What is the evidence that sokk bvlh 0b -bd3g0/as 34sts1ound travels as a wave?

What is the evidence that sound iso2 zk 0y ishxi,hfcl3i+k*;,l bt*d/b a form of energy?

Children sometimes play with a homemade “telephone” by attlh8vin2 lw6o /aching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound vi8hl2/l wo 6nwave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency y43b)mzthy / qor wavelength t3mhzyqt 4 /y)bo change?

What evidence can you give tham8x3a) ia- 5(xqqdy1lvnd2wa t the speed of sound in air does not depend significantly on q)-vq 38 w5 addlx(yn21axmai frequency?

The voice of a person wh,86) ldf gg0)b cju)jzcg+ua ho has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipeaqp;u,15 c .wu esec*qs?

Explain how a tube might be used as a filter to reduce the ;o4lr/ /pgpv;54e* ovkp ioq gamplitude of sounds in various frequency ranges. (/;o4*q eloo5 pgrp/ig 4vpk;vAn example is a car muffler.)

Why are the frets on a guitar (Fighk,t-qgjp:aiq6eqe t 25 *; uc. 12–30) spaced closer together as you move up t a;u2qjk5h :t,cq6e-* ipqegthe fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initialk*/d k6qnxwj95;iys(lj n b-dly you 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 kj/k5by(*snxi- d nl69d jq;won diffraction.]

Standing waves can be said to be due to “interferenc 7 kyes9sxewr af4qi6d(h tb86.oy* .ge in space,” whereas beats can be said to be due to “interference in time.” w o(.b7x8hqfs*e6e9ygs4ya r. idk6 tExplain.

In Fig. 12–16, if the frequee l7dznb i+o+q 32usw s4 /lwx7+icc-kncy of the speakers were lowered, would the points D and C (where destructive and/2o3s ueldck7 +-4cnlq+iww+x b i7s z constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearjdj((yo7lfm/2 7gc7 r+rxw z aing 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 heacjwxr7fyo zl g72m (/daj (r7+dphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waveji:sdn 4htomiey3o08 e)aa, 1 s shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly di a0:i1)d 84oinao ytjh3 me,esfferent frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obsep* ech;sg(,c:8,jg/u og h6dq5rdkosrver move in the same direction, with the same velocitkh86 co5g(pc*ded j o:gh g/r,q;,susy? Explain.

If a wind is blowing, wla sn8w us8pegt+ 27,kill this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocit enup+st as lg8k,28w7y changed?

Figure 12–32 shows various positions of a child in moku htu(td)6 o-tion 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 reaso ut6u- othk()dning.

  A hiker determines the length of a lake by listening for the ec xew.(zm0*g/-) t ntyash x6dpho of her shout reflected by a cliff at the far/pzxhgen0 s*y ax .wm)d6t t-( end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the watz z*x(4es1;gl e1 lqdaerline. He hears the echo of the sound reflected from the ocean floor directly bsa 1 lz*eqxz( gdel;14elow 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 wav;b1mg9 ug.ll:zpl, ,y k bnj+belengths 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 is0zm(d jhn 2z 3fgajsz0 -vci.1 drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,fh jzd s(.zc00-2mv a3z ijn1g    s (b) by the fishermen?    s

  A stone is dropped from the top of a ctqwkuswp,:5: omq+ ip m,6l:nliff. The splash it makes when striking the water below is heard 3.5:mt s w5i+l, nmqowpq:,:p6uk s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a c5 xvi0don;a. xc./mv0g)zz ehuge 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 f nx;ziz.ovc) dm/e50vca.0 xgar away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distanc2 n1nt eb ;z0xin.sdm/e by the “5-second rule” for estimating the distance from a lightning strike if the tempern0z mns 1. b/ne;xdt2iature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 zqu*r hk ve-(,dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a s rw7) b:8ivcblu)(jlsl q/j*zound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce 7g m*;i8mwv ta(mo nvlx6 ,)1towjni .a sound level of 95 dB when fired simultaneously at a certain place, what wilt*n; mom)8an v7ti( v1gjliw.6 xw ,mol be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distanc;wkbl.wj- snetx;tsy . 5 +c9ee from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one en ne swl 59.; ;xwecb-ttyj.k+sgine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ;m-an8ity f67u -wps jratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of-;pyt anuj-s6w if78 m intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking mf bqg 7l6oa:b wtn4c8.n)/cwin normal conversation. Use Table 12–2. Assume the sound spreno.l4 g8c 7q6 nwbw ctm/b:af)ads 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 eardrum whog2c da cilb /,3u3nf/9i(hz hvse area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B isgmdf ka55a*(z rated at a5 *mdfz5g ka(40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each 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 froy1 7gw-, v oab0n2rcnpnt of a loudspeaker onc 2nr,gow1 -y0nv pab7 the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detec 4+ g.mcvcqist; pb5r9t a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Smsp;+ bc 9 c54qigt.rvection 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the lw1i8 :u-dxms intensity increase? Increasisl xu-8d:w1m e by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equc 8u: )9itlahtal displacement amplitudes, but one has twice the frequency ofct8l9tih au): the other. What is the ratio of their intensities?   

  What would be the sound level (in uo2wp:ro*hhh bu8-r *dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules 2 r*-:rhuopob 8 whu*hof 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz to 9*us 5q8sz)l,bnqphyne that has a 50-dB yz5*splqsq,9nu8bh ) sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that anc:k-1x6/x; f6 ;;cj mvmdzh2dsufm fm ear can detect when the sound level is 30 dB? (Seefu;: vm6smd/fd;z-6;1fmxk hj2ccmx Fig. 12–6.)

  Your auditory system caq:y 9e9fjs :sbn accommodate a huge range of sound levels. What is the ratiys:fs: 9qj9e bo 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 ve.rle)is .*n frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Undv e .r)ne*ils.er what tension must the string be placed?    N

  An organ pipe is 112 cm long. What arf(3l 7wa : o2-4ocz7fjpacvife the fundamental and first three audible overtones if the pipe i:- fl 4 7pcw(fovc2ioj7 azaf3s
(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 acrosy;ny+7n 3 sq7ggrpmu1s the top of an empty soda bottle that is 18 cm deep, if you assumed i snng+3r1ymqygup77 ;t 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 or1f je 7(pvue;ggan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes req ;p1e7j e(fugvuired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has 6s,514 q* l y4 :zkrodw5txoodzgr(ija frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered oi4xlsr5o,d61 zy:g qd4j5rkw ( ot*z at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 vdwo0o: 2 qbp)z);f nozl yl8-m long and is tuned to play E above middle C (330-:nb8 p)z0qwfvl oz;oy2dol) Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C 2x0xe7y wy1nb(262 Hz) whenbw yny01x 72xe the temperature 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 at92x+z l0j ed70djqb, ocffts , 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute z(o9hmee7 m2b in Example 12–10 should the hole be that must be uncovered to play D above middle7me obmz e9(h2 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 z *lkxu(p g:/b p4-mb4dpq bv9264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open o:pgpl4m/(- bdbz ukp*bqx9 4vr 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 isz 1sjip ;qob) o8hdv7b hwzxv,6( ;+qq open at both ends. It resonates at two successive harmonics of fh)qo +;od spbzi;x6 zwhv,q7q8vb j(1requencies 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 nl;r 3 v3ji m,6bms:ll$^{\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 presentl7 zr un 1ccgg2p2syzpjib8kia5-1cm).9xq: within the audible range for a 2.14-m-long organ pipe - j7mz c9uab2yi pk:sz1 g)gqc 2p.r nx1ic85lat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm longs b,*h xlic27, hiz6 c8w9rmca. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible raib z7m r,8,i9lhs*chcaw 6cx 2nge) 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 aa q65fo8x ed0vdjust two strings, one of which is sounding 440 Hz. Hooq68xdv ae5f 0w far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 H4 *5nys4-b76xehc,gfttd ahzz) 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 operat5 yby,i r0ym)aes at 23.5 kHz, while another (brand X) operates at anm0iyyr ,)5ba y 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.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and pqmc0az* . u7phy(0nc9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explaiamc*y.0u 7zpnhcp(0 qn your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 8x9f8mqb d-vpHz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recal8bdq 9mpv8 x-fl Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle 5zyi i/ wb1wd1C (262 Hz), but one is at 5.0°C and the other/ 5zi1 bwyidw1 at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fh-jk- u 8 d;xout3pja2ork B has a frequency 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 possible frequencies of A and C? What beat frequencies are possible when A and x-juad j-8; 3o2kuh tpC 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 on0/:+eq cyn owqi-ie)b e speaker and 3.50 m from the) ec+:ibq on -eyq0wi/ 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 vibrati3*ym9m t1,s v izxt/heng at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be te1/yxmm3 tt,* ish9v zhe 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. H7m5 umpb0xurih 9 :7t un9td/now many beats per seco/:7n 7tmbp 0dmu5uir xh9nu9t nd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cv ln8,b6 tq0) mxcmiz;u/la,nertain fire engine’s siren is 1550 Hz when at rest. What frequency do you del;,lau6q)v m0mcn /tix,8b zn tect 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 whose sirenh;p )k/e,sw nn emits at 1550 Hz moves ats, epnk)/nw;h a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving t5)i6gr yzsp5* f (nop0t0pfqloward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies ef(ls0nypg o6fti p5p rz50) q*xactly 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 equippedj/:**vtf9mfhf hltj 5n, rh0z with the same single frequency horn. When one is at rest and the other is movif h vmrtf* zljt5h* hn0,f9/:jng toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends o- (47ifu xkk4pobnr-mut ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 pxn7o-fmuk r4ki- 4b(m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fls0f 6nqgb0,v kies, the bat emits an ultrasonic sound wave with frequency v6gkqn,0 s0fb30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on tid .8rt l f)w bz3k.-;zquvh;a moving flat train car at a frequency of 75 Hz, and fqdkiu .tt; -3vzz w.br8;)hl 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 ultrasound waves to measure blood-flow speeds. sr z7p+g*up8i r 90gn gj w(,l,rhxms.Suppose the device emits sound at 3.5 MHz, and the us0ph zxr,rg (*i+gp smnjr.98lg w,7speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

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

  A factory whistle emits sound of frequency 570 kd ob)3y v5qp2q-nmffs.l i3,Hz. When the wind velocity is 12 m/s from the north, what frequencvd 5o l)k3-q2yfis3bqmf p.,n y 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 its speed at 20 a.2k(ty 3blaimexs4.e.vg81z :el tq $^{\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/mv(o;yli4d4o p 5x9 uds (a) What is the anglv4m oxoy;u4ldid 9( p5e the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet wher8y ;h(wzu knl8y5pqf7y2w a(ie the speed of sound isyzwk5 pln8 q( 8hy;2u(wiy 7af only about 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. Det,i;9dsg*q5 vypi,i tyermine the shock wave angle it produces i,yq y5;s9pdiv ,*git
(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 6nb:;h*h3x m ;a mpwyz$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead agc4:kzh7q wg/i6jux;j-) m+snuxpr .nd see a plane exactly 1.5 km above the ground flying fa wq6 7)ng4jxkihuz-/ c ;+purm. sxj:gster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 62h epiku6ij ok/p7)g20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximuo ukpk)27i6e/ip j gh6m depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are theyr7 mfn) 7iu6xre in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum hasf 5l umdb5a6 b/u6t1qp a display called a sewer pipe symphony. It consists of many plastic pipes ouml65 ub6pd5af 1q/ btf 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 maog i t(k:c9pl8g:1 vtybiqem c*+8i( ekes a sound close to the threshold of human hea+coti:g(9 qlk8iig* ty :(ve8mc1be p ring (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB o g8,1kq;we nkhn7 x6iwf6 ek+sound are hear+qwn6e67okw;ken1x g8k fhi ,d simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105-0-pw rpdl5h7 xi:z yo bu6h,t dB. What is the acoustic powzp 5xprh7o l-6dbuti0wh y,:- er 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 out3c6n-cehh:aay;8p ix6 ma- pjput drops by 10 dxy8p- h:6ci ;h jaa6- epamnc3B at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over ) /0m0 q1gt)xt3oslgidx wmp,j( 3ah 3voo0uctheir 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 engtvx0oh3(j0txs)m g,l c 3w1um3iqo/d) ag0po ine?    W

  In audio and communications systems, the /zy7zdl3mapj vp- m28 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 tuff b(fhaev7me b:jf*;fp6dh9+ (i /fcned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a(6 az3+k* blkcfsok 57al w5po fundamental frequency of 440 Hz and a mass per unit lengtk s(wbl*6oofp lk+az53ac 57 kh of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube dm.7q b/xhh( 5wq6ackfilled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube aqm k.wdhxah75(/bcq6 bove the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near 9wm5u )wgoqrxs(jtf9 ,kuff.pv*:b) a tube that is open at one end and also 75 cm long. How much tension should ber5:t(m*,ws fj)o9wx vfq9.k bpfgu )u 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 wabegm 5cm kue4rj+f9q) .ks7pj18 i3dws observed 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 purk3 rbrnmam ,v9)z). aru8a, wde tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sourcmvu8).,rkrd,w ramn 39a)b azes. 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 other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationaulippth3 ( 1 tv,jm(3kry. The conductor on the stationary train hears a 3.0-Hz h,p(m 3ptuki3 tvl( j1beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachejv +7v w+5j:omh:rqgn s you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fajv: :qnmw5+org+ jhv7 st was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of c5dg,98 q: uttfzh kl0u i5kfw9 y*pxz/ars just by listening to the difference in pitch of the engine noise between approaczw*xq kz : h8dluk putitf/,g5yf5990hing 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, so *mp ,s ytyjy10km:-w2,tqijf unding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is mps ky*:jift q- 10,2 ,tymwjythe other?    m

Two loudspeakers are a ps6 *gzgqmt- -8jlh7at 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 speake zgl7ta6m *- h-jpgq8srs 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 the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/so *w:fk zi4lpj57tp3 y what beat fzk3f54w:*plot 7y pijrequency 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 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 w/-;r*.jbt9 bechhz)0 xhu q kmhile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 zt-; m jh/*q9xhekbu.r)c hb0kHz. 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 souv3siemt1.loqrb87.t8lm*3, uiv y h jnd pulses as it approaches a moth. The pulses are approximately me3ms31,qy.ori8. v biuhlvl8jt *7t70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from onej:i (7psf9sb2li1 ohg Alpine village to another bli(g9:i p f7o21shjs. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular 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 the presence o-f hl dewnn;5)f 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. Calculahl;5 nwed-f) nte the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing 0fyf+zwr s04i rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-lonyzff +0 4irws0g 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 rw3m i1 iy2* tqhh-sk:threshold of hearing for the human ear at a frequency of about 1000 Hz -2y*twh1kihm:qrs i 3is $I_0$ = $1 \times10^{12 } W / m^2$ 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.ybyri(y. f.6/ oy uhy-0. An observer on the ground hears the sonic boom 1.5 6 ur h.fbiyyyyy(-./o min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1,;d 6eeq ,lgziuv7 dp 5tc7n/q5 $^{\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