What is the evidence that sound travf j 11pxtgxb29els as a wave?

What is the evidence that sound is a form of sbjyk2 8c; v)gy o0y5ul1wiw7energy?

Children sometimes play with a homemade “telephone” by rv:xt-3oy62* eajlj x1e y7jqattaching 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 othq -j:j17 lo6ay xx 2jyvtr3*eeer 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 frequen*p23oj cl kqejwn9uh(s((c s) cy or waveleng9 p kw*jhses(2luc(on( )3qjcth to change?

What evidence can you give that the speed of sound in air does not dj:y9s(3 d0dqd l wflqd2-s 0v6:zfwgjepend significantly fz (:qs:wd 00fy- jlq6d3v9 2jsdg wldon frequency?

The voice of a person who has inhaled helium sounds very high-pi0vx*ofb901 yp8nop/ uh8nsqm tched. Why?

How will the air temperature in a room affect the ck 4(,r(ph. xf/ca 1qousqyq2 pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude rqgugzzd96j l:ym9l -j,;z.jof sounds in various frequency ranges. (An example is a car muffleyrzj;z,mjgjz6 d lq99 u:lg. -r.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together ajdj hcy;zu gs /8ew:y)sk- v3d, jf;-ys you move up the fingerboar c)j dfszve:wu3y-dj; ;jkg/shy-y ,8 d toward the bridge?

A noisy truck approaches you from behind a building. .a sv1s vxaz(-80bzpu Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hsaa.8 z1ub (-vsz0vxpear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to lx o7xn, ecr 2wkp8e-n7c 5ad;36twjv be due to “interference in space,” whereas beats can be said to be due to “p7acv53dlexec; ,t r2 x7no-6 nww8jkinterference in time.” Explain.

In Fig. 12–16, if the frequency of 2x0), zzmlodiz *v1zcthe speakers were lowered, would the points D and C (where destructive and constructive interference ozo li0 2c z),mx*z1dzvccur) move farther apart or closer together?

Traditional methods of pro5ngvqvn*8zz,(, zau mtecting the hearing of people who work in areas with very high noise levels have consvz,zqa 8 n*u(,v5 nzgmisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds 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 show (h g 4gmez-8-gclwf5;hskxd- n in Fig. 12–31. Each wave can 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 farther apart? Explain5w-ch( z-fh;4 dmxggkslge8-.
(12-31)
(12-18)

Is there a Doppler shift if the source19cwjwbl t r.0np 3r.m and observer move in the same direction, with the same velocity? 9l.nwj 1mw0c.r 3btrpExplain.

If a wind is blowing, will t g2vnko.l/2im7nqw t/ 26mf alhis alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocit/n2 7 iga6l2tol/mn2fq. wmv ky changed?

Figure 12–32 shows various positions4s- zlvq/ h uxo +wsx548oe,xa of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the grounds4e, 5h+uz -sxv8ox a4 oxwlq/. 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 liq+ekim*u/)dltfi; 9r stening for the echo of her shout reflected by a cliff at ther9detu qim+i;fl/k)* far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wate 9/0qf/qoct:y h uf va5;mafd.rline. 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? 9aa;o.5 vqmf//ht0 q cy:fdf uAssume 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 wdyyfcgp;4o a /;i;f *$^{\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 fogg7it1e we1 p1h*k ju;1xiu5tpgy day. Without warnitei1t;p g51*eup1ki wjx 71hu ng, 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 it makes when stri*s (a 8;ldleix(yez3.d r vw8aking the wate3sldl(ir(wd8y x*zve; eaa. 8r below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hug1v i0uu,ycnjsq*c) 5se stone strike the concrete pavement. A s)cn*, uqsc0 ji51v uymoment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How 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-secou - 0kwrnc-. )iz7xw:wwxpe)u n0:ccpp ypr-3nd rule” for esti)p xyi3kc0p:unr):7 - e c0w.wwpurpwnxc-- zmating 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 sound at the pain lev,/ o 0jv)nqoxgel 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 so:f1rla 0tgjdbldj 6. *und whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leu; jq qje2 ntl7z8k/lv-ft2g/ vel of 95 dB when fired simultaneously at a certain place, what will be the sound le-j v2qqejttlkzn8;ug 7l// f 2vel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain disj 7ct jgbg(/:h2bi ah/(cws +jtance from an airplane with four equally noisy jet engines is experiencing a sound levb(b/jc:(+w js gag7h2 /tihjcel bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-nua f,uu zxp7u/mvz/q q1rfgp3 61;m1 aoise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities z/mvup ,x11/1; u azrq f37fq m6apuguof the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal com 2:dcn,08q40bdzfs x/, gsvj)z oqlrnversation. Use Table 12–2. Assume the sound spreads roughly uniformly 2nsqc)dl0dzrjqx:,m0 , b /vof4gs 8z 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 whose area ibz blrr 6+i + vlxo2g6: r9jqk*h+,fwss $5 \times10^{ -5} m^2$ (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 amplifier isi pqq7s26 ;uB is rated at 40 W. (a) Estimate the sound level in decibels you wouldu;7 2sqspi q6i expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB whg2vfb7aefza+p1cov;q c3 v t:(xt .8yen placed 2.8 m in front of a lou(. 3b;+tvpvfvozx:a1 ccgt2ae78fq y dspeaker 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 typicall *sio.v0gvts(wl3 ev(y detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint:vs( 3w(i lgot *.0vesv See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wilf( to3pkx.+usu8 jnk*pq h;3txb5g6d l the intensity increase? Increase by f56b3pug dxosth k*.3q p(+;nku8 jx ta factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has c dd)cjo8,ov.4i g c,kwkaj8wnpl+l c//:ex /twice the frequency of the other. What is the ratio of their intensiti vc./dp l8, ooi /c,+j8gakl:xkwnc) /jc d4ewes?   

  What would be the sound level (in dB) of a sound wave in air that correspo2h fmf-l 5qj2wqy:me(, d*q vkk x8t.rnds to a displacement amplitude of vibrating aiq (rflv 5qm2ykhw2tf*k ej.qm- , :x8dr molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-H0y3bd:: 6mivfbv:u5 k tpbp l:z tone that has a 50-dB sound 035bi:ltby:u6d: kppvm :vbflevel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wmtt4trrem89ygxh2k g-t8 *h 5ck364spmz bd5hen the sound le* 3kdrstxmp884k56hm 2 -mz5tg 9thcyr4gbet vel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sounvik 8j5p )f- 6vtk+pgud levels. What is the ratio of h j 8pv)k6tf ig+kv5up-ighest 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 frequ/k-y bn 5,2xfjvxlet1ency of 440 Hz. The length of the vibrating portion is /-, ejlv15bfnyxxk t232 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first tho0)3gju7 k iwexi yd,8ree audible ov, wy)jx3gio7kie 8du 0ertones 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 fre 1spd2 st+co/.la/wkn quency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a close/k/n 2lwcs. asp+do 1td tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organue lr ;l41w+d(nixxjf ys2+r9 with open-tube pipes spanning the range of human hearing (20 Hz tr;elf4n l+y2rjx9xsdu1i ( +wo 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 thir o.*b*dskz; vld harmonic. What will be its fundamental frequency if it is fingered l;* zbsk dvo.*at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middl l3,:,jrr/g 4th wzzfcae;y5 fe C/r45 tl:yw3fg,jfh a c,zezr; (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) wheos x8*1qr8qtn n the temper*sto qq1r xn88ature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at w 5.+z ka;fbs2ynccw. 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 shoz nhm96t /3avsuld the hole be that must be/asz3n9h tv6 m uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hq4w j5 yv:q )y td2hdfw.m8zc+z, but not at any other frequencies in q.2dmcdwj4qft:h5vyz y 8 +w )between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonatesnu9: 99ky,at+)f. c gf1n+pm fmbukbk at two successive harmonics of frequencies 275 Hz and 330 Hz. What ,.9kcap ff++yb ) bkktm9:u un 19mnfgis
(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 xbfgstm:(1 l5fk; c2u $^{\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 raiei:bfd4:vo s2ip: p1nge for a 2.14-m-long organ pipe :o2iibepi vf:41:ds pat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal du3r5pl)c q ;eis approximately 2.5 cm long. It is open to the outside and is closed at the other en e3rd ;l)uqpc5d by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tcrwu)awe 890*ymxy eo) x)vb. eqkz)3rying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the o9))w y.uezx eo)* ywrmecq8)x 0k 3vbather string? ±    Hz

  What is the beat frequency if middle C (262 Hz) anfo rkm ezsj/ 9pbniw(3+0lp *,d $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operatess fhxd*4 :kw.p at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz oc .dsk4* xfwph:curs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9 i yaks( ezam354lo- 7;es0z3u d; yzwcbeats/s when souu 3ciy0s4lzo 5w em3k(z sa-y;7e;dzanded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are)hr9a z /5hp l3uqqc :zl*is0k tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat fr h:ski/q)qp0hcr zz9lul3 5a*equency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flukb6jml +6ucg 5tes each try to play middle C (262 Hz), but one is at 5.0°C an c5bml6j6uk g+d 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 Hz )b-neq3f3pi b; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, fi3)b- b pne3qthe 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.v6fgy;zce52c avkt,joo r2o l6 40:cq80 m apart. A person stands 3.00 m from one speaker and 3.50 m cfzoak5:vrcc62 tl0 e2yj,qvg6 ; oo4from 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 c2s5cir /)o-mbekub.t6dp2 ivibrating 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 be 5m6sc- otred2/c2k i.pu)ib bthe 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 wavelengths4 i9wh+ziit /px 6)rim 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = z9 w6ihi+itmp/xr 4)i20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sir:3d sddmwq;ns((3 jvk en is 1550 Hz when at rest. What frequency do you detect if you move withj (:dns3v3w(kq;dms d a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What fi1sew*f5o5k(9 0.a nijyl uzgv v 7r2rrequency do you detect if a fire engine whose siren emitz0yrov*ku9wil 7rvnegf5s 1.2ia( 5j s at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freq fc9/6n gro6nyuency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencifgno6r c n/96yes 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. When one ilf, s750m kquws 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 the horns emit? Assume T = 20 , m u5skf70lqw$^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soasbg0wz:hyoc e( 7 6)bund waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s Whatay ebb6() :h0s7cgwzo is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at5 l:cclq4zsobbwq ( 45 a speed of 5 m/s As it flies, the bat emits an ultrasoniqcoll5b qszw:c5 (44bc sound wave 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 was played on jt1s. 7 dey0.ozfd1,o2kdjfr 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 statiy. o1d .skjfrjdftz02 1,e7odon. 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 blood-flow speeds. Su6y 0(jkvgewx2 ppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing ine2g yw( j0x6vk large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves z y(f9bhc:yc- 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 sounogp)8 she7 9ldd of frequency 570 Hz. When the wind velocity is 12 m/s freopd7 hlsg9)8om the north, what frequency will 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 qr6dz7h 8wx*k9w5q g qmoving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What is ik-s )*;::wkhfu vs jwthf *v wk h:);isujsw:-ke angle 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 idp *hwga :i)s*juya ;xim.+)where the speed of sound is only axi y;m.s*:a d ug) )i*iwpha+jbout 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 thv7 n8 4rzt)erje ocean. Determine the shock wave angle it pz7r r)ej4 v8ntroduces
(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 *xurm,hba1 jdw/ lz7-$/theta$ 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 above8ks gz)b;.v;3imx;rmj 5 fhjro,f, na the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See F;i;r3ns f,) 5o.vxjk;rm f8 zgbah,mjig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound puls nu08qxvn 9h.pes downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to pv u.hn9nxq8 0work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in thejt,ka4on( e.haaem o4.i .gwt0v86ze human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calle/34gs/etujlyjlz ,(u g,d4c ad a sewer pipe symphony. It consists of many plastic pipes of variou,j 3j teu ld4,gl4//a(zcsy gus 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 r;sjpx0o7h n- to the threshold of human hearing (0 dB). What will be the sounn h; x0rj-sop7d level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are he: y2 lbg6kof34 ppb)nnard simultaneously?2p4 lo3bb kg f)nypn6:    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What 6br90f-uq* r( jep hqth de--ivv*ag 5is the acoustic power output (W) of the speaetaer-qu0 5 gpb vi-d *qf6h h9j*-(rvker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W out)pph4v .sdjv9 ev)+vfi+zc 4bput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the phvcp4z)+ vjpd+f9i)se 4 bv.v ower output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protep av e3/+ 9vphp yf4ucllr.52hctive 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 eah. pl4l3f9cvru+/y eh vp25 par has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications l ;jx3,.p tzj5hqeg,tsystems, 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 t a*cfy.hey ,+u( .fbqvo 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 violioi + si2*d aty.t9n8jyn is 32 cm long between fixed points with a fundamental frequency of 440 Hz andta+y 2 9y sdj*8tni.io 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 intun pw2.q6bl6 hdhn2cv 6lt-z +o vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it doep lhbdvqct w622nzu6l6hn-+.s so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of m*yiyq *-7/2cczyqsxwass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in t z/ccsiqyx y*y* 7-w2qhe tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one f ndp gkdv*1s+my(ze62 ull 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 500–100jrapvm( md:w+5k9s fsg q4 /k-0-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exaf 4 ks:dmrsm9g/qa(+5wkv -jpctly 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 wh8d 0txntid 2u5g;xfzgj-: c) * onviv(istles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train appz)5 xdtgcx 8f(viv;0 uj*no :nd-i2t groaches. What is the speed of the moving train?   m/s

  The frequency of a steam trainm51:o:himuijh q ; -rb whistle as it approaches you is 538 Hz. After it passes you, its frequency rom:5i 1h j:;qb- hmiuis measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate0zq stc5t79 yl90tsn k 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 k9sc 7 qzyt0tstl9n50 halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togetherln5l4rvc6 n qx8(2z oc, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How v(lzr6l 5c2n4 co8nxqlong is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past lnxr:eky 79boijs*-9b90 s wca 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 :bk0 o7-x* cj 9s9lsyri9bnewlistens 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 normally about 0.32 m/s whay.;lyrtxgu0wd. ;ovd0 1ny7p t beat frequency would you expect ifon;r0td.gyu.yyl0; d7 v1pxw 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 moth is flyin+ s05jtph*bpkg 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 t0 +pkhj sbpt*5hat wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pul) w) etepyt.g0ses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms lone t eg)t)0yw.pg. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send s;h lcposte87 y;8d.*)in,w2r eclrg mignals 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 o2.gthesp*lrc ew8rl; oc ;mi ,d)7yn8 f 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 canqd8 k9ccq 7c1 41el(z qp/vxfc 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. Calculate c 8 vfqx71kcqp/4c9e(1 lczdqthe fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invu6hs0vmx/huw (u13z jt * )uffolves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, r sut*)uxf0 v1u36jh/fuwm (zhinging 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 humano06 0m id:eo(jhkzx1n ear at a frequency of about 10oi: 6k0xomje(1 h nd0z00 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 8zj*obtopj;us/)13 5 yf cjlwobserver on the ground hears the sonic boom o js5 j pojz1y/ftu;bw8c3l*) 1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1xekaf4 w7h dwtl)63kx8 1xf 6e5 $^{\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