What is the evidence that sound trandru810ouog , vels as a wave?

What is the evidence that sound is a fo44q9zg j)vyola 9sy s.qj(n9nrm of energy?

Children sometimes play with a homemade “telephone” by attaching a string to thesp1ks *j+2hr ltgh t41 bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sot1 2 s j1tgkl*phr4s+hund 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 ai*n z7iij(s6z djyvjntal :05q.22ebrjf:r;tr into water, do you expect the frequency or wavelength to chl6izr:s2f rdbj y0*;at7 e 2 z (vj:nijntqj5.ange?

What evidence can you give that the speed of sound in air does not depend signifu:o( rv5iam1hicantly on fre5u(h:v m io1raquency?

The voice of a person who hag3,o)smy)o jx s inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect ttg.y o-44k4px 5tsgf lhe pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the am/7c1 q:zn qfbzplitude of sounds in variouz bczqn71/f: qs frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar 62dt6 6yy-wu6ppks zp 0fjyt:.xz- sf (Fig. 12–30) spaced closer together as you move up th:szf0dk --6s 6j yt26zt .pyyuxp6fwpe fingerboard toward the bridge?

A noisy truck approaches you from behind a bu 1a (,fb7+ t mcmvcffoi:kd62zilding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — if(ktf m b2c6,v: 1 mc7zfad+oyou hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be2ez-9a jsrg nl8aj;r;tbd :)m said to be due to “interference in space,” whereas beats can be said to be due to “interference inl2agnde-jr; s ;9b 8)mza:rj t time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would 9mfaw7+th v m4the points D and C (where destructive and constructive interfa ft4hwm+79 mverence occur) move farther apart or closer together?

Traditional methods of protecting ty8 hdewl5oh a7d,/e/9( t+bisk c6s kche hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. Withtweb a6celd/( /8h+ o icss5k,hdk9y 7 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?

Consider the two waves show8wn kx/7h fny2n in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Figk8n hn7f/2 wyx. 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 same direc ohnsz2yhx,b0ae ;: r;tion, with the same velocity? hx ;;rnhs b oyz2:e,a0Explain.

If a wind is blowing, will this alter the frequency -+ncwql) ek5hof the sound heard by a person at rest with respect to thk 5e-w)h+n lqce source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mon8u :8gqd-ust-b hgz4b4 kj3fditor is blowing a wdthj3-z8s 4 bq d ufgub48g:-khistle 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 reasoning.

  A hiker determines the length of a lake by listening2mpez. e,6lvb for the echo of her shout reflected by a 2epzmb6l v,.e cliff at the far 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 s0)x vs4 * pkjd3neh)wp4cel+w hip just below the waterline. He hears the echo of the sound reflected c 0*n4+3ede hw)jxsvlp ) 4wkpfrom the ocean floor directly 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 at 20 wgy5 p ,-mbcuyk.kuze(1m * o705ircc $^{\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 dayeb hm522h:q qqftw8e6 . Without warning, an engine backfire occurs on hee5 bfm2q8hq6t :q2wanother 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 top of a cliff. The splash yj87rie 5xk 7 -ulm o0k3-guhjit makes when striking the water below is he05 ykk8h-e7u grj3ujox-l7imard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge sto bhxq5k()wj6hqf ;k11:kcp zjne strike the concrete pavement. A moment later two sounds are heard from 1;:h5 bqxjckpwjz)kf1k 6h(qthe impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance .) kxthi-;/u oxha5tn by the “5-second rule” for estimating the distance from a lightning strike if the temperatutxa.on/ht u;-)k5xih re is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 ,29/umq3j cic (ehwqqdB?    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 so ns2zbp77x;22uni nmc und whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simuld ;9werxxgvvn7 ,pxhh0h o1;;taneously at a certain place, what will be the sound level if only one is explodedx 9vx107vh; dgen;;rhxw,p ho? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane w2k8,dq id g4c .ky6i*si0,cd gd6at zwith 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 ki6.cadt,kzid20 gsd*8g 6qwd,ci4 y all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of bmwmzba q+w/v/.sn51y huo-158 dB, whereas for a m-ohwnw a1q/ysm 1z.+5 vbbu/CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakc f/d8 ucxhx/o) d7rk,qvf u.m:aic(* ing in normal conversation. Use Table 12–2. Assume the sound spreads rougcr(xa f ./fh:dukm vu) ccx8i,/q *o7dhly 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 who*/v6s/5gefu2ovb me,kpn:k 98ou abjse 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 modestd clv6;w1gm1(qkcz i1 amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m lw;c1i6dqvmzg (1k c1from 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 fronzfey/ yxv6s1)ro6y) et of a lo r6e)z1/f)v xsy6yyeoudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Wha +ob *rei/k;kht is the ratio of the amplitudes of two sounds whose levkbk+/o ;h *reiels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what f b(.i9ppmb dg4actor will the intensity increase? Increase b .9pd b4gpi(mby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudenr *d:8j7 f4o-0i /ellq ulggxs, but one has twice the frequency of the other. What is the ratio of their intensities?0n*4 8i gueqd o7lj:lx/f-grl   

  What would be the sound level (in dB) of y/lm k rl 7lwjf6od-52a sound wave in air that corresponds to a displacrjmko5l6dyfw/ l 72-lement amplitude 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-Hz tone th* 7togsji4nw0zwis2(at has a 50-dB sound level? (See Fig. 12–6.) oi0w(ns*4 gj27itz ws   dB

What are the lowest and highest frequencies that abcm5tr 07 aur4n ear can detect when the sound lerucbr t0 m745avel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound l i::sjp yq(ip eg*jn0-evels. What is the ratio of highest to lowest i pe jyn(: -psij0igq*:ntensity 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 l)rrt ukt 7 )t33t7qxrqength of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under wht7kqtrtx3utr73)q) r at tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audibd w.x:-rmri y)3gjk)h le ove)xi.kr- ) rmjgwd3yh:rtones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would yorwt-tnh; e**lu expect from blowing across the top of an empty soda bott-h*re*t w ;lntle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spannizu2t (jf5tm nu -c hw3drrl-9/ng the range of humandu2jwtt3crh nf-9 5ulz( - rm/ hearing (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 a frequency of 540 Hz as its third harmonic. What cx m-9bww3s:y will be its fundamental frequency if it is fingered at s9wc3w-:ym xb a length of only 60% of its original length?   Hz

  An unfingered guitar string is 1dt82ekcz rnz5 k oi *7.dmqcw83 s9)pjecwf: 0.73 m long and is tuned to play E above middle C (38q krt7zc w2df w: oicnpkee5c3z9 *)m1d8 .js30 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 le11tmqs)nt h.f ngth of an open organ pipe that emits middle C (262 Hz) when the temperature it hfm1.qn1 st)s 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 20 ,ik+f b/lnjhb6m4b.x $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in s. e6.zc5f,:d/brul pixa,qm Example 12–10 should the hole be that must be uncovered to play D above libuqfs5:.cx rmd.e z6,/p,amiddle 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 cangub6b61xgyu0th65 n4ksj ) oro5g j8q resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. ( 6)syugonuhjkqx 4j0tr b g1gb855o 66a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m l;g l+;qra,thq q w5fv6ong is open at both ends. It resonates at two successive harmoni; afl+w q;v6qgrq, 5thcs of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 ,tl* j q8kdr7 oi+nmka*svq)9$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible+gs7zrbo )+f l range for a 2.14-m-long organ p+so fgbr)+l7zipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It isd/3dc- p+b9k*zox om a)eyj;s 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 in the graxe3sdk *y+ -d); c/m9pj zbaooph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one4bvgt.),d q n8 tl8uwl beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far ofd t.nbl8u tvlq84)wg,f in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and: zzxbsnkkb8+ a 0(kt3 $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates at(tr.tpin,v8aw a yb5 k*h xyp4v n77:q an unknown frequency. Ifh p:yb7kt4 ianv5x 7ta.y,n pv*8qr w( 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 wisq6fq epsm:xi87/u4mth a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Eiefu4x6 m87 /:sqsq pmxplain your reasoning.    Hz

  Two violin strings aep5 )(b etmxki7k 8 qa,2mmos3re tuned to the same frequency, 294 Hz. The tension in one string is then decrx m,pe( 7kbk 5t8)qio2e3amsmeased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mwvr c/l:z0ry3:pc4l s 4xlev8iddle C (262 Hz), but one is at 5.0°C and the otv0/s:v rczxwpl3:c er ly44l8her at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has alg:*hag 7h e.d 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: elg*ag d.h7h 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 ogzz 1*lvaskc tgbmi28e;sdf; r*r2(8k)jr h- ne speaker and 3.50 m from the osgjzf* rg amksehtkvl81(bzr i)28c-;2r ; d *ther.
(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 tuner s-y a9(e5bl eu wrn-w5hears three beats every 2.0 s when they are played together. (nwu-ysr5ew(lb- 59 eaa) 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 wavelem tm0: pdas5 yis7x9e83p xip0ngths 2.64 m and 2.76 m in air. How many beats per second will be hea03ts y9peipd0ps xi:mm5a7 x8rd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 pter h;f)t*jw *tp4 1yq 9j6hdHz when at rest. What freq;t4pt69fpjqrh1y ej*d )hw *tuency 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 a6bsez v/bg jgd-n x(z95y/fg7 fire engine whose siren emnj y59 ( /bvgeb6xz-gzdf/sg 7its at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in :. g9 vr,h;,lbfjmfgl.urt6xfrequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies e jglfrf.9t:um6l,. bxh,r;gvxactly 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 equ *1ph pu8+0o5 zpnz0w 7fqiysaipped with the same single frequency horn. When one is at rest and the other is moving toward0iq* zowpyp87fn0a +h1szu5 p 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 out ultrasonic sound waves at 50.0 kHz and r8 0xqs 6aytg.weceives them returned from an object moving directly away from it at 25 m/s What is 0. 6gswatxq8ythe received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 4*q ooht5bh ev4bxq93 zo:a5d 5 m/s As it flies, the bat emits an ultrasonic sound wave wb4qea:5z3bx *5hoqo9thd o4 vith frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experim5dzx6r()ew2e 2 hsfe (:kxxmfents, a tuba was played on a moving flat train car at a fxsdz2( rhme)2x:xf5e6k fw(e requency 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 ultrasound waves to measure bloo oj*;o dyvq0y+a3ta8 sd-flow speeds. Suppose the device emits soun; 3daj0t8+yo aqs o*yvd 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 directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wakc7j ec+oh*k+mxn ; 4ib4lan7ves 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 ofs6x ap8c(sp rr; 8gg; mpk1y(z frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are 8pry;g8 m gx(pr16spkzs; ac( 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 itsl4t6 r3)tvc:8mxuc flg13eiy *3nsf f 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 w2lt7wz//ac o4 zf+nithere the speed of sound is 310 m/s (a) What is the ang/7fto4lza2/n tic+w zle 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 where the s) y z*y5sl8/ckzc 0mhvpeed of sound isv 0*zy)cz/ylcsm8k 5 h 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 85(gk (nv 1a:z7zlw: vzz00 m/s strikes the ocean. Determine the shock wave angle it wz(g zkn(::71v z lzavproduces
(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 vh(dqw80iz60t 7 nl gr$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exa j2dqf3cg e dpba05fl uf.l1*9ctly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic lgcb0 p uf95.d2 *ea3d 1flqfjboom, 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 20,000-Hz sound pulses downwek 6p,i0pkopw:t)z 2k ard from the bottom of the boat, and then detects echoes. If the maximum depth for which 0op pkzk2kt)ep,6iw : it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octave mdpg)x:v/ba,;dtjf -s are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a /nu7 l/ )* 0hlzucjkcp;sp tp2sewer pipe symphony. It consists of many plastic pipes of various lengths,)0cu/ zpu np;lh7ct2l* sjpk/ 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.w8h//jx4cph+ yr;u9 8y20l vuxaddxs 0 m from a person makes a sound close to the threshold of human hearinga c8wvu8+l ypd/sxr42y jx0; d/ uhx9h (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 8h ha+vpm0 :1t.pnwi+ 0 yeu3bu7-dB sound are heard simulbh+u.0u namip:thwe3+ v10 y ptaneously?    dB

  The sound level 12.0 m from a louuc;s+t.eehu vrwq3ba6h (bnt14ba+(dspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all d( 3e1qa.ne6;c (vrh b+4utba thsbu+wirections?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. T1vfset 2 i*2v-oycli7he power output drops by 10 dB at 15 kHz. What is the power output in wattso ei7ct1y-v2i2*vsl f at 15 kHz?    dB

  Workers around jet ab +ta0 w-i66:vn4wpl,h xmsgzircraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a dista z:- ,b0 mnlh4siv6g6 pwaxw+tnce 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, thz6:y n s65zgju, bue( g*n:phle gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to yy: ur4tm km37, p:q6waomb8la 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 ficz m(jj 6,t 7j-wlt3ybxed points with a fundamental frequency of 440 Hz and a mt-j67 z(wjljbt,y m 3cass 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 rs9r0f 4q,obba 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 s0rofbbq 9 ,4rlevel 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-h*ldnqm0.;zmg6b eu 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 the string if it is to produce resonance (in its fundamenta u-mqblz*6m 0h; gend.l mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one xzuaz:)t3( mm 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 two sources. The x,8hog)c .qcx ;xrxu7 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 o7;c., x)h gcxqrux o8xther. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The co8ke t0j)xtazvyt4na+vp()9u nductor on the statiot+a vu z (e)yxatkvp9n840jt)nary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whikx)(v( jwvaj3 xt5 dz;9c*+ qveg; upnstle as it approaches you is 538 Hz. After it passes you, its frequency is mew(vgx;3vzk dj +n)ue(jqc 9x pv;a*t5asured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listec6s2 z1uni59mp9hza yning to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octavcauyis 126 z5m9h9pzne (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. pd6 hth/i 9hf)dl j0w4The shorter one h j40h ht)/lf d9iwp6dis 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of m h197hw 5)5 fwg 4t;p zkxyzjyg;ljx7a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig.m5 zy7w5tyxw jh;k4gjhf1x pg l9 ;z7) 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 the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow i39 ll3f0.gc7yko oyj an 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 cells? Assume that the waves travel with a 9k.ojgy3cfo3y7 l0 l aspeed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speam knw 2hwx69 6nfm(3.(9xo,e thlstzed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51tzh,mfw99 o (e3th ms2 6.xl awn(knx6.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it app xmqrv;4pp gt/ l-(7xk xq+nl( rlet0n6j*p8broaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so th-rbqqp7ln p4 kt j(pxr(lx meg8 6/l+nvt *;0xat 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 one Alpine vim+ 1qem mia) m. eyi5.(5gb+oahx;imhllage to another. 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 ;.mmh1hy iia 5a) +5.mexg qmibmo+(e 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 of60t zo/ze14whzh2 0pjf+m mbn 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 fundamental frequenciew2+06pfhob 4 t 0 /1zzjmnemzhs 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, slen4 g u 1arxs5,wn+hoxg:der 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, ring gr+hgsxx4:1aw5 nou,ing 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 thei0 lm/oqmc53;rhfej7 threshold of hearing for the human ear at a frequency of about 1005lhoi /j0 ;memrq3f c70 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 01qu a x-(anusat Mach 2.0. An observer on the ground hears the sonic boom 1.5 minxau na(s1u-0q after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isqv3qdk r(m u*y7w/.t74 ;jaxz6nlzrk 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h