What is the evidence that soc)h2ac7(0-i2-tx sckn ws nreund travels as a wave?

What is the evidence th2*,+ sjo+rbnc s pq3q/ 70frhn1itiotat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to thx1f.wk9u,duqxl03 hh e 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). Explain clearly how the so3f.9hhdw,u 1ux xlk0 qund wave travels from one cup to the other.

When a sound wave passes from air in7+yl *cikxqe cub;:8tto water, do you expect the frequency or wavelength to ch;*iy uxlc+ekq8 : c7tbange?

What evidence can you give that /7.1bn sy+lhly vmj j.the speed of sound in air does not depend significantly on frequem/b.lnj .v sy7+l1j hyncy?

The voice of a person who has inhaled helium sounds very high-pitche9 hn ,zn0 u8:uxiifal.d. Why?

How will the air temperaturftk*tnir)j v. .ya5s, r8* vvue in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the ampl83*de gnmu5geitude of sounds in various frequency ranges. (An example m ge5*d38e ugnis a car muffler.)

Why are the frets on a gui9 igl0avi wz. +we6,xc2;lpyytar (Fig. 12–30) spaced closer together as you move up the finger2c0 z gaxy.wlep;ilwi,y6v +9board toward the bridge?

A noisy truck approaches you from behind a building. Initially youzgk 5clb-,zex/ d.h n -hmyy5. hear it but cannot see it. When it emerges and you do see /ecnhm gz .5l-xkz5 yh,.byd-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 “interferencei c feohz79dx(rdjx:1 +6s1iv in space,” whereas beats can be saov d 1cif+x7 rz6ijh:e19xds(id to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakeq 5*l8fy,eo4 7;ojtwfpxeav ( rs were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart*xf,l t 7opev y( ef;jaqo458w or closer together?

Traditional methods of protectnmf3i4.y8r i14md:ngyktt 2eing 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 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 ambie4fi3ni1m: e yyg.nt8t k mdr24nt noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31jjw:1a ,z* z*etjz/o r. Each wave can be thought of as a superposition of two sound waves with slightly different frzt/*,jjez awzjo1r :*equencies, 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 observer move in the same directiwg w+ pp)c*)m vkd6v(uon, wcu mwvpw+)pg6v)(d*k ith the same velocity? Explain.

If a wind is blowing, will jcerbufw*-0 821/jozg (uv7dmoz gk7this alter the frequency of the sound heard by a person at rest witkz/ um r*ez(-1j2g7vgcfbu w 70dj 8ooh respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various pofgao ir ;jy-:-sitions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the grof a;jgr i:-yo-und. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by l-)7c 5pgk lsm 8gvu8thistening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the 8)g-lh7 vcskp5m8u t glength of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears wan0 ya+ i mysluggn/)y6,6w+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 does not vary swiy/+sa gn 0 +lywng6am)6,yuignificantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelyysrjv. ia7 6)engths 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 odmd wrzu5, m8.f tuna on a foggy day. Without warnirm d.,zw58 dmung, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splas, /t e o6.dxv1vhi(uubh it makes when striking the water below is heard(6o. v ,dvuihexut/b 1 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strikekgt3 y.b ss7,g the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concreteg ksb, yt.s3g7, 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 onec+h:1p tn8:43a izgzj ca1fqe mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) +8zzg:a 1q pnhjc:ia f1e4 ct330 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1209my5.iq-lhc :b sqdc . 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 whosp7b vk(b4wgv /e intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousl 7 o)fsgi9qoj20o 8fxxos 3p9pysd14p jb,b0by at a certain place, what will be the sound level if only one is explode4ogjb0fpspqbx1jxy9o0 ) 7d s8o ,fp bios3 92d? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certaiqc+,ll7-x80s nkgkg6gi l+ xd*jt j5an distance from an airplane with four equally noisy jet enginesag, si-qn +8+kc gt*xgj6llxklj 70d5 is experiencing 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 sign1 psi0dd-si( 66oxqya al-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 ni6 qa0sd (xy-o6pd1 isoise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outvb.fnm)r-z:wanf6 ( yyy3o l*put of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniflo n:w3y 6-zm.y b*navf()ryformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose are5xz*kcbog v99a 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 rap k50mew:)*b(idkkrcu0ot )k ted at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estd0e kk):ucw ok*mrptb(0 i)5kimate 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 registe bi3q4hrw p yi1s/0gg3uby b02red 130 dB when placed 2.8 m in front of a loudspeaker on the 4 yuihwg qb1gb/sb02pi03r y 3stage.
(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-u,i ha4s lxqw4k 0y.ietect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes.xswiaqlu,i4yk0 h-4 of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripav *i5cfy,jo+)q0g 0t exv gm,led, (a) by what factor will the intensity incregv5o*0m x)yji,aq f,ve0t+cgase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has nekg;8p0cwbj- 3u h 3itwice the frequency of p 3bwjci;e k-u 3h80ngthe other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds:j-dhbgr; / pkz: vuq/ to a qb :;k/- vg/:ru pzdjhdisplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level 7 at;qgd*sr ryb4m.z;fvkl3) to seem as loud as a 100-Hz tone that has a 50-dB soung3za; t7v)lqf*smd r4;byr .kd level? (See Fig. 12–6.)    dB

What are the lowest and 7 r.risg op;hvxo, w.9,jweu (highest frequencies that an ear can detect when the sound level is 30w. ,uhx(.gs9 r;ioe7pw rjv,o dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of s w3v6py uvxg z*u.3p1wound levels. What is the rappzvu3163w v gxyw u.*tio of highest 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 h9o ryq v 1s( 4.bthr14cuka;uz/vcf5xas a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has qzo1 s4r(1r ;uv/5b.ccf avth u9kyx4 a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamadpnu s w:-*v2w a:ehzp/- vz5ental and first three audible overtones if thepvhu: npz/szadw:-v *2-5e aw 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 ofxt;edvaq 5c7i 22dopy6/n1x j an empty soda bottle that is 18 cm deep, if you assumed it was a closed tubedxqt nxe67o5;/c a1dj22y i vp?    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 pipeske/wuf9 p p1a( spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengpf1e/uk pw 9a(ths 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 harmoniyq l *ckm6 blht0:)q9v ea9lu/c. What will be its fundamental frequency if it is fin:v/* 9htqlm 0lkcl) 9abyueq6gered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to pladbl2x., ft0p q5wi, j)lcgf4xy E above middle C (3305,ctfpq.wgx) di4l2jbxf , l0 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 Cf g x9fbeer:v9(j*lt ( (262 Hz) when the temper9:xjr (etv(lge*9ff b ature 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 20 kydzo08.1oqc $^{\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 sh qsa0--sl c,aq y1tn9pould the hole be that must be uncovered to play D above midd-t1cps 0a,q9 a qslyn-le C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, butss0jjiu o j(lp)8.nsf5yj 6 3u not at any other frequencies in between. (a) Show why this is an open onypsf j jljj6o) 0s3ius5.u(8r 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 resonate8q24v lnq4hmdn flq19 s at two succel19vqmqh 4 n d84fq2nlssive 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 vgp-7bzba y578- rl(4nok tqs $^{\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 withioxyc-sk+ ta .,/ wij1 8xx/tzin the audible range for a 2.14-m-long organ pipe at owixtxtz,a+i/8 xsy1c - .j/k 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 and-/m877adcwzaioi. l ;c 6vmeo is closed at the other end by the eardrum. Estimate the frequencie dc;wv76-comim aie8o a7z l./s (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 trying to adjuscfqs4 ya80 3blt two strings, one of which is sounding 440 Hz. Hsl yacqb f8304ow far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C*csbz +0bz/; ypz.t+5i4xf6jmd ekpr (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 (bray6bnl;k04c k c;8eos und X) operates at an unknown frequen8syc; lo4ec k 0;6nkbucy. 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 operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when wcm*a 6nj9azj9 0l 4kz:xme;dsounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355acm ;j9 xz:l*djmwa 0zne69k4-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz5n um2.exmk43q2*hwlfo,y0 e xkc+.(w n t gez. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are pt3m..numg 4 qx*y zew x+w0fc(l2e,5heon kk2layed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle C (* (sqap*xsrr8elo;:.-u )y.jlam ihcfk9;u o 262 Hz), but one is at 5.0°C and )r ck m.yr :*.j-oqsae*;xu9oih(fua ;s8pllthe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forkh3 oqcp6vf2p4* nqeh -s, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are h pv36*qc4-ephn qo2fpossible 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 apaghn7bg g 5zl86rt. A person stands 3.00 m from one speaker and 3.50 m from the other.57 6ngghl8 gbz
(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 supposedu5mr, jmc51fss p5pz l.wsv )q:p4i t: to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what fc 1s ,ztp.s 5r:lm5 is)jp4vuqp:m5wmust 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 mkfjip 6x(lr)b49g /yo and 2.76 m in air. How many beats per second will be heardj xgp9rf oy 6)lkib4(/? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of tt8 b.cwny0in hck: (/a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you c :ntn tbkh (c.0y8/wimove with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing sti- o3uu)jr5dwv3r c)usll. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s ucu)r)udv5orj3- sw3
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freqhmqv6ayw5av9 2. qvy g/ckly1h51q+ kuency if a 2000-Hz source is moving toward you at 15 m/s versus you moving towarw 1y 5q + vag6.ky 5c/yhkqqv9al1vm2hd 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 xn13wxawke2m .j9 h.c(cs. dc the same single frequency horn. 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 frendm 2h(a3ws.ckcce.1 w.xx9 jquency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wave6na/iep ( jrs* y(,hwvs at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound/v w6,*jp( (hrnyeisa frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a s7 dtuf3ob(6f:ph 0fa epeed of 5 m/s As it flies, the bat emits an ultrasonic sounodf p h(6buf 3t:f7a0ed wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movo.vaps 0*e5ko*sb3rp qd0mv 5 ing 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 the train car appropbs 0 modpk*0.vqr5evaso* 35ached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to md9qvx-n k02u 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 dirm0 n2 xv-qku9dectly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of freque f,v+t+ do4mnxz184qz u.po emncy $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocitx ;fvjvvz q2bd:/ *kx3y is 12 m/s fr;f v *xx 3j/dkbzqv2:vom 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 moving on land if its speed as(xs+ssgno5 .j*1r9rg u,ev s t 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 wum )+hvfmsq d71j m *gx02 7bolulx34there the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplhb7g qxj0m vo3su)+f*um 4 7ldmt l21xane’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 sp-/a2xsu gc7fg 74nronw+w ti.eed of sound is only aboutuox7.2nt-4w c7 nrg fa/gi +sw 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. Determin4 p)fl(anyp2a e the shock wave anglef()yp a4lna2p it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle 0khou3r9pznx - syzml27 z*y .$/theta$ 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 thewt8p ulw,shz:q7b*2 e e7hb l6 ground flying faster than the speed of sound. :l 7lshb,utz 2b*wpehweq8 76By 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 device that sends 20,000-Hz sound pulses downward fro6cjehk7 7t it;m the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what i76t;etjh7 c kis the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible(:s*m.nnkejss.vf7e q:fkp)4dwju gy n )9q 0 range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dispdth,pgwgx x v 5+c61*qlay called a sewer pipe symphony. It consists of many plastic pi, g*1xt56cpq w hdx+vgpes of 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 sound close to the threshold oqf /l ,qm;gp,yf human hearing (0 dB). What will be the sound levelyp; ,g l,qmf/q of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound aypysn(93ym*kz)7j gl re heardn( 3*p kjl ygym)zys79 simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. 452kxa xqp du ;+2pcuuWhat is the acousu k 2x2x;udcqu+4pa5p tic 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 eh(d; si0fd4wpower output drops by 10 wh;f( e4 id0sddB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective dev8qh nznz gh3sie ,+// gelne63ices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power interceptqhi8z,znl e e3g 3hgnns6/+e/ed by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications s k: c4z-mpe;siystems, 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 tunex(;8/4 scg6xjl cpkpgd 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 fundamental e k2g94lwtcu*c+ln,p frequency of 440 Hz and a mass per unit length oflt gp lku,9c*n4c e+2w $6.1 \times10^{-4 }$ 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 fille)ir; ci w74xj3b v n:*2mujlszd 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 wh)xj :znswb 7ui3m2lr*cj i;4 ven 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 stri7p(jdo4 sweovs8ol;ov)p0 5 mng of mass 2.10 g is near a tube that is open at one end; wp ols(m0o 45oevp dsv)87jo and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as1 0dx3mr9/yos fsr1l mz1 o3jt/ai +bj 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 ran:e( 6fk;sh)qhd dyxq5ge 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 sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sou6;qeh5 )dkyd hs:fx q(nd?   Hz

  Two trains emit 424-Hz w wjb+6( qc:nw), ujzsthistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency wwbsq6z ut:(c+,j)w nj hen the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whislp5xw)3l e q09 nf,tohtle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity5, tpfq e ol3)n09xwhl)?    m/s

  At a race track, you can es gp*-apqoe-g ,timate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certaggppea -q*-,oin 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 tp+lh -7k u9sobddoqr60n7:mtogether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How l bkuo h 67d:lpsdrt+-079 nmoqong is the other?    m

Two loudspeakers are o9rxv s2cbt 9r 48u,:azq4.dh no.nslat opposite ends of a railroad car as it moves past a stationary obr 99an8u o,l brxss 4hq: 2.dtoc4nvz.server at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he 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 aor1m yppaba2 riv8m* *c,t8e-jpta is normally about 0.32 m/s what beat frequency would you expe **p iv-a m2p e818yatjmrpbc,ct 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 while the moth is flyinw9wyuywp i 560 e:zk3yg 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 batw6 yiweykuz p0:yw 359 after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulcse m e:e:kd;9rga-;uyni4cr 4b6: dzses 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 nd:4 bs;64ri:ekuz-d ;: m9egyera ccthe next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wsx w 9gul+hgca,o6bq(e/p3 0pas once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the 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 ab l apgw+ xc3h0uep/6,qo9gs (s an open tube.

  Room acoustics for stere vmcr1zr0r3e;gg t v)9o listening can be compromised by the presence of standing waves, which can cause acoustic “dead spotsvrrtmz901 rg ce )v3g;” 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 rov1cw )1u4suis inv zx6u dlbh+ 7u7,0rds,” 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 made to “sing,” or emit a clear, loududw )0174+vurc,17su n uvbx hisl6zi, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold o8 hpp4 n ph0sg0c:wqsax 1ai,;f hearing for the human ear at a frequency of about 100whqi084ahnpp1a0p,sgs: xc ; 0 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 hetm y0+p .upf;sars the sonic boom 1.5 min after the plane passes directly oveu ;.sf0 +ptpmyrhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is sjg 3:it*f3(pg 3exqq 4nh-bm15 $^{\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