What is the evidence that sound travels as a w5 n8g/qk ppr2rt;*bmgave?

What is the evidence thar b 0jt/lrfe8t6cs.f4t sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string toqv96rks80w0ubf 9cg 31bjqnx the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Ewn q0c68x30bvkr9 1qubfj g9sxplain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency -xs76*q,i urpd/ ombbor wavelength to c sbr* 7bui-/m6 ,dqoxphange?

What evidence can you give that the speed of sound in air does not dd4rmc6o3z7j j4k h+ suepend significantlys446o mzj +cr7 dukhj3 on frequency?

The voice of a person who has inhaled helip22x eys )u 9d3 dvm.b:tv/lhhum sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pi 7fm4r jr/+hmmpes?

Explain how a tube might be used as a filter to reduce the amplitude of cyg,.( *ntkhssounds in various frequency rantg.c*ysk,h n (ges. (An example is a car muffler.)

Why are the frets on a guitar (Fig.qcze4e+d p)p:0 lr-v.6c 1idp trw4fo 12–30) spaced closer together as you move up the fingerboard toward the1dw opr .dep 4z0+e6pfccl4-r )tiq:v bridge?

A noisy truck approaches you from behind a building. Initially you hear i r*k,j rg71u9mns2nataxl1*wpw j.;nt but cannot see it. When it emerges and you do see ta*7rwgrus1n1axnpm2j9 n;l ,w.*k jit, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “intwy +ckfsyd 4*)bam 3qv9n(t 6lerference in space,” whereas beats can be said to be due toqdk(b)asv3ylfw*nc +y 964 mt “interference in time.” Explain.

In Fig. 12–16, if the frequency ob*+m6d5pn x 4obqlck7 f the speakers were lowered, would the points D and C (where destrlnd 5c7+kmoxb4qb p*6 uctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the rcv8they .jjy):5m,b s 9ew+i hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technol :8es.twrm5ve9 )cijhyy,bj+ogy, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can ry4 xxgd zd)hg *5bubv (70;ivbe 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 componen 4 iydrb57*ug(vdhb ;vg) x0xzt frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the souhi)r0m-d +o1fl1u j b69r jgwwrce and observer move in the same direction, with the same velocity? Exfl u9r6 md+hbwi0o jw)-g11r jplain.

If a wind is blowing, will this alter the frequency of the sound h)p w3un8p pn7+h hi-zmp/ clj oz(l8u0eard by a person at rest with respect t(8/lipz unu7c-pwh l8 jpm)o0 zp +h3no the source? Is the wavelength or velocity changed?

Figure 12–32 shows variouq1bvszcz)d /h7 x r4h;s positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the hsxbz/;h hd rqv17zc4)ighest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening e w:n f 9(mpy+3snva;qs:cpmg .gr,g 7for the echo of her shout re (n pga9n 7mgsg:rv.:w+,q ;emy pcs3fflected by a cliff at the 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 waterlinalb )e.em(x 0ie. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and)mbe0l.xe ia( does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths,qgmmk7oj.m(n / v, vr 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 a h7kduhtm9t *gr*q (z+e hgr77bove a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How mur ztrhh7u7em+q9*k* dt 7ggh(ch 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 splaslj+ /3l c)joz) iufn2oh it makes when striking the water below is heard 3.5 s later. c flun2)ijo/3ljo) +zHow high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stri*i,ms+rkwv,s ke the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air aksm ,+ v*,rsiwnd 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-se1sk.e lclr4w3 80la qrcond rule” for estimating the dista qercsa43 l.ll18wkr0nce from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity ofv85xpk;sgv l t7tn ai 9.2e-azq2h9tl a sound 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 souui21,mke 0cor nd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simul0ln) t +ektlq:taneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’st0ltl ne)q+ :k.]    dB

  A person standing a certanew-skr + t6qxfgrhqj66; 42uin distance from an airplane 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 shw626q;hx s6g+rket4 f-nj qu rut 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, whereas fotk/w*g y 7aow(r a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =* aw7wg t(o/yk    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conversw2(e;n f ko,ffation. Use Table 12–2. Assume the sound spreads roughly uniformly over af ok,ew2; fnf( 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 are)g lh4gyy9la,i*3y jba 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, afgt u,b7r36kwhile the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect kbt7,6rf3gu aat a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in 1 c(igna*+z xwaj8/lvfront of a loudspeakerazvw g+j*1(x ai/lcn8 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 soun xx 0) fxz* g2l/fep8pj4lvxa1d level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose j02) xaezx*l8v p fxlp1x4gf/levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, 3 sw)0qsft*hspjd,7w(a) by what factor will the intensity increase? Increase by a facj d7w0 fswss,ht*3)qptor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice to.(we4 u+m-puwxab ic*83 ua ghe frequency of the other. What is the ratio of tcuuu 4 oie(.3-*+m8gaa wx wpbheir intensities?   

  What would be the sound level (in dB, jg4 ui.i8h*oyizer )) of a sound wave in air that corresponds to a displa i,ho e*)uigz.4j iy8rcement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must haveow (vj+n*kha 3 kps+c.i6xz-y what sound level to seem as loud as a 100-Hz tone that has+s hpk-+nkv i3(6 x .yzjw*oac a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies thj dx/qn (pjk a;zq7d.9at an ear can detect when the sound level is 30 dB? (Se7/qd9;qp(jxad z.j k ne Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is t 93memyof(l +zqkb3fsqr 4d 35he ratio of highest to lowest intensilo5z(br e f3 s43dk3+mqfy9 mqty 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 440 Hz. Td u2cvty;mh sa -./srf1f9w 1the length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the strih fw1s - yars;d/vtmuc129 t.fng be placed?    N

  An organ pipe is 112 cm long. What a bo:w-chkm t 980kp9lr *r)iqire the fundamental and first three audible overtones k:- io )80crqr wkl9*imphb9t 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 wou*u4:jmp8vhu+by /q dnld you expect from blowing across the top of an empty soda botbv4nj:y8uuhdm/ q+ *p tle that is 18 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 spanning the ran/ekbh+t -4hrn:g7mq xge of human hearing (20 Hz to 20 kHz), what would be +47ehnrt -/gkmx bq:hthe 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 j g5:f9qgq y*tx765n rqcbjqwse2j+8Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only wqbjfnr8ecyg5 q:7 625qjxq9st j +*g60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lo yyw1x7brg5 (yuqf1x,ng and is tuned to play E above middle C xf q 7wxr11gby,(5uy y(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 leng3ng4fmn9c c+br5)yu e th of an open organ pipe that emits middle C (262 Hz) when the tebnf4gcy5 cr) m3 9nue+mperature 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 kind;1 ::csahs i6my-20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the jiyn5 j .dw+as+v-z/mflute in Example 12–10 should the hole be that must be uncovered twvm/.y jnd -ai+s5z+jo 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 61tint b 3(/ofy0ku3f *tk8od0g 6 Hz, but not at any other frequencies in between. (a) Show why this is an open or at(fkdt/3 *o30tyi0 gnkf8obu 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. ztt,l *s6iq kt8/+ f5,gm uwxztge, /uIt resonates at two successive harmonics of frxi m/z tttk6ws+/elgu, t q5gzuf8,,*equencies 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 s h 4:javf.;ed$^{\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 a +c*dqxn3kz4 within the audible range for a 2.14-m-long organ pin*qa3c+ 4xzkd pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is ope)jeluxyh +o ( ju(-t4y0p5bib n to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the stai y ebp)+(lb0hy x(o4u-j5t ujnding 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 beat0 88vh kvd;54 hhtocw: pgaf(k every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the oth8vvt gk ck58w da(h f4;:ph0hoer string? ±    Hz

  What is the beat frequencyyq(vbku fk()g+;u7et v2 pso4.x bun+ if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at thl3;;9ot q;k:)3ybrlnkxbb t86b oy 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operatinl6 h;tt yb98:qby )o;xlbrt;nkb o3k3 g frequency of brand X.    kHz

  A guitar string produc,nxt3m,nq0ul g .zh 4jwt pr2/es 4 beats/s 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 re4tpxg t,j h 32,rmwnnuzlq./0asoning.    Hz

  Two violin strings are tuned ;nk2z y p7c0ay(zbnu(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 pla ;(n 0pnuc z2ayzy(kb7yed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middi4s *kq)o dz6ale C (262 Hzo)*z 4s6dk aqi), 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 441 Hz; w8hrq 518xv44iznhx x dhen 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 when A and C8d8ixvz xx5rh qn41 4h are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from o*n0h 5. c37ulq5 mfmmbsryg8sq*ucc1 ne speaker and 3.50 m from the other. qyh*5 fqr.c3n0c8lg 1*ms7uc m b5s mu
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a v8fz,rkh nu g 7fka9 d:v0zd):piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what mu8khvun:v0z 9d),:d f zka 7gfrst be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats ,uex2(esy3 8g hqdgh *per secone3 qhdx*gy(gh,s 28 eud will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s si+xmcc5 za7p ( yen.0 2dls kz7l-w,tqxren is 1550 Hz when at rest. What frequency do you detectz k7, tal c7+dc2x.-p(5yszn m0lqwex 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. Whatp4 2ee4v t:pg,s wli2qehs f86 frequency do you detect if a fire engine whose siren emits at 1554i2 pv pg6lw,fe4eteqs8s2:h0 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequencyhkq ym.lj i8we;7h6w) if a 2000-Hz source is moving toward you at 15 m/s versus you moving towah7h.jwil )86 ;wykm eqrd 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./jshs65c49e -6 jn0d hfyplpn0gts6 i 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 the horns ensh6ishclep9s4njg6 - /0 6tdj5yp0f mit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and r xgk*ez9s,e4xvs7 ;np0rk 1mheceives them returned from an object moving direcpnr1vs4,eem *khg zs 0kx7 x9;tly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fli4(iu*ghb p sk dk/;ri+es, the bat emits an ultrasonic sound w+i; rubi* hpgd 4kk(/save 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 a movid d-qwrq*czkb0gn z 9 7:6wzy6ng flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if w7 g-:r 0dnw*q cdq6z kzz69ybthe train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow sp w:1ofm(m /kyneeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expmyowf:/1n( km ected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect u 1uzm7:bhm5 icsing 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 570msyhc2kl4f +jo+uj2 ;yld 33i Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest,s i +yj;l dk2c+2lyh4m3u3foj
(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 if its dk5ze26sip66au;ly k) rew x: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.j f(*y*o* ml.9r6 pphfcud.dz3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of (ddurm l **fo.j pp c*.fz9hy6the 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 atmosphereui 4vjvm c9k 8:j:kxr* of a planet where the speed of sound is only ak4vm i89cu jvr*:x:kjbout 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 ;dfe35ie*,m:cp)yu pkzr /tg-qq p:dshock wave angle it produces uie eg,ykr q:pc35t ;) f-dd p:mpq/z*
(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 t/u.rmjsalx /qc)y .yz56zi n 673xjr$/theta$ 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 gro*bsm3q;pkmex 7+ n /qhund flying faster than the speed of sound. By the time you hear the sonic boom, the plane has t *3+7 pe hsnqbkxmq/m;raveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downwarduxtj) y4zwn 76khce3k-u4s q 1 from the bottom of the boat, and then 1n qe k4)t6c 7wy3zjkuh4s-xudetects 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 the human audible range v+1b84 y+aoqm8 wawyhv9*xa l? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a smf ohauo q5.hs3 b.mm*tq4 cq,2ej)b0ewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. )qem , qh5*fjba 23.m c.qo40btuhmso
(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 thu4nnea )p .+y*d1qvgl e threshold of human hearing (0 dB). What will be the sound level of 1000 such mosq.qe pnn +1gy *va4d)luuitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soumtqnun19 nu:)e yp.6dnd are heard simultaneously 91 .6mqny:uu)td nenp?    dB

  The sound level 12.0 m from a loudspeaker, p6azbfo/ud*o6qih g*k0+9 tsglaced in the open, is 105 dB. What is the acouu s gbg*6o609 iot*+qhd/kfzastic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The po8m5ur80 -;xyrz29jnd pjcjml wer output drops by 10 dB at 15 kHz. What j2l80 ;xu5pyrjj8-d mn rcmz9is the power output in watts at 15 kHz?    dB

  Workers around jet aiol 6f/3 nh/zuurcraft typically wear protective devices over their ears. Assume l /nzouf/3 6huthat 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 unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatioopd vbfj 9wh(qjr3ntiz97)1+ ns 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 isw hjglc 0;nxwo(y*r g9ea3/d 8 tuned 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 bet(+lc 5,a, /xklkqaluqween fixed points with a fundamental frequency of 440 Hz and qak ,q,x (ca/u 5llkl+a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fwtr lpmn*n9tzmvy* 9+k+c+6oilled 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 waterpvtlmnck+ + o9mz*t9*n yw 6+r 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 thatf cvlh5.riw2nx i4h l,y8 u(k4 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) l kc8 (ixnu4lv42i.rhwfh,y 5 with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was jgg/mztn:8yz i; b *z-observed 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 tone in the 500w87kqx7 fegc;ed58qn –1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound87 d kg7encxwfe5;8q q level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on th-kqrj/ 1mg-wu;igbt.xni / a7e stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speedanx-gtwg /.b7j-qr;k iui 1m / of the moving train?   m/s

  The frequency of a steam traiff .cpg,d o*w fff75l7n whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was thef fp,wof.c*7d l7fg5f train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of carsl8u7- qh2tpu gcis5:w 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 g8h ti:p7uul5-wqsc 2it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding tomic 1mfm z-d rcwlq 1.r./:-i;etgv:x gether, produce a beat frequency of 11 Hz. The shor-rvmelr-c qt d:m1:ix1wm z.g.fic ;/ter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad 1 s q/0ftr(brk;cpzh6ia )1j lcar as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If theipqrf bl1(/srzkct ha j;6 )01 speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beae o(q3lf d;6k9saxsj x2: 7vqet frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow aj; x:e6a osdk9(7f q e23lsvqxnd 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 a64x,yfmgv*pf *t d 4e8h x7 k9k5jlyms moth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects ofj*8gkd 5 lfx764ek9tymyvhs, m4*p xff the moth?    kHz

  A bat emits a series of high fr1elxb dh,m;t:z/wjg3 equency sound pulses as it approaches a moth. The 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 from one chirp returns before the next chir;wx:/zdbe l h,t13jmgp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sendyo((ai/ 5 v ;zhi/g fwvi/+i) ygk0 syn+gpq9u signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m low/yi/igk (5vz g(+ 9)ay;/spi 0u qvghyoifn+ng, 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 can be compromised by tzh2j 1ul b.q, 7z:idwkr;ilu )he presence of standing waves, which can cause acoustic “dead spo:qzl)kjizl .wud ui,1h2b r 7;ts” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lon b *iq-:wh3)hebgfsa+g, slender aluminum rod held in the hand near the rod’s midpoint. The reg-w:ihab +qh b)3*fs od 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 thresho q90aonv: (yerld of hearing for the human ear at a frequency of about 1000 Hz io(e9qvan 0: yrs $I_0$ = $1 \times10^{12 } W / m^2$ 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 :wg,b-yb2zp c2.0. An observer on the ground hears the sonic boom 1.5 min after the plane pa-2,c:w bzgby psses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15c2 m159 5kge nzsvwr4f $^{\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