What is the evidence that znupi k :m0a+.v0c0tenixq /2 sound travels as a wave?

What is the evidence thatm et,+0shm3ql7prx+p sound is a form of energy?

Children sometimes play with a homemade 6e x b426sejsh“telephone” by attaching a string to the bottoms of two paper cups. When the string2s s6j4e6xhe b 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, do you expect the frequency or waroz,og j( x(s4velength to chgj4,ro(x szo( ange?

What evidence can you give that thx vh2bl e23;b9 tuemyd: az(,j7dlt;re speed of sound in air does not depend significantd72 y;bd,rmtjzl2h tua vxlb9e3( e :;ly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched.2qdia+ne2oul ef 61( r Why?

How will the air temperature in a room affect the pitchn3c+y*pue yx c2 up.b-r.l cd1 of organ pipes?

Explain how a tube might be used as a filter to redu qb2 jp(-9qvqhce the amplitude of sounds in various frequen-jqv ph9qq(2b cy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–5jk7dld,qk67ytczp2a a 5z4/je w nv4 30) spaced closer together as you move up the fingerboard toward thjz44jy kvzld7ka2c5n6,/t ad5 wp 7qee bridge?

A noisy truck approaches you from behind a building./w:idre)l/vi Initially you hear it but cannot see it. When it emerges )l rd/v /ewi:iand you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due tkz8wwsa8*mzm9e (b j( o “interference in space,” whereas beats can be said to be due to “interferenc( m s kbwa(88*9zjmezwe in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, yg o6xo+.qn, lyda3+qwould the points D and C (where destructive and constq3,lo.odyx+qag + 6nyructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hear8lls6f0f;,sm.kggw o.zqc6z ing 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 ..k qgsfmllzo ;s ,6fg8 6cz0wit 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 shown ina:q5y-bb ;a7jow ..jxrxst(b Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequenciar(o5tj wqsj yba.b .: 7bx-x;es, 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 souradi*q u02dga)*uq k4nce and observer move in the same direction, *) *a4ga iqk0d unqdu2with the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound (e4net6zvd4a mck mmu,a )/ o1heard by a person at rest with respecmac zv4t6d)mmk,e un/(e4a1 ot to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positio4ys,a nfazvu8 3.vm i/zf1 kt4ns of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. As z4fy8afv /3i4m.ua,vkt z n1t 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 l8 zw;g yl55, kriipp7iength of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. Shep,i5wy ; p8rk 7ig5liz 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 bc j 96rh:lss*hrls7d 5 phr86eelow the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound*h:srdh6 j79 shlrs lrc5 6pe8 in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelen)u v-b9tjw:zzqd 1 s(ogths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just ahp 7y;c (cw- q8:q8ttw lz68ysd flck8bove a school of tuna on a foggy day. Without warning, an engine bacsdkyq88y 7h ztcqp(-;6c f8 cltw 8w:lkfire 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 top of a cliff. The splash id ub*a4lv3 -uvefl0*c0r 5e6p cx(frk t makes when striking the water below is heard 3.5 s later. Ha* b pvu*30v d- 4ll5fcr(cef0xke ur6ow high is the cliff?    m

  A person, with his ear to the ground, sees a +rfcuoe3t5 g(*ul9cghuge 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 f3rg*u (+cog 9t5ufe clar away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-i0s(c 7x7 uhzxsecond rule” for estimating the u77c (0xi shxzdistance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain6hh4q fqe6qqdzts/ b 3.te6s+hc -k7a level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sounce,xe4,x*b equ(tqr+d whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneydljil4c0p1 ,ously at a certain place, what will be thic01lp,j 4d yle sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airpdz/tzdl)uy39 lane with four equally noisy jet engines is experiencing a sound level z/t3d 9yzu ld)bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-not.grn3e (bb1sise 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 each device? 58 dB =1eb(sgrn b.3t    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conversaggyjvl2* 1(fsuih a0mz0d7 *ution. Use Table 12–2. Assume tv0fuah*izg72myl( s dj ug1*0he sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whosrt3h,(fn ty+ de 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 tgr1t m4dw*0lxaw* 1 auhe more modest amplifier B is rated at 40 Wt1lw4d u1wgax*rm*a 0. (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 d;r tn ujtdyl.(idd(op8:c; :.8 m in front of a loudspo8j:(rdt;nu dt;(: p dcldy.ieaker 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 r/2 t9 2bpspnrux3d5u difference in sound level of 2.0 dB. What is the ratio of the amplitudes tns9u5u3 x2p rpdbr2/ of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, 6wz9r3q kesn5g1xe,n (f w 2vh(a) by what factor will the intensity inz2 rn k 1 53feg6whnwqsx(v,9ecrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal dhus uz+a*xdc8e)zr z c;6o.4 yisplacement amplitudes, but one has twice the frequency of the other. What is the ratio o.xoau8du ec *4rs; zhy)z c6z+f their intensities?   

  What would be the sound level (in dB) of a sountlu zeh6 b2l/td7x3o8 k1c7eyd wave in air that corresponds to a displacement amplitude of vibrating air molecules of 06el7b1 / t2kz87y3doecl utxh.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what s*3m ,xrjxir6 +sbw8 lround level to seem as loud as a 100-Hz tone that has a 50-dB sound level?8*rx mx,+rbw3ilsr 6j (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when o 2iur5dth6p,the sound iod hp,ut52r6 level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is )xj+7 z 2pdc6) frflmzthe ratio of highest to lowest intensity at zmf+jc x rl62)7 pfzd)
(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 lengtho ka zx2wc 4n1 (83rby2gindb. of the vibratin.yco(kb zax2wn id 2g31br8n 4g portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundame kygc.;o( 5g2:n- qywaf ,tsyfb uj1(1fqbn f/ntal and first three audible overto b;k 1-.aq(y25q1n,ff syb ggwuft/ cf(y :njones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across/vfz 7k,arh*s the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tubs/h*r kz,av7fe?    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 t*ax)o s tpkq+1he range of human hearing (20 Hz to 20 kHz), what would be the range of the lengt+tqx ao1)sp k*hs 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 thi1wb :hfz 0q4u(kpv:merd harmonic. What will be its fundamental frequency if it is fingerkvhu( w p 04:fqeb1mz:ed at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 malh7ep(o qen70 md(ga );0ijm long and is tuned to play E above middle C (330 Hm);0ajmi p(de ehq7a7( g0lnoz).
(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 thal ,zbly3s 5n56e:u 1 tudubg;st emits middle C (262 Hz) when the temperateu s;un6sdbbz:5u l y31g,lt5ure 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 ezz+fvo8vz8 9;p hzeo45:rih20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute inrsgb ky1 xx3/2 Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hsbkyx 32 r/xg1z?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440g w-sxod+q+- d0 u1kio Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this qk1sd0+g- duoow+xi- is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two succihb/mq )z gz(:essive harmonics of frequen/zzibgm):h( q cies 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 4bfqkm */:gxa$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-lopg rri/,y, )o(ou0l* ol;oxptng organ pipe at 2r0ox u* ;,op/ i)y(olgr lot,p0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is ap3h n90k d5 4djig,ecupproximately 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 in th hd0cpk9gd5 u,3 ei4nje graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two wcv 9 fza,pafur4b 0qz1b48-nt w5 (shstrings, one of which is sounding 440 Hz. How far off in frequency is the other string?(0z 1vwtaufs54wcf49 -b bz,h rqanp8 ±    Hz

  What is the beat frequency if middle C (26wc yb:qs: de4m.l)0qp2 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates awdhl j1le55wrmp*o 5/t an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of w*l dlp5h1/mowje5r5frequency 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-Hk96xt++ mjvqmpn9;x gz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational fre ;pkxgnmmxq6v9j +9 +tquency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The t1w w.8o0kchkxension in one string is then decreased by 2.0%. What will be the beat frek h1ko08 x.wcwquency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two ide.kk mzv+7gnz9 ntical flutes each try to play middle C (262 Hz), but one is at 5.0°Cn+mkgzv k 79.z and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 4q.f hivjg c576uzn4 f:41 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B q7:zig cfu 46.h5j nfvand 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 one speaker and cyc8o rby )n iwj1( 38/zwvyr,3.50 m fro/yzc1)yjy iw (rvw88,b3 r cnom 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 tuv wlivu;+n 12cye;5urner hears three beats every 2.0 s when they are played together. (a) If one is vibrat;vwre12cv5ny+ u liu;ing 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 wavel sxz)e; crxjq/ ird0+3engths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20 /e0jq3i+)zxrs;c rdx $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequea8uea b20en (cncy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do yo0(euc28aebn a u 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 firrsdp3,y ty jpapn/q.9u u9s/7e engine whose siren emits at 1550y rtu 3.qjunppd9sy/ as9 ,/7p Hz moves at 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 sou1c0,z5j xia n12 tdcumrce is moving toward you at 15 m/n02uzimt 1 j5cd,ca1xs versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Who n./6i 1y0skf.bxrys en one is 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. 1n b/.fkyyis6xr0s . oWhat is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soh wzx,+h(zf 4xaxb :c-8; w8pv flfag7und waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the recei(;4 l vx fxc w8a:fb+ 8wgf7-,zaphxzhved sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the be*d+bh l mvs;ec++h- hat emits an ultrasonic sound wave with frequency 30.0 k b hh*;++mscdvlh-ee+Hz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tub(,e/18 z nl;o z:fajaqqs3 :aoyw8 o(lzkyri6a was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the rail6 so i8o3z;oln1r ((eqa8qfy,zy lkjz:/:aw a way 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 ultrasou;;g ovo6 qg3 +vf nu:da1bdv*dnd waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is 3u;v*fb vn1q6odd+g:oga d ;vtaken 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 uslsv4 p cc8r00fing 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 Hz. When the wind velocity j-q s5u ynxv ;3snozih /ksnu9g1d(d+t6. h2 iis 12 m/s from the north, what frequency will observers hear who ars9t3 o k/-yi.sn5q(+d gnujxv z1 2hdi6hns;ue 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 movinq tcw01 yn3x:i*jkwcu9: ah m *9xumd7g on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What i fb0a(.z8vubj) 5r kwas the angle the shock wave makes with thb8aw ( )fk0zubjv5a.re 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 ofzv cqce1w c6 *.wv 4)ako4wl.p*r oxh6 a planet where the speed of sound is only about 35 m/cao.qw cvc*rw)o6xz .4p*4eh v1lk w6s
(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 a /esn*9(4oj /eefvd ppngle it pro j* s4np9veep(/fd e/oduces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle u.: yio xha( .vljg/ i7-d5bvf$/theta$ 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 e6.g/ur(r8pu3 9a rlmz:jelty xactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determin:ea3r6jlrpz.gr/tl 8ym uu 9(e
(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 thatf)lcxf((grsype3 zd4fa89 e: sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the max: ffrp( f g3ed(a) 84zxlyesc9imum 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 there in the human audible g+n6o-oh (fuj4hgbb(range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphbe:n mjn he2*ur s))(hrw(2drony. It consists of many plastic p*h 2(:ju2d)brnh(ene ws r)mripes 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 ureb j2k+n3k olq3;x5 from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1e2uol qn bkxk+35r3; j000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-lp2sc:g5 0srydB sound are heard simultaneousrl 0yp:52scgsly?    dB

  The sound level 12.0 m from a lng) ).3lwqcrzoudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) )w3 .qnc)r zglof the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drfmlds1fa (.2vops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz?vmfs f1.a2( dl    dB

  Workers around jet aircraft typically wear protective devl 0 vwee8 zf1jc k+r6z9o,1uxh0f j9xrices 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 hrfj0+xz9 eeoc8zf1rvul ,hxj0 kw 9 16as an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gainzra r9-2u ob,.*z wasj*uh2plk itonycz*:43, $\beta$ 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 levz- x-k cq(gr-,-zlk ; i,bqa 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 ((c kj5b a-mctfixed points with a fundamental frequency of k-abmctj (5c( 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with w p*yju7y7, *vss2qiaxater (Fig. 12–35). The water level is allowed to drop slo q7uva7j ixy*s, ys*p2wly. 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 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 a tube that is open at one e1hy* /t7e:mi;t pvc r9*zcpto nd and also 75 cm long. How much tension sho/cm v o91piz *ttc7:h ery;*ptuld be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observefabnu ;ujuck+o68 e- u- 5ni:td to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure:mda 6j,ur)ruy. efsra) 2gzlxp/; k/ tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determi)/m6j e :d; akgr)2uxz a/.p rfyu,srlne 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 stationary. The conn c.lv yi: ndz1tpbxcit//- 59ductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving trai9n.1d xc/ti vcny/zbpl:5-t i n?   m/s

  The frequency of a steam train whistle as it approaches you is 538d5 xawrvh72bog6*cfu3(: q(oweue 8e Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constaah(o6eu5eod ( x7*3wg vfeb 2cq :8ruwnt velocity)?    m/s

  At a race track, you can estimate the speed of cars just by liste+j;jrnei 0ipqkf:ts ih.( frz eg)6 5-ning to the difference in pitch of the engine noise between; :i kep.-freh0z)5 f+i gj t6sjq(irn approaching 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, sounding together, produceu gj5kyg: c(uo: co*3qfbd 2l2 a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is thegl :do 2qcb3:52(jokucf gyu* other?    m

Two loudspeakers are at opposite ends of a railroad car as it mb8s/t8tdx,e 5bwej/noves 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) h8see d b,8/jtxn/t w5be 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 bloi8tth-ze3p3)e u -+ g jxsssi7od flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from thisu3-p7+ t)gx -e8j s3zihstee 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/(lt(,wnajl ar(er h2m2c0n )us 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 the frequency of the wave detected b0nuj ,rh2( a wma2cnl)t((rely the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approac64r,1hdnsm4nr q- 8zvje0syahes a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 msn ndm yje1z40vsr,4hrq- 8 sa6 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 us9k9v eu/lh4g2g0 p* j7:lb cstno hev8ed to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musice/2glojs8eu t 07hg 9c hb49kv l:npv*al 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 s)jg271u;l ivwsnxp8zr * yyp v;ey/m.tereo listening can be compromised by the presence of standing waves, zu rxnw *m;yiv;p)82sl g.e1y j/p7yvwhich 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 frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” ib;:1ug6gv*b ; px56lsrq au ahnvolves a long, slender aluminum rod held in the hand near the rod*x6u: l g bqp5v1 us;b;aar6hg’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 of hearing for td u+ds/4x cksk2qyp.ar * (h sf4wap04he human ear at a frequency of about 1000 H/wpcu4q a 4.sapsh kd2x s r4*y0(fkd+z is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hearhm9. *ho1o crzv(6f5w w urip/s the sonic boom 1.5 min after the plavm fh/rpi(6.ww91zou5 h *or cne passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is;8/bdzp)wt jz 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