What is the evidence :7,x1o uh- ttnnq x2lothat sound travels as a wave?

What is the evidence that sound is a form of energy?lojwfh*.lcw9, i ff 5:

Children sometimes play with a homemade “telephone” by fbmoq42x qx (-o 9gg7 px/+haqattaching 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 cg/q h(xoa2m-xfxogp4b 7+qq 9learly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect th;6x +xo1xzr sge frequency or wavelenzosxrg 1x;x+ 6gth to change?

What evidence can you give that the speed of );7bz r -u cql mkft-7lyo/;ylsound in air does not depend significantly on freqlyz-o;c7lylrf ) uk b-;/7m tquency?

The voice of a person who hv(fk e t*wuf:)as inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of ofibk3h 8z6had;rt,:j rgan pipes?

Explain how a tube might be used as a filter to reduce q36m g0 ex3 1mh. -yothzw0mqmthe amplitude of sounds in various frequency ranges. (An examplewq0 3q -zmmxh6oem3 m.thy01g is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced -n9-mx b(cdao closer together as you move up the fing(dm 9cb -aonx-erboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hmz:* zt1y c7tx yk6xh2ear 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 nomk:yht y*xc7t 61xzz2ise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,”b ;*yh;r.v xn5xxx/px whereas beats can be said to be due to “interferen5;b*x px vrx xyh/.;xnce in time.” Explain.

In Fig. 12–16, if the frequency of the speakep-:8xyfk;b-bimf o 8 krs were lowered, would the points D and C (where destru-:pffk 8obyxmi;bk8- ctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peopzh*c r vt06k,zle who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise level,r 6v*zkzt ch0s. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be h0). t wdzk(ubvk 5-qgthought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Expltzw gv.0qd(-)bhu kk5ain.
(12-31)
(12-18)

Is there a Doppler shift if the source and toz/v y iom9pss.ge+k,9n ( *gobserver move in the same direction, with .i* m(y/g e ,ngo+koszp99svtthe same velocity? Explain.

If a wind is blowing, wil-;a*u fc;a tq7bm,qj kl this alter the frequency of the sound heard by a person at-ajfm *a7;tqbk;q uc, rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. *90x t0xnnu/4zeku*zl t c0ev A monitor is blowing a whistle in front of the child on the grkl eczxxv4utt0*e nn uz9/0*0ound. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shoovux,7klk 0o3 ut reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of tk0 l,7ku oxv3ohe lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shipylak* 7;:2 rtd d4kwpw just below 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? Asad7p*t wk;wd ly2k:4r sume 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 m x8/m8xk qcs6h 9xrxcu,2(yk$^{\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 a ptqm53e/pgj5mzj,)x bove a school of tuna on a foggy day. Witj,pj 5q x5emzmp)t3g/hout 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,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash )al+,j l*9t-ujrapgbid r4t5 it makes when striking the water below is heard 3.5 s later. Hot*,gl a l9j+udbr)p5a-it jr4 w high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the cone vik /t* n usz)/m3+s0er8vs+k )jplpcrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concretj*evmsret)p vi uk/ lz0n3s8)+/kp + se, 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 disir mw v-gt4o9 jojr+9;tance by the “5-second rule” for estimating the distance from-r+mw o ji;9rtgjo49 v 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 pain level of 120 dBe*2n;cthba-0i;8hax g, x p ea?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound lev7h.;vyo..vl d4as rq4krl3 :vm rigc6 el of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultbr67i,qmi 8zkmh: 1yg ig1im 4aneously at a certain place, what will be the 18h17zibm gkmi,g ir6:4m i yqsound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplacj/owt;z:a ;du f y1a6;7xkpzne 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 aljo7 6au;pa/;; wztfd1 z: ckxyl but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rat8kwnba//g 5 c yab,sli9k2.h uio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensi, hbka a5wlskbc9/i 8n.g/ y2uties of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of soundtb8h e b9pbt5, from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on t5bbp e8t 9,thbhe 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 zab2)z v i3.knwhose 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 7d2b*)l4 ukzzlt) p*g-q tvzaamplifier B is rated at 40 W. * lvu-*pktzq) balg42d7 tzz) (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 z)8-f /fyllbzy 8ukj*dB meter registered 130 dB when placed 2.8 m in front of a loudspeaker on/ zyl kbl8 )yjf8-zu*f 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 typily/f.jq ml;+a ok.6ag0 p7 wpocally detect a difference in sound level of 2.0 dB. What is the ratio of the a6l p7+ofowj0la ..m ;qgpy/kamplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a s kovo *d,ic ce fs(s/a*skm k,;oc,j.,ound wave is tripled, (a) by what factor will the intensity increase? Increase by a fac,sk,,s*e;ccf. (c dsjva*o,o m ikok /tor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twiceeyk/4+lxnm i3kvr0s 9 the frequency of the 9e4kr0l+ ky/nmsiv 3xother. What is the ratio of their intensities?   

  What would be the sound level (in (g 1):hsmxts, pvij ,kdB) of a sound wave in air that corresponds to a displacement amp:,ik(h)sm,st jg 1v pxlitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have zi 37xs;a* 3dna4cxc a7dp9tq what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound lzx3aa ids ;aq9c*4 c7dt7xpn 3evel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies0 coifatv72; v that an ear can detect when the sound v72av;c i0tfo level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the rr(3, cvro. zwkatio of highest to lo,.(c3wkrr vzo west 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 f: mah+61* gxqsvtz l(hrequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placedazxv*hqh 1mg (6s: l+t?    N

  An organ pipe is 112 cm long. What are the fundamental and first three wx5ldnyc a;,s;s8hda92bxe 5 audible over; cd,8wyne5a axdls; bx9s25htones 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 frequencyxz95drm4 - hpb would you expect from blowing across the top of an empty soda bottle that is 18 cmd4 rb95 mz-pxh 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-tuh- j3) jcy w.fxhy0k 4krqs0-+t.mzpj be pipes spanning the range of human he-qfxywz +jph j.0 kkm3ry ht)j0s.4c -aring (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 hak8-u:f.p8dvry8 x zce s a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lenp8: 8 y.xuekvrd czf8-gth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mia y4p*.ew li1u u)/nsn/aqs v-ddle C (330 H)awli-u1 .s np/se*u vyq/na4z).
(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 or;xae;9dq(o7g i0dxjjlqe; m 0gan pipe that emits middle C (262 Hz) when the temperature e0 l j9o ag;xme;(qxd;j0 7qdiis 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 20nyyoeqqy w( q()v677k $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flul hr v*zdzom,znkd5 24,r. no7te in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hodknz,m4 z2l5zd .r,rv *hon7z?    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,5 br3bun/2ipqx m7fp 9 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this isr bx9/iup25 q bpm7f3n 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 rhf t:5j ;5lsetc j-o t27to+2cviilv ;esonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whatt t;7 oojitj+l5;f-s: e5 vch cv22ilt 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 t3//n)xwn,6zp vwtpp$^{\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 audo;-ti k af2ayjfc 2m-;ible range for a 2.14-m-long organ j;-f fo -2ki at;acym2pipe 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 nw:z7obl 3*omir n:.m0k w*;gfub l,iis 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 cana;n* m*u. n3 bli0fb oi: ,kgmroww7:zll. 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 ever913 jr. lx 1 w2lrqtdp8o2qoxhy 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in8wlhxltq3.o2 12o1 rdrpxjq 9 frequency is the other string? ±    Hz

  What is the beat frequency ift9fbt v00z vr;j q*yf; middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates amt54yr3 5, h3ytv f2 d,xxigult 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultm2,l,5t 5 g3f4dvryy iuxxht3aneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tun q4 9:nyw15r7y i .anwzjv-vfying fork and 9 beats/s when sounded with a 355-Hz tuning fork.w yw-j:iza .yq vv157r4 ynn9f What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to thew*2v.s qiuw*fuxcr + cd+(0 kq same frequency, 294 Hz. 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: Recall Eq.+ .xq2+vr uuwc*( cqi0ksw *df 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play .)rled )xui q79chr ab (b *y;:xjgsv3middle C (262 Hz), but one is at 5.0°C i3j7vy)he(brl);*r gacx. qsd :x9uband the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hzh 4+ -3 0bmcch1 nep ;zjuhzsma99.qtf; when mb9nzcj+apq- f.cz esuht 9;3 4mh0h1A 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 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. 5aue+ ria;cm0 A person stands 3.00 m from one speaker and 3.i m r0cau5+ea;50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hea; 8fersk4(ihci 6*cbjrs 6c ki4if(hrbj se*c8;three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats percnctqgze;8ee 6nq(r- 3z(j i( second will be hear6q( ner -(e;3zegtci(n8cq z jd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cfke hj 6qy3+fybh;f8-ertain fire engine’s siren is 1550 Hz when at rest. What freqh+;h6yfby j -fqkf8e3uency 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 frpoo ,w o.xc-raucbz,j1.*wjum i 1 :g2equency do you detect if a fire engine whose siren emits at 1550 Hz w.p ajm. 2xobowo,c j rg*ci:u ,uz11-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 source is moving towardbt4 txirz1 .1ul mr4/q you at 15 m/s versus you moving toward it at 15 i1utmtr4./xqbzr41lm/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 hta9kjz*jbg larz (. e*,b*5z born. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat fkbbezj5z9j*l*b a( *.t, a rzgrequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ulq4p: +1 oznwpbtrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequency? nwq 14zop+b p:   $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s Aso69lqw weo.w ) it flies, the bat emits an ultrasonic sound o o 9)wew6wq.lwave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba zy a0cwfk4tihb; p 1(b1)g+hjwas played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if tth4z(0hc )1j g;pibwfka+1y b he train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloo.) byzm j-wgr6d-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What ybz )mwgjr .6-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 ultrasgvg0 r 4 d5av-z:d.kcsonic 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 soundu.r*uq5 b0r9ur 8mp8inh t gu6 of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers heghu8*06 ip 9quuubr8r mt.n5rar 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 movs,n z;55b bt 4dsh*reping 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/p;f ,/y i52evtne+0thzs9taq ;ffsv-s (a) What is the angle the shock wave makes with the direction oftnfe+vzv 0-hfqey,9;tf/s5; 2pa t si 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 8sp r,k( sg)oua planet where the speed of sound is only a kuossg,( )p8rbout 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 mi- nb5 qj(3kwexl: x.y/s strikes the ocean. Determine the shock wave angle it prodi kql5.(j nxe-y3w: bxuces
(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 w*,*0kxcbhrta33bd s $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhe.a * fp*pgt,qf/: epif5cc o7oad and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the o5t*p :/gqe .f 7o, *pcffiacpsonic 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 wz .cxx3 dre5 76:odyo20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoesoxc:r ddzow.3ye 75 x6. If the maximum 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 audiblycl;7t5 v haa4w6u;jh e range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer p *xwo+z a.1 ;-l3hk qylifbje4ipe symphony. It consists of many;ozyejh1l +- k* xf a.b4qliw3 plastic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold of humqa74 p*cm q2mman hearing (0 dB). What will be the sound level of 1000 such mosqammm4q *qc7 p2uitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are6xu( artkkdcx(tgo6 me.1e16 heard simultaneously?mtgcue(1ko ekx66rx1 6 (d.at    dB

  The sound level 12.0 m rv)r d;u890 4re curwhfrom a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) reu )rcvdr4h 8 uw;r90of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 o7m3l3y9 4j hgj*ppt avup;w, Hz. The power output drops bh94 wy,jl3j3a;7uvgppp omt *y 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicall(fn z/--o9tgb zbjn-l4clh 1d y wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and-z49ol/j-n-dnt h c gz1 lbfb( 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 communicaz1 qz5 t:3v)1e0jqu ukm2cinhtions systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency s-w.tocg-i*no +7d dk1$\frac{1}{2}$ 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 3c/hnt) w9+,vzt, f eyy2 cm long between fixed points with a fundamental frequency of 440 nch t+,ye,) wv 9f/yztHz 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 xc +mc 8as8ro*4mbra0 tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the framxorms *8r bc+4c0a8equency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g (c/jbw 6oo*uq is near a tube that is open at one end and also 75 cm long. Hobw* o/q o(cu6jw much tension should 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 obseg 7vf w/z69u0hwcqy6 srved 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 tkcf)( kqy+d:p one in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m fartkqpk(cf )+:dy her 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 conduc6agvi 8c m 25vo/wivo2tor on the stationary train hears a 3.0-Hz beat frequency when the 2a vog cm2vi 658/woivother train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approach-:wj0 wwj8 n6rdhf ke. dmb 1udj:y30ges you is 538 Hz. After it passes you, its frequency is measured as 48mrddjdk8j u.y1j3 ww0n-f 0 hgeb:w:66 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of caidxdk* ti5x h3jj)c 88rs just by listening to the difference in pitch of the engine noise between appr ti kjj)5 8dd3xh8i*xcoaching 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, produce a beat frequency o /v3d,a;u86q idnvmq1v me/b nf 11 Hz. The shorter one is 2.40 m long. How long is thu6 /i 1q3vmvemaq,vdn8b;n d/e other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pastrby 87 iv;+-s sao8rql a stationary observer r-q v+7;r8i8ssabol yat 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between 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 naeyu53f6rzgdc 54 nf ;ormally about 0.32 m/s what beat frequency would you eu5 a5dfref zng4y ;63cxpect 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 while the mot*/cf ag sp./fch is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflecfa.c/c/* psg fts off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. Tuuerrpk;xa4i d)f gkmeq124 mr03 d*-he pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moegxf31rir4 );-p0d2uke kr mua qm4 d*th 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 1.oc6ygtf(/dn l vbe4used 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 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? (Seg vb6 olct4(./ndyf1 ee Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be h-5 o*,/ukv xj,tgc/e*sor bxcompromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamenu jro5x- ,/xeo/tks cvhgb*,*tal frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstrationss/7kib0( t ng ihp(2m, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with th msgiib( 7stp/(hk0 2ne 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 the human ear at a frequet7 f4fzf uhp h*-:f.mwncy of about 100zwh*f mf-7fhf4up .t:0 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0.euseb)wmf(a)kh(gt*s to:8+0/ kl t h An observer on the ground hears the sonic boom 1.5 min after the plane passes twul8 t et (:oekbh+g(s h)skf/*)ma0directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1(wpf1v /op2oqr5qg1 z5 $^{\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