What is the evidence that sou j) zz(zi9l/;s.off fund travels as a wave?

What is the evidence that sound is a fosd6z fr. iv-) 22x lnas3ug2y4j f:erorm of energy?

Children sometimes play with a homemade “telephonm.gb 131cqx2s3klm kae” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child s1ksg1bl k.c x q23a3mmpeaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave pat+xq;c1vdz2(6 w;9pamu f kv0n1dxfvsses from air into water, do you expect the frequency or wavelenxdwpaxkn v1ff(6 ;vd c19 tvu0zm;+q2gth to change?

What evidence can you give that the speed og kzs)uu3c-s3m um -i +tih/q,f sound in air does not depend significantly on frequen)ch-,i +-kuusmsg33 mq t/zu icy?

The voice of a person who has inhaled helium sounds very high-pitched. Wwkku)w 7ou 9/yhy?

How will the air temperature in a roomkla7q+9(df( cudz dfc8c e1:px8-*aezvmk / o affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of wqxy f+ q;okx s6.ez-;sounds in various frequency ranges. (An x+k6f ;zwx.-eqs qoy; example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaceg5kryuv;o h 31d closer together as you move up the fingerboard toward the by135ruh v ;okgridge?

A noisy truck approaches you fromq j/9jyr4mz)p behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — 9qmj/z)y p4 rjyou hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats cx )p1emdu-g4566mo4 recyf blan be said t6yu4g o mdx4rc)mp lb6ee1 5-fo be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wo.cjq:ki(*)qq1px5/ nbqr* r z eeqr7 tuld the points D and7qqrj/)q kbe5(rz.r**iteq:q nxc 1p C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of proteb3qzf6eb3 fh *cting the 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 technology, headphones are worn t h36bz qf*eb3fhat 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 wavepfm.ny+ j 7cij/1i2 zys shown in Fig. 12–31. Each wave can be thought of as a superposition of two icjip/2zm 1 j+nyf7 .ysound 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? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obsyn8:.b :yev5 5g sq5taeau ht3erver move in the same direction, with the same veloci.:au38y5b e5tgvet:sqan5 h y ty? Explain.

If a wind is blowing, will thi5ku4p9socb 7ss alter the frequency of the sound heard by a person at rest with respect to the so5 bc7p9 ossku4urce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a s+ *ykm8kcvolj tf+g30wing. 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 highest frequency for t cgmlk3kty++ *8 0jfvohe sound of the whistle? Explain your reasoning.

  A hiker determines the length ofku uu+-x4s)a t1mb+1(tde dof a lake by listening for the echo of her shout reflected by a cliff at the far eaudos41+(x-tfu uk 1te+ d)b mnd 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 sslanjnxd :k+ +(byn-7sspk6,o+ x7 y oide of his ship just below the waterline. 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 (yy ( kxxs+ n6 nan j,b:dkosp++77s-loTable 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wav9gv*n 4te54a7 4e csrk(acgi a;tizq+elengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of whp)9s-d pdpj 9 eyz+jm7v+-qx 7bsr8 tuna on a foggy day. Without warning, an engidwjdm9p+ p 7z8jr-b+v-9e)phss yx7qne 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 makesot*c q:z wg9)s when striking the water below ig st w9*:)oczqs heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees aizjaw, v2:f4kw7 yu y- huge stone strike the concrete 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 wwf ,4a-j 2yy7iuvk:z the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rug,1j 7*hvg sbwle” for estimating the distance from a lightning strike if the temperature gv17 ,bwj *gshis (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of63 i2pzhz6 dwmon6;to 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound le(8w flwdkl)2+q)vi fdk 6ap1m vel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers uuqg3f70 em,y j6e.y 7q 32msymqh u:cyz38ifproduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is m3 8 eu2 7yqqe 6f,my7h:yjyumc .i f03uzgqs3exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain dista)i .okp cg,w8om5frz+nce from an airplane with four equally noisy jet engines is experiencingor5z wp,k cf ).+gm8io a sound level 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-noise ratio of 5n:oeka ;e/w -h8 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for kn e/aw:;eh o-each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a perck a79d2*wbe/awj.u(3kel hason speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly ove3a2a wl*bcekjhwad /(.9kue7 r 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 whosz56 et3;wfuw )nojc.ae area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, whij- kfdz4;9fzk 72n/q- s wk,/hlvsfe vle the more modest amplifier B is rated at 40 Wzqw/ f-2vk vssezk/-;fj94k, 7fndl h. (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 130 dB when placed -tfq u .lhk* b8 croeg.h* 6kazzp;1i92.8 m in front of a lou kze9k uf. rl1-*pa6cb8z.;g t*hihoq 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 typically d/xj:8 yy vz2; 1mc8fbiyge 3sletect 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: See Sel8cbzf/:iy2v s 3gymyx;1j 8ection 11–9.]$\approx$   

  If the amplitude of a sound wave is t 2jtb, q52q(wvo gl0fmwq pa;h3h0(z wripled, (a) by what factor will the intensity increase? Increase by a qaf( twq(v5wbmhp,qgl ;00h2zo23j w factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes) gxvon) +kr s h2o:(b4wsr(5(fiaax j(ky ba,, but one has twice the frequency of the other. Wr)xs g)i ws(r ajk((vnk4a (5 +:hbo,y 2foxbahat is the ratio of their intensities?   

  What would be the sound level (in dB) of a snz 3pksmv6xi) / :fai,ound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm atimiv:f,k/a xsnp 6 3z) 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hzj m5cyzcb2d )wog8sb1z l/ z/* tone that has a 50-dB sound level? 8z2 myg 5/lz1zb*d)cw/s c ojb(See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whexkt o*6j1 txg5n the sound level is 30 dB? (Stk j x5*61otgxee Fig. 12–6.)

  Your auditory system ca0ciwnf u-4b8ztq-d ii rl) u/4er4+non accommodate a huge range of sound levels. What is the ratio of highest to lowest intb rd nuil0ti-f+4 uo8zi )4r-4cw /qenensity 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 f wwztlvw -e(c0tb1worz 0j :v1 c9nb67undamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under jc-(0 :wzo cw17bn9et16 0btrlvzwv w what tension must the string be placed?    N

  An organ pipe is 112 cm long. Wt6 u,ygau e2vl .f42r (mwk:qky7tva)hat are the fundamental and first three audible overtyk u2)wey, k rvqu4 .7mv(tata:6lg2f ones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of an e1w3m aargnlvr 3j m,./mpty soda bott3ma/vmr.g ,31wnr ja lle 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 spa6h(mhjmoh unt)4 bl 5h)bf. ejbd/5/mnning the range of human hearing hm.j)j o/ mub5fh5t4/(bd )6ehlnbmh (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What willov/;z y .lxg:wivg+ 2x be its fundamentalx.i:gg+xzw oy2vv; / l 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 tuned to play E abovtb* bfst .o6bd2q ul2/e middle C (3lb6 */qt2tb .dfs2uob30 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)oveg33j*ni4i:- fws5 hr *;dk kxh*fea 1nhl ) whenj-h*:;i n)r 3gndih1 fs*ol5 xa4ve3ew *fkhk the temperature 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 h-dybxp7i5tr 8 7qck lz2w:b920 $^{\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 s(q lbxc /pw7yny; 1nt/hould the hole be that must be uncovered to play D above middle C at 294 Hz?n;tcw(/bp1yq /xly 7n    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 26b/p:*so zn0 zf4 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Sho0ozspz: n/f* bw 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 resonates at twai-d:wl i32chy)jdkir9*, svo successive harmonics of frequencies 275 Hz and 33is9 :k *3j-)iilvcw hdy2d,ra0 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 ,1* hpudchkm ;r8p6gs pttag29r 9 2wy$^{\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 areqa1q4s4z swkgc 6+ wh; present within the audible range for a 2.14-m-long organ p 4 kzsqq1;gh4ww+s 6caipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is a/3ixb+6jg.mxwm3ndn l 4pc4 icst3 *hpproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the gc34sxihldbp/j.ci mm*3w nx 3t+6n4graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryinf* *a6e* u/jbastq k4hg to adjust two strings, one of which is sounding 440 Hz. How far off in frequency iqhef*ab **ksj a /u46ts the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) 3.m czdy dofpa vd,(rz5i6,c3and $C^＃$ (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) operates ;x uhgheh: m+3l.cpf-at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 500p e-h.c3ugl+h hxm f:;0 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produtoko,6:zjnk ,ces 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 reasoning. 6n zk:kt,,ooj   Hz

  Two violin strings are tuned to5qk 5 q /dz1pxz5j6xug the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequenzqdu xp56q5x /k51 zgjcy heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle C mk9e0. tda :cvee:*lu(262 Hz), but one is at 5.0°C and the othertvd. c 90eul:mek: ae* at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Forfpld0nlrht+ 4cqna q;-e z me;)7rs-1k B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. Wh-+-efzdte n r0sla)n74lph ;mc 1 q;rqen 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 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 one spetn9vdr.5ix 7u8 cdv-29v ;zk rrowk6saker and 3.50 m from the ot ncv 92 du.rrkoiskvz-6 w8v9r; xd5t7her.
(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 cl 4gw4+ r5gxj7+vhz6mn*c tvpiano tuner hears three beats every 2.0 s when they are played together. (a) zhwg46*nrvv cx t 5cjm4 gl+7+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;kykk+:7asqhr83+f5c idgo g wavelengths 2.64 m and 2.76 m in air. How many beats per sec5 +gd3k:y ksq+oaifg;krc7h 8ond 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 Hznlsh b0;y05ehk+qk8qs *q9 a-byxf: o when at rest. What frelo0e0* q8q xb:b+ -aqs9sy;kfh5y n khquency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do dbaocoz6q+/ )you detect if a fire engine whose sireno6/a)dbz qo +c 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 frs*4ox e8m89dzapy ,gmequency 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 frequencies exactly the same? Are they clom ,9s eyagp8 4o8x*mdzse? $f'_{source\,movine}$    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. When7)k j0/bzab8s;eksw t one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequenw0s /8k kb;)a 7zbjsetcy of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sounsb le,b127ld m czh70pd waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received so7spcd1 lb e20z7 blmh,und frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/slyn+y+ b /s:ct As it flies, the bat emits an ultrasonic sound wave with flnt/:+yc+sy brequency 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 0 7dig.nqotnj88ls6sa 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 station. What beat frequ sj6.8g0nds tq8onl7i ency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter us :4q:pq+b dkkles ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed+:b :pdklkq q4 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 directly away from the sound source?   Hz

  The Doppler effect using ultrasonic uxu/ 0kgwe 87bwaves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hx 4w:1 pp32nijfe xmf-z. When the wind velocity is 12 m/s from the north, what frequency1 3pxnf4 2mi :pef-jxw 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 moving on land if its speed at 20z lv( gk2mp9a9,v/x0 pmnu/ kq $^{\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 ojgefx )z2airosmpv51/d4d* , f sound is 310 m/s (a) What is the angle the shock wave makes with the dg z*a14,sfxjpid mvd2r/e) o5irection 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 atmosphe ok1g ham,c ujv:c3b bd3/,a-pcak+ork/c/n 8re of a planet where the speed of sound is only about 35 m/s+ro1,/c-hb8kan 3cama/gcu,vc /3k db: pjok
(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 850ppm+p+o ia0r y,3r8nu0 m/s strikes the ocean. Determine the shock wave angle it prodi+m3, upya80onp prr+uces
(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 w1:r)afpuc7 $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plaxlsia4 lk;c.1yzq6b9ne exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the s1q; .9lil4b6kxcyzs aonic 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 4pt k p9a*wj)piy+rn*sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for*w+kp*t9a4 pijn p)yr which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaohcxz7 -) n v40y,ucflves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sy,: qivi*8dq ytpaqt,idop3o).h2yo ) mphony. It consists of many plastic pipes of variooip, pdtid8q oy)y :)v. o3ah*i, q2tqus lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold ;uj-i 9o,jwtn of human hearing (0 dB). What will be the sound level of 1000 su9 wn;,-j otijuch mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound m e9jqyqo1wu4 6agy*/ and an 87-dB sound are heard simultaneousluqg1m*y w j 4aq6oy9/ey?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What h/okx29s,z)f za h *bnis the acoustic power output (W) of the speakera)s/2x z nzhho *9fb,k, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. T * yqntjgy-nc;)n-/ oksm2e 8khe power output drops by 10 dB at 15 -g8mncy)y; n-n qj*/oke k st2kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. -ih.rn i4iax14*ggox92 iik v Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 d ga 4rgi k-h .x1i42o9iinxi*vB, 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 communications systems, the gain, ikk9i07q* n3 8pjwzas v2n jg y1u*u:t$\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequenqy1, dmns pr t:ha8k2*cy 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,bw5ypphpy 5 xq a 64/1-*czlia pj-de 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass-y 6xjdaz*q5 hp/ 4i-,pybe pw5p1alc 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 vi1(tir th3dj1u bration above a vertical open tube filled with water (Fig. 12–35). The water 13u i (hdttrj1level 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 frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube t9e(cf eq; doifn4fd:c, v o(-ihat is open at one end and also 75 cm long. How much tension should be in the strifiec( :o,vfo q4d-9 ;(cnef ding if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resoic)9mx 1 r:qn2j dz.dsnate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources fg:y, )i4u6o p5lvwihd*(v ol. The sound is loudest at points equidistant from the t,: ouw4p if )gi* v5l6hlv(odywo 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 frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Od (s2guyb p,ebor7 )m 2fz.*mh:oc6 wene train is stationary. The conductor on the stationary train hears a 3.r:*,y e(.z b22)b efgop 76umcho dwsm0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as i/p5wac8n r nfs +ksz9zj1yfp, j/ l4u6t approaches you is 538 Hz. After it pass/w s s+z94u fajl5nkj cpnfp,8z1/yr6es you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening t6yfik8n up zb+j.yf6y)t 4 tw.o 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 haly+4twfy8 bn. z)ku66i yj.tfpved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soundin,c2;zdc aos5,lpdv 6 eg together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other? clsc, dpze a526dv,o;    m

Two loudspeakers are at opp5s a g i)o83s7gsohqy:osite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical soundgis78yaq shg53)o s:o 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 blq j*,eiog 4bx7ood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were di4g,i7 qoxb j*erected 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 wmextfz-w n 3;hie(u+:hile the moth is flying toward the bat at speed 5 wi(xeuf3m;ehtz n- :+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 frequency sound pulses as it approaches a moth. The5w2ff tunj7) f mk4jt 3zt-o)f pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How fart2 )54ku jt w of-m3f)tjnffz7 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 signals from one Alpine n ub8b37 j qasyk,o 1,3m;kpxqvillage 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 long, and it is called the F sharp (or Gy7kpu,x1jbn 8,q o3; sab3 mqk 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 .scvju:9et4 mby the presence of standing waves, which can cause acoustic “dead spots” at the locations of theutsm.e :4vj9c 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 rodsfip8g7(t3cs:sj :x yy,” involves 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 madexsy (38:ijft:p s7 ycg 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 them4yz:gy+r d4ogyw d8/ threshold of hearing for the human ear at a frequency of about d4 yzrm8go:+yd4wg/ y1000 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 observer on the ground hear78rraaivye f. v0) e:+0p bgxqs the sonic boom 1.5 min after the plane passes directly overhead.f. y0r8iap)gv aqe:7xr +bev0 What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is . )ujjz42 dktb15 $^{\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