What is the evidencelj9kygzw4wc)u i /x6 - that sound travels as a wave?

What is the evidence that so3 -uv(m:e(jqz pn nhi d2/v.glund is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to 94hbql33k- 60 oc pqej9fm5y lnc6i, kyej+x uthe 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 (Fi 3mu9lyc+cq-nhf69 y5 q 3kojij ,xe0bkelp64g. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into wa5w9ze9s i. 5;ercoqrb )/wuk0ty h ov,ter, do you expect the frequency or wavelengthi/w9eehqz v )r.st rb5 ucy,w5oo;9k0 to change?

What evidence can you give that the speed biz6:qy 3lzci 4ce dsu*x5h;h.s: 0naof sound in air does not depend significantly on fbdu e5syqn:i zc4. l* hha 6x:czis30;requency?

The voice of a person who has inhaled helium souz)uw (sf pzr( ii*/t0bnds very high-pitched. Why?

How will the air temp;w zl;9-y )lwloe3y9oun px/perature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to fr78vtk: *atcxk pm0yp) i9q5hfpz9 9reduce the amplitude of sounds in various frequency range0zpkt)tv 9ax k*rfcm58yqih 7p9 pf 9:s. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mov pablu,e:p-l63zcnm 0 e up the:lm lnb,3ep pua 6c-z0 fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially yoo o1):uw8rfpqu hear it but cannot see it. When it emerges and you o1)r:uwf8po q do see it, 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 “interbo o y5e4f4br/g6s1v uference in space,” whereas beats can be said to be due to “i6s/ fob4eyrvu5obg 14nterference in time.” Explain.

In Fig. 12–16, if the frequenc*y1 2 .vho3x0za tulg9 mjn/x)fd3bkvy of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) mo.lm b 9n 0yv13jdotkvu hz*)xxa3f/2gve farther apart or closer together?

Traditional methods of protecting the hearing of people who work in are (pvv/ub7fy s-as with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects tfv(vb -/spu7yhe 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. Eagal p*44o c8vdch 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, (dp cv*go 4l84aa) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if tdc / 5bk3j,kj emfx:5ahe source and observer move in the same direction, with the, km:a5c/ fbjx5j d3ke same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound 0y4l fos7s yglm6/vghzw0k6 3heard by a person almw 70s0hgsk64 ylgo 3vz/ 6yft rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a c7ytn3mit2-g 8 xe-fudxyk b)(hild 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)78(--tx3ni uydkmt yx2g feb the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengtz: xxv59 /sbrph of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo pxr5/xzv: 9bs 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 waterline. He heag4 3k (jyzfy;*ncdoi 6rs the echo of thofy3( c6dijy k*gz;n4e 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 does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a6l1;nj reobedtx0(3fu .0ye9bm h)trt 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 tul( pn95ehx:xk(i oe0hna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a95hlx0ek ( oi(pxh:en ) by the fish,    s (b) by the fishermen?    s

  A stone is dropped fov fp.qi,h tqn xk,knav(0 6/9rom the top of a cliff. The splash it makes when striking the wapkvi/ ,a v9,xkqqn0f(nh o6.tter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the cvszk+ zhk 1h(6r jlp-*oncrete pavement. A moment 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 1j-zh*rhvz lp(sk + k162–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-seco i 5vn(ln(1jrv c fdxx7y2c )l7/lbfs(nd rule” for estimating the distance from a lightning strike if the temperature is (a)v fdvbj xrl(cx y/ (l27nn75 fl1i)(sc 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity ofs/8wguyfmn ,7 9 mgq7z 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 sound whose inte2uz .y;so -o1thpdz/dnsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prc(k 1- 5:8slj czxlr kv;vg-deoduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound lev- d(8j1ksvcl5 vkcez:x; lgr-el if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distanc:j8dzkyak x27rrmi98 e from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound l8yzrxa 2r ikk9d7m:j8 evel 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-mzi,z*khny 8x*;dc o/ to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each zz;k/ *h8*cd,nyxi omdevice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a persona34xm5gr ma w6 speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centeaa r4g36mm5 xwred 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 strp/o77pbu bb8urd z,3 cikes an eardrum whose 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 ratedb-f74hp d vv5g:yo 2u)ii fok2 at 250 W, while the more modest amplifier B is rate2iiy7hf:bp vkfougod- ) v452d at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered g1dd fm/ msz0,130 dB when placed 2.8 m in front of a m dsm ,1gdz0f/loudspeaker 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 demu l7fxi,0w -q5j ye m*d+u;jytect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose leveljw eju70f q-l5,;*yx +mymduis differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what facto/htg ) .bzrv+xr will the intensity increase b./+hg)xvz tr? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplit.k/* ,, gc y.q qvco8ckulyu/1ti h6oaudes, but one has twice the frequency of the other. What is tcqu,*y,/k1.o gy.k t86viha/cluoqc he ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air t)sbz-x;xl y z6hat corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300; -)xs zyzlbx6 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a f /yanq c8il:re+vy i qf9d/,3100-Hz tone that has a 50-dB sound level? (Se/8+f:9 iyqcr,lfqny/a ev3ide Fig. 12–6.)    dB

What are the lowest a7ya1mufoh+fjq(j 4av aiepl4 a:e15 qr (v1 v+nd highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–fv1y:qm 7ov ae uj51+ e i4a(jqvpalr+4(a hf16.)

  Your auditory system can accommodate a*hcloj)bqv j 6 l-:4 3wo3d2fewcryk- huge range of sound levels. What is the ratio of higch3 -f6 y- )3do l4wq*kw jcr:b2evjlohest 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 fundamentv)twpej9 0*wt al frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?w)9t* v p0jwte    N

  An organ pipe is 112 cm loc/fw)i -usl ;qcbhx 81ng. What are the fundamental and first three audible ov ;qbswc-i8cf /)l x1uhertones 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 edu6m4b2 tidis g1)k)q s..v qe+3nrk txpect from blowing across the top of an empty soda bottle that is 18 cm deep, if you asdv r4k .+.ik)n1tesi 63dbq2 qstmgu) sumed 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 pipo)2:ge :l5sk2n-z79x j clr(rp m nwtne organ with open-tube pipes spanning the range of human heark:n)-p ew5t9sxrmgj n(7l 2oln c:2r zing (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 tcsnoet 5ez(z ;i/j/:(1r gp vhhird harmonic. What will begvzt/ he5p;(/1i se (ojrzn:c its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is 0r ust 0d9hf4p-err*ytuned to play E above middle C (3304ru *p 9 sfyr0d-th0re 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 ks+yw8) 9otn i0h1cl2gf +z lrthat emits middle C (262 Hz) when the temperature i++sok1 yf linrgh09w 2 )ctl8zs 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 rubtlu;() 10-hxdtxf20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the/ r (-zc1szme+a1 r6)jsbd-cegdoygh8y nr 42 flute in Example 12–10 should the hole be that must be uncovered to plsay sdee8 ozjm+-41c6 )hgb 2-dcr/1rg ryzn(ay 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, an oohfn, 4tpz4l l*e.7rd 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed e.z4pn,r7 *4oo lf htlpipe. ----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 resonates at two s9 s9uu;e by j0:ox;rtiuccesjuyir; 0 e :;x9u9osbtsive harmonics of frequencies 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 3 y+,b avomq /xou:n6y$^{\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 -tdl 3kab/fvr-s ab.7 nt0zz1 present within the audible range for a 2.14-m-long organ pipe vlzdzafb t.-7t0sk/a 13 -brn 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 open to the outside qrj7 ze:z80zpwd fr9hiih;14so5a4aand is closed at the other end by the eardrum. Estimate the780fsiozhja piaw4e91; zhrrd45 z :q 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 try+v)spdyr fr;cj;)z mf9 -. .n c,j wmu3uhky;king to adjust two strings, one of which is sounding 440 Hz.r n+;py.9;mkjj ufy.c3srhk)mucz;), d-f vw How far off in frequency is the other string? ±    Hz

  What is the beat frequency if minsyumrjf ;o;e)k 98 )rddle 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 (bran9giu :h:tqtyiu y9 g:t5r;kqe rr8 y.1d X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a s:i5 .g rqy y8i;r: u9r:ttek9hygu1tq hrill 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/s when7brano *km5 :q sounded with a 350-Hz tuning fork and 9 beats/s when soundedam*7nb5 krqo: with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings aregpxrn4 oo 0q89 tuned 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 played 4g9on8 qr0oxptogether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eachpbmfvced-2lz.6 w 2 qqdifb106)i5ai try to play middle C (262 Hz),0d6.bwi a-)q2b imvp1fdqf6 c elzi25 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 /p*qee d5zua5 a5 xt2cv)0yjm; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A aea5/ vx 2dm p55)0ae*uycjqztnd C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from o2a 5lx0uvx7m tz9on h)ne speaker and 3nomva 2)h0l759x uxtz.50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are suppose qsk9bojgco14 5v9p*b d to be vibrating at 132 Hz, but a piano tuner hears toj bvco5 99qkbsg1*p4hree beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavel,m1hrp;5 uq qlengths 2.64 m and 2.76 m in air. How many beats per secondq q 15m;lpuh,r will 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 Hz when at qwsv0udvw w241ea;;w rest. What frequency do you detect if you move with a suqae0241w ;w;vswwd vpeed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire enginzm accv-.2vn/ e whose siren/.vv2 azn-c mc emits 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 fgepct ;:f rnsa 2:x*u4requency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it n*4 ; rxa2:fpu :ctesgat 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 singl h+u*8e+trmly klkt/(-jbt 6pe frequency horn. When one is at rest and ty+ p6/b j8llk tuemkr(ht+-t*he 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 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHj+8+pqvmxwzrz6)8 yqwi*ydrw :n;w3 6ff+xn z and receives them returned from an object moving directly away from it at 25 m/s What is the received sound fre6viwf w dqz+nr6zm)8r yn*+wxx+; qfwy:3j8p quency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fliarx -du4y34l:haztt2es, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflecte:l2z aya hd-tx34rt4u d wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fm69cc:qhy) fv z82 mgwlat train car at a frequency of 75 Hz, and a second identimc2gwf8mzq c): 96yvh cal 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 ultra0,f*2ihr8z hlp gg 7gpsound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s direci07p2r8 p gghf, *lgzhtly away from the sound source?   Hz

  The Doppler effect usix r,sfl.u-c 5ing 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 sty o77e;,) 9hihnd2myonq sr- 6mu k;round of frequency 570 Hz. When the wind velocity is 12 m/s fromro, y9;niud7r;m )eq7h-t2s 6hkn oym 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 movin n*jzf)5v.h hag 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 spee*pcd3ryfxqt1*0m- s gd of sound is 310 m/s (a) What is the angle the shock wave makes widg3rx*0s * y1-cpqmft th the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of soun *1h1dd6rweqq gt/+sdd is only abh edgdd1 w6t 1*+/qsrqout 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 thr *gfrg)ol5t1)(w o, *o3ifhd6(hcq/ vzbpzy e shock wave angle it produc b 1tp co6*ho(g/)zro( v)y,i lhrqf wgf*d3z5es
(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 8x 5n e*hkqd6z(1o vds$/theta$ 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 flyie6;mg )pfj -8qyjpa9z ng faster than the sg 6 pm8zjq)f aj;py9e-peed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar devisbd gd xu05teb269 gz*ce that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is desisdu6z 5 0b dg9*gt2bxegned 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 audib 3mvxuf ukn9:,le range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symps: gug 0- me :u 3u ilmp-jho/:qyc4toqe5j;5hhony. It consists of many plastic pipes oflqj3 tupo g;yg/: m c h5joe::uem s4ui0qh-5- various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sovgp70 sb )xuw q)zn)s4und close to the threshold of humzvunx ws4q0s7p))g)b an hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level wapgr,7nmc 7;ps aa.1 zhen an 82-dB sound and an 87-dB sound are heard, pa pmsgazncr; 7a.17 simultaneously?    dB

  The sound level 12.0 m from(0 chzx;zt3t8ddrk 2 r a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radia;xrkct0r dzhtd z(23 8tes equally in all directions?    W

  A stereo amplifier is rated at m7bmn*mq3i2l150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. Whatqmn m2* 73lmib is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protecth bpg8+ bor,8;;/ y6zix glcktive 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 z /t8hoib;+cb,6y p8rxkgg l;. 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 syst y(vdqq53 1rxxems, 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 tz- eze7*m wed3uned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamentalew( 7gcr .h3 2.mcoxyy frequency of 440 Hz and .rgw.yy ce2(h7 omx3ca 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 intoq+ 9;(yxbi.rl zdoo-+pe0 wskh,j f;y 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 frequencyy os.f;xzyi dol+w r, j0bk-(p+ehq9; of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube thatai2f+c 5-rzm2*+w efrcjr+iw 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 moi- 2*2+ij r+fw z+rarfmcw5cede) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate aiw;7k a-e;ps1 v yfoq;q4e:rqt)hm, ks 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 500–1000-Hz range coming from two soc t ,y1t5-ez srv2y2ncurces. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the freque 1ec2,yst t- r5y2czvnncy of the sound?   Hz

  Two trains emit 424-Hz -(bml +8n8v jbd5yzvg whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat vjdz-g ml bn5bv+(8 8yfrequency when the other train 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. Agf0j/8 9amed v0q e.fa/q;rpmfter it passes you, its frequency is measured as 486 Hz. How fast was the tr/9q jeegrqama .fm/ f 008dp;vain moving (assume constant velocity)?    m/s

  At a race track, you can estimate the s0 p/qklsyo+ *apeed of cars just by listening to the difference in pitch of the engine noise betwe sqoy+/lpa*0ken approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding tognns6s4(6zgz dether, produce a beat frequency of 11 Hz. The shorter one is zng(6s sdzn642.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a 3yheijb7;2i(4h3rrko c6 te wm(c: gystationary 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 by3t:ob(ik6ceg y7rj 2 c3(4hw;rhyim e 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 zob.k(w j +6tgis normally about 0.32 m/s what beat frequency would youo+b6jt .zk(gw expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whileib,nq0.r cit u 0b5p wkps.*/ gw(a;ra the moth is flying toward the bat qirbt5wucp . r(aab.;,/n w0*spkgi0at 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?    kHz

  A bat emits a series of high freqqb32 umzg/au ) f;9oh(5ulzx sde:sd5uency 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 sef3l gxu(zs)5uob;5dums2:9 qah/dz o that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was onceuqjgv 34gh4dy3.-n gwjbd(c6 used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss q3ghj.cvw3b(gnj d644 dgyu-, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromisedgisj (c/eufg:c/hs, 4 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 wcg/:c/,ejf sshiu(g 4ide, 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, slender aluminhd4p g506bhxvum 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, ring0d4v 6p5 hhbxging 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 thresh wf xh5.0ixd-hold of hearing for the human ear at a frequency of about 1000 Hx 5-0dhif .hxwz 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. A1kfj(pwrfj,1w 2 )6 ,pkw buiin observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s ,ffkj,b6 www kj ()1uir1pi p2altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 fdl6(*8t t0dqcl( bjh $^{\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