What is the evidence thmjrg :a:( kyd7at sound travels as a wave?

What is the evidence that sound is a form of kl:o l10fs1xe jh: m9denergy?

Children sometimes play with a homemade “telephone” by attaching a string ru /7x28.8capi b yxwuto the bottoms of two paper cups. When the string i xbyxur8 cwa72.piu 8/s 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 thew ybd u8xs(1;q frequency or wavelength8 ;x1suyqw (bd to change?

What evidence can you give that the speed of sound in a8f(3isyr6vroj;sz( air does not depend significantly on fr(s3zo;8 vrj6(f ai syrequency?

The voice of a person who has in +fmv/* wxsybito(t*1haled helium sounds very high-pitched. Why?

How will the air temperature r4knpmum g 631(du-zhin a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude h*w- qxcg*l:c(z8dht of sounds in various frequency ranges. (An example isth :dccq-ghw *(l x*z8 a car muffler.)

Why are the frets on vf,5y w2eovvf 3(b-y-f9qhq h2)vd*le uerg4 a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard towarb h eq4e3 (y-vor2u2w,y95e-dvv*fglvhfq)f d the bridge?

A noisy truck approaches you from behind a buildingbqxf(ym 1 29ah. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency nbfh y 2ma91xq(oise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in sz9cvf;*uo,i c w 2dkzk4kyj+ft o7 o/5pace,” whereas beats can be said to be due to “interference in time.” Explain uct5cz;vkw 7+9fo o2y4/ jd*kokz f,i.

In Fig. 12–16, if the frequency of the speakers w3r 1l/ne)jiogi p4s,iere lowered, would the points D and C (where dest34pi/or) sl,i gj1n ieructive and constructive interference occur) move farther apart or closer together?

Traditional methods bbaqby b:8 .-s gu7or:of protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce nois:r8b: uby.bo 7 q-absge levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the 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 ca3drz3i s (cqb; 1xr*kaqsf):pn be thought 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 fas1*x3d bqiqpsz: c3)(r rk af;rther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift i 36ej,mmgk6u b6x.pp j.den*e *iy7inf the source and observer move in the same direction, with the s y.k6,67.j p pm neje3i d6*b*nmxieugame velocity? Explain.

If a wind is blowing, will this alter ttou55 5w 93idkjbv+ro w*f*qzhe frequency of the sound heard by a person at rest with rewt ubwo ri5+3qofdk55zj*9v* spect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in mog nw*(wm(mrp.tion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through g(nm. r* (pwwmE, 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 :+u5oo) tj gh+v3bjq uher shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of ): gbtj 35u +qhjvo+uothe lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sidvtz6gtb 61 /k ;m;lw5 kssl5lze of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor dz m5 /k;1v;ktt6 sllglbzs 5w6irectly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengt z 5lt ah7 3c4qxibr5:d6jkyd8hs 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 above a school of tuna on a foggy da5 baa(v20jpm6(a z xqqy7cq*ay. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much j5aqqaz0 yp6 2(v q7b*aa(mcxtime 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 clb3g+m)ats9 x:f rlkt+ a pw6c8iff. The splash it makes when striking the wa9tc+)fx prs83tl:k a6gm baw+ter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hu9j-i2z8bw ovap) cmrm3 +wan/ g ,oe8zge stone strike the concrete pavement. A moment later two sounds are heard from the imp ,r+zczoam 8ne32-/abjm9 ivg)8wwo pact: 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 distanc3hmak . 6hs:zee by the “5-second rule” for estimati 6 sz:hhmeka.3ng the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soun r+j9v w,s:k b37qyeyqd 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 int t zh:fon,s m2imhqk..mkc ;5/ensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prod2i(z izjx eu4rv4 /a:nuce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, notiir z4u: x/eajnz(v42 dB’s.]    dB

  A person standing a certain distance from an airplane w68tfbzsm e tb1 83p*bwith four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level woulb 8p38 t wtmbz6f*sbe1d 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-noise ratio of 58 dB, wherea f9zi+fi-9i xss for a CD player it is 95 dB. What is the ratio of int9fs-+x i9z ifiensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pers2dip5jx c;ejjp *sg7km3 , k,non speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly unxen j5jgjdc*2,;s km,i p7p3kiformly 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 wwjvd1cd +s9 xub.n5y8 hose 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 t 7r6cgps.nf8she more modest 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 loudspeaker connectedcspr s. 68gn7f 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 wheniov4qk3 dygebmc;m:4g 6u )q; placed 2.8 m in front of a loudspeak6 mm 4: id3qeobucgy;qvkg4);er on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2j4ji in/.nyrc wwnc ,:6*zgm+.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: Sj*jniz. n6w:rw, n ymg4i+ cc/ee Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensri7kwj f;49w 4ii;vhgity increase? Increase by a factor of4jrwh wif4i ;7 9iv;kg    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitusuqt kqd k-93)des, but one has twice the frequency of td3-k sq9utqk) he other. What is the ratio of their intensities?   

  What would be the sound level (in dB) oz*w(mku pu9n;8 t8qrb f a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 9(*nt r;up8kwqm uzb 8Hz?    dB

  A 6000-Hz tone must have what sound level to smd5o7xo 2fm j8eem as loud as a 100-Hz tone that has a 50-dB sound lexo 2fj7o md58mvel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sou9 jtqs1ee :t9und level is 30u 9:qeste9 tj1 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of stk9+1 b7-ntlrr kezl9 )sjw1 aound levels. What is the ratio of 119-krlsjan tew +tzr7 9lb)khighest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 5vyufy -91x q; m;wexcq+x*yd440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.q mxcx5-efvq ydy1 9w+*;;yux35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three a1yvn rv;bf x76m(e(lfudible overt6fyml;evvbn1 r fx((7ones 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 the top of an wbzl2yhl6rh5:x4ytho 71b 5 u empty soda bottle that is 18 cm deep, if you assumed it was a closed tub lhhlr5b4y16wbxy2oz:u 5t h 7e?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe orgu*n7 mmrsd j o7j8b5,aan with open-tube pipes spanning the range of hum 8 jm* 7b5nmjra7os,duan hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What w1 pulyb.t ,0 (ac(dwg 8js*pg5q 7vmqwill be its fundamental frequency if it is fingered at a length of only 60% of its origin. dub58jlg1 ,pacygw(w7q pmqtv0( *sal length?   Hz

  An unfingered guitar string is 0.73 m long and issu4h l9mw ,. 6adjidl+ ct9iu4 tuned to play E above middle C (330 Hzsdd9 uu.w,+i4jc94ha6itl m l).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits mw((jw zuffu *1r 7kag+iddle C (262 Hz) when the temperature isz+ *(wuf1gf kraju(w7 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 atp7 rscxw:)ji)iq,, 8oune7om 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 shou0b b9/,0aykn z 5ww-lf ,houqmld the hole be that must be uncovered to play D above middle C at 294 Hz? l,uwb9 qnmwk0o h /5f-, 0abyz   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 vuwaev 2d/ j/8at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is a/w28je advu/v n 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 resona ket av;k-1b )brs3zx.tes at two successive harmonics of frequenxrs -z3)1 keabvkb; .tcies 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 c/yt /f6;mj6a0b v aua$^{\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 ./zp)*pkm b7t8ir-0 qqbylis for a 2.14-m-long organ pipe ati-0/*pk7qtp ylb.izsr 8b) qm 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately j6gjb;3l2o8 adnx7cg 4 j 9ixk2.5 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 cana xgkgj j9 23j68n l;4a7odxicbl. 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 ek p4lqewnu34sw0 by9 ;very 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ± wsyb49pw kq 034; nule   Hz

  What is the beat frequency if middlx5.d)e 5qvm uj ung*08gt8 lcpe 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 at 23.5 kHz, while another (bran- cf7d a0 mw)ncw37xqwim,h4ya)6fijd X) operates at an unknown frequency. Icac 7yw d mh40)fnw)7j aw,3iqi-6fmx f neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/si pk 1nrf6a:5f when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning. 5:rk ni6fp1af   Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension inn(t;op 6ry6h6qndk- b one string is then decreasrk6;nthbny6 - oqpd6(ed by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mif 9*ut/nsos )bb 9t3u)fa;cs7z fk/xiddle C (262 Hz), but one is at bt9*k;fs stx nuf)3zs 7o /f)bu/9 cia5.0°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 ow5 5tiy7vv x;hzfr,+ qf 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are poss,+h75 trq;w fv 5xvyizible 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. 9wrfe9w 02+td q4rez jA person stands 3.00 m from one speaker and 3.50 m fro+9q0wt ew9jz4rd 2 erfm 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 suppose. nkz)vd4s ggu8g)d vg fp)6hl6d o.4zd 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) .ghgdv)8.4zn 6dp gs)vgolku4z 6 df 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 a bfqh4)psgd emj1:e1-d6i3pmy3es7 n nd 2.76 m in air. How many beats per second e sfs: i4p jh yqn7d1b-e)e13md6pmg3will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hzrs9 wdn;emv 54;yrw*dm,l wz8 when at re;l,4n8wr wy*v;ms 9w zr ded5mst. What frequency 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 frequenc8nfqd: q1ra i0.-vaw 2y7pfq qy do you detect if a fire engine whose siren emits at 155 q7.2wfn d8aq q-ip0rfa:v yq10 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 source is :mwjuld(h)a5h6 .r zemoving toward you at 15 m/s vz:dh (ru6m.5hlj)ae w ersus 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. Wpb v.+l,qn3z8yxqub 7hen one is at rest and the other is moving toward the p3nlbqx+ ,uqvy87.bzfirst at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHzerkooc9 s7;.v,mbz -z and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequecmor,.97zs ek;oz v-bncy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits a3pa .at vyq,q,n ultrasonic sound wave with frequency 30.0 kHz vqay,t,. q3pa. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moad868qttw2f o0y pah+ving flat train car at a frequency of 75 Hz, ana0hfo a+8 2tw6yt8d pqd a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blqwf ucz:w /c -sw.ng+4ood-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:f gwcw w/sc+z.-4 qnu/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 usin)gpt9xd: xi.q:d, 6skw3 zlpdg 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. W b827br mn ;(f(pnrxeg-a ;beqhen the wind velocity is 12 m/s from the north, what frequency will ba;nr-b;r7bef mpe( 8qgxn2 ( observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object movingn8 y2iaj2skyg/d-87mzutarq7yan 6 + 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 h6n*t)b-vheg sound is 310 m/s (a) What is the angle the shock wave m)ev-n 6b*hght akes 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 wwre3*zw9rku v1hbr1y(7 n jtfe; .eepnp/.g,here the speed of sound is only abof et.3be,( w v.n j /rrrn9e*k;1gy7zpwp1euhut 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Det)w vcag yr q.mt83tp4:ermine the shock wave angle itrcmp.t q8 wgv3y)4:at produces
(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 1nnrpq((jvxk5r6l t1 $/theta$ 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 exactly 1.5 km above the ground k.vwt t u06*ch-w uc2tflying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled akhtuvcwt- *.uc2 w t06 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 senjq- wgx39bvv oyt5a0 b *lb15eds 20,000-Hz sound pulses downward from the bottom of the boat, and then deteet b b 953ql5vxjvy bw01-ago*cts echoes. 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 the6e 2m.kp*y; 5su 2xj8v0 kxo(sutsezz human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a disph3 toy elw344dlay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, whih eyl34t43wodch 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 oga6d hzs /vu ff e f.xva;1zks896io*-f human hearing (0 dB). What wilu/do;6v g .zk1v-hs* 8a6efazf9fxsil be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 8b2- sb*9e r3dckjdrk97-dB sound are heard simultaneously?rjcb-rs*d dekb 9293k    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What ict1+aw*;*pa7) hh3dyhl ;oozlak5a zs the acoustic power output (W) of the speahzzk3hl* dtha *y1w;po+)7a aaloc; 5ker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 kw7mqp vz -* 7qz. *vjf+y+yotHz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kH*fkp o 7y+w.yz q-tv+ zq7v*jmz?    dB

  Workers around jet aircraft typically wear prote6hy-oo ype kib1,* uz4ctive devices 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 has an effective radius of 2.0 cm. What would be the power intercepted by an unprotec 1ze b-u*yy6p,i4okhoted ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications syste,sb.r*sv0. 9tthek ae ms, 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 1y+zwb 7i-yl/sj-5x 1 kqvk)awv3jan :$\frac{1}{2}$ 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 betefcg3h5hcek ; c60 4ilween fixed points with a fundamental frequency of 440 Hz and a mass p 6cc he;g54cflk0h3eier 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 in:jwqmhl b90* zh1m*vel/o. 5b*u ntx uto vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water 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 fr/ z0* .ox qb*vnbwh :l5umm*luet9hj1equency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube tzdv y:voqa5.8hat is open at one end and also 75 cm long. How much tension should be in the string if .va:o 8vzydq5it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to rehcn(j 3bc2 r/esonate 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 tone in the 500–1jt0 gkrr;o-sdn*/k; ,fo3r tal* yc-z000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exaclt /;; -dz a,ok-k*o*3rj n 0gfysrtrctly 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. T+fw4;) n wpkjyhe conductor on the stationary train hears a 3.0-Hz beat frequency when the other n4j)ky ww;f +ptrain approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After it m nn.ff an)amhc/* 0tt6 o+yb-passes you,.ma)tyf fnt h*0b6nonm+ -ca/ its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estxbf/u fs4bd/9hpc,gj055 w b nimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by ojf,w/g9cxsh u4d/bnp505 bf b n the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Thy6.e5g r75 prj4v4mrvvf+lld e shorter one is 2.40 m long. How long is the other? gm65lep+r.v y 4r fvd4 vlr75j   m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stw3di3ufi s+u7y- ,surationary observer at 10 m/s as shown in F+i, duyfsur3s-w7iu3 ig. 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 aortai9sp +,1nfnmx is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves +ix p91ns mf,nwere 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 moth iumy)b* )msvk lv, tk(ex 0sqgk0u3 w,2s 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 reflects off the moth?, ws2 u*k()emm,)0 sv kty30uxqbgk vl    kHz

  A bat emits a series of high frequency sound pulses as it approefqg a9 uzmoi(.gl5,8 aches a moth. The pulses are approximately 70.0 ms apart, and eacl98 u5(,gz aqeio.mf gh is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Figc zi9b5t 9mt)x9j wnu 0yb;cbx46m-rc. 12–38) was once used 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 axm)w jir tn cy90x9;6 tub-5cz 4mcbb9lpenhorn 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 sterb;h/9g8f 4tv ubxwyf 4eo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a whfb8 4uvxg t4;9byf/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,” involves a long, slend sq vh6c+h/u)rer aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with h )usvq/6 +hcrthe 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 -5khn(q e9eim18num ;sq7 aloof hearing for the human ear at a frequency of abo eaqk el7hn 5umio(98-1 qnm;sut 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. An observergu281ili54 b lsi 52ynnfavf; on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s alis2fi;uln4v12f55yaibg8 lntitude?    $ \times10^{4 }$ m

  The wake of a speedboamyk(am(g7 tmblvywd65m- e 0/e7ej h :t 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