/)kgcw1s eo* eipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal j,0 b :vsk. fcq1 d2gtcx;voc3is approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information 3tf b,2s;v0q.xc o:c1dj v kgcin the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every t n1ny3rvy*lo2)g 8on 2.0 s when trying to adjust two strings, one of which is sound lyg8 * 3o)nn2rontvy1ing 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) ; wf;bo) :xblbv ba0.m.h6e tmand $C^＃$ (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 gc-i8e- qhgp: X) operates at an unknown frequency. If neither whistle can be heard by hugeqg-p:ih8c -mans 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 sounded with a 350-Hz tuningqe)rl63l,3, p yw rwbm *fcvkfrel.;5 fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is errem b)y, *ll fqf5c.rplkw33 6; wv,the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in oncm*kv5y ,t/j 9.v jyshe string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.5c,jt.9 jyk*vyv/m sh]    Hz

  How many beats will be heard if two identical flutes each try to play middled- p6*qlz )vjr C (262 Hz), but one is at 5.0°C and the other at *vz)rjd plq 6-25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, bbz n.oy5g(o e( )wu17tlhs9lA, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is hw lu5(zb ) 7oy .(helotsgn9b1eard. 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 person stands 3.00 m from w6rhqwzr*7) p c 5ka n;k;/cpwone speaker and 3.;p7acrh qwkkw;rnz6 /wp ) 5c*50 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 piano tuiqw3 ,fui/t*t ner hears three beats eve/,uq*wi3tfi try 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavele1zv t(mhp: 2zxngths 2.64 m and 2.76 m in air. How many beats per second willz2z(pv tm:h 1x be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engcrqw:bj)6mg 89 erxj my:+4jjine’s siren is 1550 Hz when at rest. What f9w4jj:jbc) q mj6:+8m eyrgr xrequency 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 en,o ;* 7z -ovnsivdo7cvgine whose siren emits at 1550 vz vi7ovnc-od ;7,so*Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift ioov)*i2qq(-p0 fpge w 6 htwz/n frequency if a 2000-Hz source is moving toward you at 15 m/s verz)*qi fhpo( g pe 0/qvo-w26wtsus 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 the same single frequency horn. When one is9s4)t)nuf 2yfr9zm. qtm0 ain 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. my)tnit9fs2.09 4)umfzarnq What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wavm1b;28vk7t uv scx :qjes at 50.0 kHz and receives them returned mxj:vk8btc sv7q1 u;2from an 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*cr rtkf 4 3q;+y yrc1xq9ki8m/s As it flies, the bat emits an ultrasonic sound wave with f34*8 1;yf rq9+kcx citrqymrk requency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopp 9vke 6-py*nl jddurc0bn 5 0;a,xc:hvler experiments, a tuba was played on a moving flat train car at a freq0e 09jh ,pbx cl:-5cn6nau dkyr;vd*v uency 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 uses ultrasour 3 ab;z)na qpplgeq.xwjnx0 -1;,ai8nd waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s direc qj ;,zbx)x linpgr;pq aa30-w.1ane 8tly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves o .pkb8zsl6j4 ru0sepv: bu1g 4f frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is-4f qh+q(nyig 89nqb (cs p5uem(dc5j 12 m/s from t(ysqn9udq5nc je8 f(h c4i bp-qm(5g+he north, what frequency 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 if itsqu8ejr ;q1 oa78lx*mvncza9wd ;)3rt5 wm-j p 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 i 0e+ dmll 9*lhb10-wrxk7zzpes the angle the shock wave makes with the direction of the airplane’s motion?bh07 * zerd+px1 e-lkl wz9m0l    $^{\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 wherxt7upwuq k .+9ics bo78x1b9i e the speed of sound is only about 3x9px. wibb87+tsu9ci 7 qou1k5 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 angl ikx/* wxom :b7fg-sl3e iik xg/* b:7xo f3sl-wmt 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 pn1;amg8pv. i f1lum8c 3b* jj$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead ank6uezoz /+l 9ts6f 5j7h j 5ao6gfq8qpd 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 j 8pqoqujs76zt lf+9 eo/6f6gha5z k5traveled 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 thataoy s9.q: s03du( qikt sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designa0.y s (:q9t3 kdsuqoied to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octam hy 5 :f))-)liqyd9pfy5l scmves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display call;lh8 ;fi5ueeo:j 8cpxed a sewer pipe symphony. It consists of many plastic p h8eiu5;j:cfx;lpoe 8 ipes of 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 to the threshol 4i:j xm7i.pas4 u-qeqd of human hearing (0 dB). What eaqxq :uj.imp7si-44 will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound iz+laruw8mk:5h 9o: z rck c,s t5jo48and an 87-dB sound are heard s,s5r+:oaz k9 i 8rcckhwo4 5zju:l8tm imultaneously?    dB

  The sound level 12.0 m from a lc3.tc q smhglqb+(+ )woudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming itwmsh)( l+cqbq .gt+3c radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outu-ee8+ vfy ,paput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What i,a-v e+pfyu8e s the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically25ko 6j /qy: (upvklr( jrrlx( wear 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 average human ear has an efqpk(juy( 2v5r rj6orx( /kl:lfective 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 syf0w)xh. +yv kdstems, 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 wux r2+1bl 2r)nftr -r 6emi-:f3ztysto a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long betweenkpg:9 3repz ;g fixed points with a fundamental fre;egp g:pr3 z9kquency 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 viblg4vvat p: 0- +6w7iqj(wla;fep g5ibration 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 is 0.125 m6t+gp:;e -a5fb wq0 v4(pl ajlgiw7vi and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar strinr7vi.yn 6))ml43l mrrmst 9 xug of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in ttr 6)su73.n im4yrmr )mvl9lxhe string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full x0q( k i- n-o d80b-url2l9bfl4rdfog 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 teh q(y* )iavy62i u0ceone 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 poe * 6uce0 yyiqiavh2()int 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 sta2g agveg4 r -tvydp+hqpza1z 0251( rctionary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speepgcpvt( vqr z 0de1 -rg+h2ayza1524gd of the moving train?   m/s

  The frequency of a steam train whistl5 kkwn9l,(nk*f 7bjs pf, lvb.e as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How llkbk kwnnj5fp 9(7.v,f b*,sfast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to zx.8+,f5 a 3cdjvt ydk bl8ac-the difference in pitch of the engine noise between approact+yc-f lzx c83db5d8k .java,hing 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, sound:..4(stxyaf w(jnbwqing together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How 4( t. :yq.x(wjnwsafblong is the other?    m

Two loudspeakers are at opposite endszzg+1v3 yr s,p5n fycssd);yz,hg 1y7 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) he listens from the position A, in front of the car, (b) he is between t ) f,1z;pc rg7yyndsyghsz+3y1v5s,z he speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of brqzt.y7jw0s+e fairfvk*8 hn8*tt 7/ lood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect in/q7r aes8tfy jzt0hi v.* wr87k*t+ff 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 6w8bw)m1wm jkat speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the1w bk)mmwwj68 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 approaches a moth. Thehh 2vl( nn 3lgfgj.q99 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 on(nhv fh.9qnlg 2j39lge chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used w4i5kg0ze 5:yx wd x2vto send signals from one Alpine village to another. Since lower frequency sounds are less suscv55dz :x4eg 2x kyw0iweptible 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 st eak2hr6z6mqi- ,xa ;3uh t5iqereo listening can be compromised by the presence of standing waves, which can cause acoustic “d2r i, kaiqthamz6eu3x6 5-;qhead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lh-:0bt m+uf3 gsmzi 1aong, slender aluminum rod u fgi0sm:at-1hb3 m+zheld in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, 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 o7 de+k07a bed-.n pzbqf hearing for the human ear at a frequency of aboube 7+npdz.0kadb -eq7t 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mw/,tydlp /iub/4f 1s;d a smf3ach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes direcud1pfs ft/ s4i lba/,ywdm/;3tly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15c ket m)u;cth2-8hgz/ $^{\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