What is the evidence that sound tra uqhm2 2y/xe,yy j5+w9hm ygcig14 p5bvels as a wave?

What is the evidenceb62f obyrb nrgfqb2 rjr :74(wt;,6jm that sound is a form of energy?

Children sometimes play with a homemade “telephonepm-* f2cf4,dg: ja 4 fd z(t0ctxi;tr*y.p shk” by attaching a string to the bottoms of two paper cups. When the string i :fa0pyrjcf (.z4s*,ikc- fd* tht2p xgdm;t4s 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 freq/qcxc(z).oh x uency or wavelength to chzh(.xc x)/ qcoange?

What evidence can you give that the sj8t9z rdh+2tcu8q4 aa peed of sound in air does not depend significantly onar8 + 9tadz2cutq8j 4h frequency?

The voice of a person who has inhawp7sznd7 h4) 337evapl 4rkrqled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipes?de 1 lm3df8t5+4fet7sv po yt a0aif-)

Explain how a tube might be u8 damhe vm q6yk:un-0g. 0hg(ysed as a filter to reduce the amplitude of sounds in various frequency ranges. (An example i8-hd0a6u0nvgykghm(. :em y qs a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as b+rnqj10o f1myou move up tqnfb j0r+1mo 1he fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but d/)dw8bqv iy0 cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of tiwy d/bvq)d80he high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferevo8eg ,gzm7b-x6)j ;u 8jjd oknce in space,” whereas beats can be sai86vjbjdo gz,-uxg; j 7m) ek8od to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of r8njk xv.e 4;ethe speakers were lowered, would the points D and C (where destructive and constructive interference or4ev ;nj 8.kexccur) move farther apart or closer together?

Traditional methods of protecting the hearing of people whtqks + ieb1h8:s;w* g+yypg 9zo 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 d1b:ig qy;s*+sey9h+kzgp t w8o 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 thought of:j(bwrlmf- b3 as a superposition of two sound waves with slightlwb f -ljb(mr:3y different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same dw4 uu k vb01u/ f2fia;lh1g-clo(t- deirection, with the same vei4-/u 1al0w;vud cfu-k1 hb tlgoe(2 flocity? Explain.

If a wind is blowing, will thiso5 w 35ima:yps alter the frequency of the sound heard by a person at rest with respect to the source? Is the yami3p s5o5 :wwavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitosfb0avoi.:es cxuqa f23 92c/r is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for th: c0/cbau 2oq32fevsa9x.is fe sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening k8+)op)w wlj)cg qz9ofor the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Esticj )+l w o)k)qp8ogzw9mate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the evh8gsk .wr5 -o4s :wgscho of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at twwsg 5 ksrv- gh8so:.4his 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:+f-h g/)wkvkvp rd/v 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 drify; rd;o*-; phl tyj(g4:rp,p qif ;uzpting just above a school of tuna on a foggy day. Without warning, an engine bact*o;p,pzj ;4 (g:uf -ypprl;hqr; dyikfire 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 it makes wfnjxa69 t-1q hhen striking the water below is he jtn61aqx9fh -ard 3.5 s later. How high is the cliff?    m

  A person, with his ear to u xud3:q)77ub avr ,ohthe ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard da:xh,o)b 7uuv3r7q u from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5- zj6ytilr4. 3e*1yiaysecond rule” for estimating the distance from a lightning strike if the temperature is (a) 3031ijeiy.t zy6ar l4y* $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sod2g:4f2ro3lk tn+3 4kg g n3/ostno cqund at the pain 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 sound whose inten1ahg gxc o1(sh j4;ko6sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simult)wu/)et)znu(y /b qvianeously at a certain place, what will be the sound levwyb vz))(q nu/t /)ueiel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an aflg0np fw t-/6irplane 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 alpltw0n g ff/-6l but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a siggwvnj: f . xq,dt4n.d+nal-to-noise ratio of 58 dB, whereas for a CD playegw:vtd ndjn..x4 +qf,r 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 sotv)nk 3-xm dzm+jf3k0 und from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere ckt 0 -3knvm+fm3 zd)xjentered 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 whose area wo, (r/hox pj/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 mo/o5ewxt gn18x 64.4 fefur un wt+zi3tdest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a lt+ n 8 g/3ne6 iw54rf41uo.efuwzt xtxoudspeaker 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 g y03jgneaas s8-x9 8aqckh67in front of a loudspeaker h8n09-7sj 8 axg aak3c y6qesgon 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 pen+( 9:uhmfp of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section fe hpn+u9m( :p11–9.]$\approx$   

  If the amplitude of a sound wave isg 1lwg.qfc- zk ui8 hamh0:19b tripled, (a) by what factor will the intensity increg9. bq k az8:ghw01mcl1ih uf-ase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equalt kd:r8p0 -kaq36 ,kjjiyq)lanl4k8 u displacement amplitudes, but one has twice the frequency of the other. Whak4 j)qjyaqi6kdlkap3,0l8u t - r:8kn t is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in ayld 18l ehuo6xn xg57.ir that corresponds to a displacement amplitude of vibratinx8dghu xl7 l1. 6e5nyog air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as ab l3lh:nk1d1ga qsq d0ir t,;5 100-Hz tone that has a 50-dB sound level? (See Fiqna d i1ll3g5,kbr;0t :s1h qdg. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when jtf8d+ jr9)* nvoiw9wqo;,kn the sound level is 3 nvj)8;r9*w9tq ,ojdiofwnk+0 dB? (See Fig. 12–6.)

  Your auditory system catvyp rg.i oh 9b/3i+6tn accommodate a huge range of sound levels. What is the ratio of highest to l+. ov /irbithy6 g39ptowest 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 77*x+m6srwjiuj5x hyirxb1: a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.3hm:wrij+ r165 * 7xyus jbi7xx5 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundap4oew8h5 6994j s4 wtgwjo/l h)iz pchmental and first three audible overtones if the pipe is h9c6wjwg4l jpz9 w48p hteh4/sio o)5
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the+5lipo/,s( :iv w7oar( kx zfj top of an empty soda bottle that is vj(f( sz w axio+5koi,r/:p7l18 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 st g 5rbw *6h8.,u0h8x*llt)u-vmeniiv4 jih e panning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths wtvh*.gr* uj6, i 880he5hlx-ib)iu4nv ltem of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as /ip 7ppd.-x//tdjxgy;q1n 1( nndy k2 sm1 mlnits third harmonic. What will be its fundamental frequency if it is/si/jndt pmkngn;x(n -/dy21d ymxl 7p11 q.p fingered at a length of only 60% of its original length?   Hz

  An unfingered guitarq ;vq(jy c+)bj string is 0.73 m long and is tuned to play E above middle C (330 Hq)v;c b+j(j qyz).
(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 o i2rjr-s.; 1zd9nh xzs-src y.rgan pipe that emits middle C (262 Hz) when the temperature isr y.;i9 c2s xsz--hn1rrds. jz 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 ,r+6)rymw,arszsrtrk *)2 iy 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should th +r uqeic5gt+4e hole be that must be uncovered to play D above middle C at 294+ 5rt+egicu q4 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at :n6afd 4mf0xs +8uwjuany other frequencies in between. (a) Show why t+um0 4nx juwfs:6dfa8his 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 bot.maq6ongf 5a3 h ends. It resonates at two successive harmonics of frequencies 275 Hz and 35ana f6.mq3og 30 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 * o/t,s-iq n3.bnuw wz$^{\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 r pyd2g/s+yw yu(dn a6jlo0 w;7wn/ i8for a 2.14-m-long organ u(r i2onj/wwa;/dpyy7y0 lwdg8+6sn pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately wn4tik:v0)p c 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequenci) v:4n0 wciktpes (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s whe 9-s,pv8zjeq cn trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other vp - 8zs9q,ecjstring? ±    Hz

  What is the beat frequency ifnb s2ne7wxq+ gnev( )x 5hcf99 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 whistlhh fctthv ;a;q6 8lcs-1)x4zje operates at 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 Hzhfvh zt;s4xc )8;1q j-hta c6l 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 35we p 2 iqis2o).rm++dfz- khq/0-Hz tuning fork and 9 beats/s when sok.q/ri 2se+zmi+fqhpdw - )2ounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are t:1 rqu wt/ nlw,;t02ant- nowm-nsj 9guned to the 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 playedt tq0-nag 2owr9t-n w1unjn ;/swml:, together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try t/,q; *mlhjqsgt;8 *eaurr x4 io play middle C (262 Hz),q,/ijhqm*;r84*are gux ;ls t but one is at 5.0°C 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 4-aycqqs*vc2v/ 2jks)d30g+ vgpq2bb 41 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible whe bc20bqsg+ 3*gkvdp jqs2vyqav/)2-c n 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 sfb 9jv1 yre/jm7jz9i; 5gg ac(gubq41tands 3.00 m from one speaker and 3.50cr 5 a1(ibgeyg9 vj qjz7b;m1g uj/94f 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*+(.-yg y:hp 2peuoq1cxah rt supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must +rp2-a xoy(* ce1 .gpyhth uq: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 beatsgjfiq h7e 9*o7 per second willfqo79* jh g7ei be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain (3u -h; xwlpmbfire engine’s siren is 1550 Hz when at rest. What frequenx-l (wup;m3bhcy do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a 8ey/+g-eh/ vq/jn9gjpad b m8fire engine whose siren emits at 1550 Hz moves bj/ehgv/ gamd8e9p/j +-nyq8at 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 0k)c7fknf-pz moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sak-07 zfcn )kfpme? 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 frequpr,1-mo-12vpnycg q-6 zvdgn in )ud-p+vp* vency horn. When 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. What is the frequency tmv ,-ggv*1-y+ n d-ncqv6o1)np-d2 p puivz prhe horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound xv g 1lorz 1ni5* qfd2x:xx6x l/xk+t5waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sogf kxxrxq:*d1xlx2/+x1i5 5ln t6zvound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a o p a ewa*c9n.6zsan lw5e..l8speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the*al8 l.. wanp 6w5 eon9.zasec reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movingmws;qvp k(4,e8z ii8k flat train car at a frequency of z8qi ( mkw ;kisp4,ev875 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 measur+yv9 )zl8niw sjguo2, e blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken z+,giv8w js9l)uno2y 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 waves of frequencu4c7g8zxaskkp)( rq3ao z, w7y $2.25 \times10^{ 6}$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 emssl0 s,el:);shehfh ijk7(kl9y gn (1its sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear,fl(1seh9 ls;s:kls0e ij h n7)k(yhg who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land i.q iru wtu(:a1f 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 where43 r*fs5v2z t jqgcrh3 the speed of sound is 310 m/s (a) What is the angl5vrqrt s zf 3ch3g24*je 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 thokl6e0: cl2bc e speed of sound is onlbe:l kc 26co0ly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave anb u7ui/9w q1tmgle it p u19uw7 it/bqmroduces
(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 9gzqnxv q+x(/6hdi a.$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a planedca,8znj2.ahi. v lc- exactly 1.5 km above the ground flying faster than the speed of so v82.ic-nah,.jc zdlaund. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar dev :wix2m;fwapa 6x5mb1ice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. 2m 5ib6aa fx:mxw;w1pIf 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 audibleolw2p3a4xe) ( i+ qcbi)xd(rh range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It*oic05skwh aq 1/ ih;k consists of many plastic pipes of varikiqck*hws1a oh5 i/; 0ous 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 aud(rn6e ci;; the threshold of human hearing (0 died;an6c( ur ;B). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soz;8c;ze( qhge3) 0h+o1oupzlqjp p-lund are heard simuhjzq ;le zp +(8zgo0;- cp1oul)p3qh eltaneously?    dB

  The sound level 12.0 m from b-w3wr.5v z1z 0ix -syil.bzpa loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, ass.x--zy z br vbw.ziws15p3li0 uming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 100i fko4e+n,kh- 0 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in wat, nok4i+ef k-hts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices oerv s10rdd43.hq5br aver their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 1q3.rd rreh0ad 5 41bvs40 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 communication;z4uq 7y xu8 9,lemnqus 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 tll nd +pm0o :+fwz:0oruned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed por* f06d79gctc8my0j3thcw hqints with a fundamental frequency of8jc9 g30yw0hqtc7md* crf h6t 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 tub,uxs j 474/ufnh2 ux wlndy0s;e 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 iss uf/w xn04,2ujx4 nhylud;s7 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 i56fl ) svys2jfs 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 fundam6v)lfsf5 2j ysental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observeda+wrts b2o8(w - 4sdyc 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 to6msn 2dwc9d n tcgrx4sj4a /5 :,hb6ywne in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. : awdsd4xg2njn6cy56sbw/ c49 r m,htTo determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whi90w bml+kt: com1ra )fstles. One train is stationary. The conductor on the stationary trai ltb1 am9mc0+f:r )okwn 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 l 9ci ;z;dtu+zwhistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. zl;9iu ;+dzct How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lis szu7 soxry ta0( tk5)x7ia7)z:zrvt-tening to the difference in pitch of the engine noise between a5 s- az))x0tik77t( yszu7zxr ot:varpproaching 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 fre9v1fb,qp +,4dobauk xleyw-) vm 8oj9quency of 11 Hz. The shorter , b ew kbfad)81mq+ooj lp-uyv,994xvone is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railr27;fgyho g h6voad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he;h7 vo f2ggh6y 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 a13fayd7v ws6,ckkf l-orta 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 thak1sfl yv6fc,d-7wk3 at 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 moth is flyingmym pz5d.s 2nq;q08v wms qz.. toward the bat at speed 5 m/s The bat emits a sound wave of 51.352z08sqm5dsv.; qqm. znpm.wy 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 approaches a moth. 4 ,c1d.9sy gybshbc5 hThe pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo fsh4by, ds95.ch by 1gcrom one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine,0od+y3qx vmu8dyde n/r4hz. village to another. Since lower frequency sounds are less susceptible to inddeu dyoxvmq/ny48+r, 3.h z0 tensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening cak v.c h5zegsq4 f8hq+,y;xk6, (xsxxgn be compromised 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. Cal85g;y,x( khkf cq4vq. sh 6xx,sexgz+culate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, cald/rwb8p ) syr1led “singing rods,” involves a long, slender aluminum rod held in the hw1)8r sp/dbr yand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequeno. vj9 vi vds+hpde/c t0-oy(:cy of about d t+esvo cy-hdi0v/ov9jp : .(1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. Anacbqm++d8)gp sjz * asoz.w4 4 observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhe4q)++m p zgsj8aod ac.zsb4* wad. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo,8tkd;evu) z5os/ irfat is 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