What is the evidence that sounn9uanmv /+c*orfqa* (d travels as a wave?

What is the evidence that sound is au(vex my7l9;vt5y c rr35ogg; form of energy?

Children sometimes play with a homemade “telephone” b5wv/u r)do nw cgy/qlw(f5g*3y attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at wwr/f*g3/l5o5dn u (cywg v)qthe other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency od 0ol )-9coj:x6xrf*z-d oa onz:p+ ycr wavelength to -* x6zrcpl :-onda0dycxoj):9o +zfo change?

What evidence can you give that the spe5zf6p7 hcnq.(u4abbnyna6 6 pd 4l ec6ed of sound in air does not depend significantly on fp6 zf 4hnlacpq4a.dy 6 6ue6c(b75bnnrequency?

The voice of a person who has inhaled helium sounds very high-pitched. kvu0l*;w sd-,*i qf- ki sx3viWhy?

How will the air temph+jupp f0.* 5jvlsg 5 9t/gvhlerature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soux.rnc ,ds/qm8 l1dpp /nds in various frequency ranges. (An example is a car muffxn1prpd/ .scdm/q 8l, ler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you w0bf 7eubi*o7)v )ag l- - gdbhapp6a:move up the fingerboard toward the br:*w apgl-ob7dp- )a 6ihvube)a b0 g7fidge?

A noisy truck approaches you from behind a buildi9 uptv8:h7fgj/atwz0 ng. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency v t/9hpat07 g8ujfw:z noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spq ng3 0 /dl,+fqjul,ewace,” whereas beats can be said to be due to “interference in time.” Exp3 ,enq+,l/jgu fl0qwd lain.

In Fig. 12–16, if the frequency of thiqnpk.7-m-06l f;wk j dij * 5-qxdzaee speakers were lowered, would the points D and C (where destructive and constructive in j me 7 xzn-p q0*dwil6;fjakq--i.5dkterference occur) move farther apart or closer together?

Traditional methods of,;ya0)hb;/tpu .m vvbuo9q du protecting 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 el)tyq9a;,bu;vmupb/ 0 huo . vdectronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought ocp51 guuqabu 3 r1.l2kf as a superposition of two sound waves with slightly different frequa pgq31.b5 ulrcu12uk encies, 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 in2 n okr)+kisc. the same direction, with the same velocity? E+ncsok ki. r)2xplain.

If a wind is blowing, will this alter the frequency of the sound heard bo4vahb3 e.:ie (qgw4i blv9 a-y a person at rest with respect to the source? Is the wavelengtho4v:.a be l3i i 9bgw(4hveqa- or velocity changed?

Figure 12–32 shows various positi 80iwp)+wl+ zn uup,fgons of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At w+0wfzwp8+), lun puig hich 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 lari3g2 n8lrg,nj)y7j g ce 3oo;ke by listening for the echo of her shout reflected by a clifngjg , cr g)o2nlo8i73;j3yerf at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterli )+.vfmbua2j yd v1o- (hd9a jr.urxd)ne. He hears the echo of jau.mx (bd 1r+yd)ov9ahd2uf j)-.vr 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air;r4,js)b r, kmu iclnx+ic8 n3 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 6usd535dz h ,hj3ko ub1sman*of tuna on a foggy day. Without warning, an engine backfire occurs on another bo aodhdj,n *3zs556kb1u3u hsmat 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 aetq:zcj 652k t(ok+z j cliff. The splash it makes when striking the water below c2tj(q :56kztko+ zjeis 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 concrk a 3i.:u;xsf q.7atqdb*( ,fj1a lfafete pavement. A moment later two sounds are heard from the 1dt(q.fuf:sa aiaf3,k lbqf;j7 *a.x impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5)fn5 *:sd9ahfto* dfg g:3yzp-second rule” for estimating the g5t n*oa )zp d:fgs3 f9d:*fyhdistance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound epu.c0 3vtjj4fr;j :u 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 intens1oktrra :ae(5k2t8 qgity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produj w7ii-x, vhnp:f7p1q /6;e envdl-vqce a sound level of 95 dB when fired simultaneously at a certain place, what will be theq pwn 1: 6i-pin7q7;xdvfl e vhe-v/,j sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance nyt+t :b,* 5juozotj8 from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [no bj +t:5zjuotyt8* ,Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 x*gliqa09kk;cv y5k4r0mcv7 a+1qcq 6 :ecva dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise forqqgckek 1qxr9 va;v0 c7:cmi+ck*5 vaa6 4 0yl each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pe sjmmu2r2e. 1(8qdsr wca/5b mrson speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly2cd2 m5.bre(m /usaqs8 1rm wj uniformly 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 strik fe1jo dh4li44b(r m+q-k*fmses 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 rated at 250 W, while the more gwlk gn826q1cx tp-w l.tx/:w modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect atc 2 px.w:n1-8k /x tglqwtgl6w 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 remugs4 b2n9ids c m56r*i3ogx2gistered 130 dB when placed 2.8 m in front of a l5g m2cionsbdix mr2*439g6u soudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0)f64oji/ex8z,hh cl e p3 : oiveo(fe) dB. What is the ratio of the amplitudes of two sounds whose levelsf)hoi e/ lc3jhefz6o8o:)e e(xpi4v, differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave idk ,1j6:r dnyw x f:(gm.qo8ees tripled, (a) by what factor will the intensiw n6fq:ej81rekgo,ymx : (dd .ty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equa w8rp:d oj/wr/n jhqzi0.9:ael displacement amplitudes, but one has twice the frequency of the other. What is the raa/:zj.9dn:jqr /p e0rwoh iw8 tio of their intensities?   

  What would be the sound levecw,u1l m j,zi8yz l p5fb+xw6z ,7gr7cl (in dB) of a sound wave in air that corresponds to a displaceme8igjwyf z6 czr 1,ublm,x5lz7p w+,c7nt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that .1m7fpk5m 8uhf /oxg +s,qcab has a 50-dB sound level? (See Fig. 7kpxm1sfoua5 bq/hf,8mg +c. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when osem:m1 nlkb-*, xe:d d0zn/ rthe sound level is 30 dB? xlddbnos/ krn:e,m-e :z 0*1m(See Fig. 12–6.)

  Your auditory system can accommodate a huyxe6xu y+sv7 2 l17rtwge range of sound levels. What is the ratio of highest to ls+rx1y7 uve2xwt6y l 7owest 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 fund(ck y)31zxqykqs*c5xg )5m w qamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Undq3 ck51y5ycx( zkqqxgs w)m* )er what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threeczmvz 3e1. 1soxj1b a* audible overtones if the pipe iss1 zb*o3. m1jz1aevcx
(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 frequenc) rcmf(hr;y ws13 eo+dy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it warrmd;w(c h3)f1+ e oyss 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 ophup 1dx 6zwx/;ra d :jz8ddk bdt* b.62-ivf;xen-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes id8 d tzwux/2xax6 ;vk.pj1b :d*dd6b- ;rfzhrequired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 .3 c, itdbpa)r2ps ;mtHz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60m2pc 3pir tb.d;),a st% of its original length?   Hz

  An unfingered guitar string is 0.73 m loq6hte ;r4 (rq00ry wy,fjld a1ng and is tuned to play E above middle C (330 Htf0aj;0yq1qrwye,r l( r d64hz).
(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 emikng)e.vr l8fij6rs gnw*l0n 9+e3b *its middle C (262 Hz) when the temperat 8+b93 n)nife6g*ekvg nwlisrr .l*0jure 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 k5ka,lm4r 2p y$^{\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 ijrua(j +f(wvb36c)o 8 4wgua12–10 should the hole be that must be uncovered to play D above middle C at 294 Hzr( ugib(jo+36awu48f vac)w j?    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, 44quoy:leh7. )sz:up; f 0 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why ths e.h:lzopq7uu) ;f:y is 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 twod* ah-jjn me( qmjo+a/j6.a:p successive harmonics of frequencies 275 Hz and/ aj(ajo .pqm+ -e:nhjjm6*a d 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 .g;-tr hq ttjf1ys *:k$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within thez ql5b25z -cv : 6m7czp(h7apotcom /p audible range for a 2.14-m-long organ pipeac p c27hmzv7pcz(:65om bp-q 5ot/z l at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long.1ci,61 vljce17 zvaof 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 r1coz1 v6 j c,7fiv1ealelationship 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 tryin j.3j zv3(pnhcgh9 )hgg to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other strinc (z33).hhng9vgh jjp g? ±    Hz

  What is the beat frequency if middle C (262 Hz)h sr5a5(ylwi 4 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 (brand4: h4h j qtgi,ru-ms)a X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simur4 ha mg)-isuthq j:4,ltaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4oo yf8nf ey)(8npf sd)7z2n.j beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. Whatsjzfnf)7. ) o8( o8pdneyf yn2 is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one hd/-uaa65 idl string is then decreased by 2.0%. What will be the beat frequency ud a-h/65daliheard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical / 4c.r;m9ny 9yrb fmpgflutes each try to play middle C (262 Hz), but one is at 5.0°C and the other4r /;npm.9f my yrgc9b at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, txrh1q(c7 ovk co9:q 2A, 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 possible when A and C are soun: 2vr(xq1c9cqhtok 7 oded 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 stan qzk*d)t vsxk,g xz4.57ygh+dds 3.00 m from one speaker and 3.50 m fkd*k. 5qhvyz+ dtx4)g xzsg,7rom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vib86.iwjor cie)x;cpt8 rating 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 8ecw6 )jitr.o8;ixc pHz, 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 wavelengths 2.64 m and 2.76 m in air. How max;v4s/tm yt8 ,ry7:jivc+ju0rp ybx*ny beats per second will be heard? (Assuxru4*s r0: xvby+vt8 / yi,pjcy tj;7mme T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequefxm9k+c;kcaa14.5 d9u)kj gayp ;uov ncy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you mud41kcy+af;)5 v.a c9pja9kguxo ; kdetect 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 you detect if a fire engine w.: ekxr..hndz4 nf6o2 8;krlxn6phmthose siren emits at 1550 Hz movf.pt4 nh2mdrkhn.z 66 e .xxl;ko:r8 nes at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freqm za3h1kkj7(js lzg /i0;pnw 9uency if a 2000-Hz source is moving toward you at 15 m/s versus you moving towar 0wzg1 3knz k 9/las7(mph;ijjd it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When onezy)sh: *4hw: zg7yzcsxryi0n bk *x/3 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.0 i z nzr:yxyxw)s4/h z7bykhc*s3g: * What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soun 52(wtqpyej 5 va68;wffujvoxz- 6k+ad waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s Wh;wyv qf-jwup6o(8exajf5ta+v2k 65zat is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies,s(:opa3lt9 hy i111s r hey0qu8 z3teu the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear iny 1it:o q rte sza91yhl8puuh3e(10 s3 the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dok,2rfm:ypl1 be4w +cmppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the samelr 1wem ,m4f:kbpc2y+ 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 ultrkd b9 ;-pt18ey3,1bz tqzaefjasound 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 frequentb9qzte;kdb3jfp,1e a8 1yz- cy if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of freqnmrv8 aknb3 :(8rb;ul wn5k8a uency $2.25 \times10^{ 6}$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 b35nvovhy en*dmk:.1 2 uac/wsound of frequency 570 Hz. When the wind velocity is 12 m/sy3uo h. mbnv5 : cw1na/edkv2* from 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 0 gvncla zuwp17y317don 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 2.3tbv 6cr63ke 4tm +xg-r where the speed of sound is 310 m/s (a) What is the anglevr 43tgr xbe6k mt+c6- the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed c ,oh fh 5x:x7mkt65bva1i oa/of sound is only about 35 aof5 , ao7 xbix16/kh5 c:thvmm/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 ojok( ri8*etj6bzp -b8 cean. Determine the shock wave angle it producj *itrko( e6b p8-b8jzes
(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 ehh-* sz:8pj h$/theta$ 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 my7g,v4tvc9). nb3zfznqkj u 7hj )a5 flying fa9k.g,3y7j f tzuh5za7mb)qc n jnv)4vster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See 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 downwardyi:a f3fozbc2r*9r4e from the bottom of the boat, and then detects echoes. If the maximum e :4r*oryfia c93bfz2depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves sh.: ir,sn /y.af.siiare there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sew3k (xcwl4w-g 1epwrbymiw8 63ba + 1xfer pipe symphony. It consists of many plastic f(-x pw8bx1abye46 wg+ w ck1l3imwr3 pipes 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 5.4vlo .592dpk8 uc d9u ruy.qsg3uw2 co0 m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound levrvlw..ypu 9uuc3 godudk5q2s 942 oc8 el of 1000 such mosquitoes?    dB

  What is the resultant sounavz /.45 0 p(*bjfy m-cwoojvpd level when an 82-dB sound and an 87-dB sound are heard svjmo w0 .c/ jyoavfpp(4b* -z5imultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 m4hyk. ss r2faw0k0 3jdB. What is the acoustic power output (W) of the speaker, assuming it radiates eq s 0m k4a.r0s3kh2wfjyually in all directions?    W

  A stereo amplifier is rated at 150 W outpu4+o4hi::t bsd n5hyhot at 1000 Hz. The power output drops by 1ntoyh:4h db5si o4: h+0 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typipitit /vm iu7t: *v3fv..h6 mvcally wear protective 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. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine? m t*u37 v :tv.iivp/ tvhifm.6   W

  In audio and communications systems, the gain-skkqgw 56j* *0r 6-zrzyvor mkdq/ o,, $\beta$ 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 tunedqa ((8/btzt ,5wvz h f5:la+adk,bvyj 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 po.zj0gfg va,;he 7v( nxints with a fundamental frequency of 440 Hz and a mass per unit v0j f; exgvn7ga.z h,(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 vibra+ca.y7 nga )1bw(zueftion 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 andac7)zn.f1 gua+bwy (e 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 tubes jxhb .b7x80v that is open at one end and alsbb7xvs .h0jx8o 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 resonafw ,pax6y,/ 4arxm3aute 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 50oja,opdp 3 /:flrusmd7:9zfl*:g cl+0–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person m:pl+,fpado*f:l3zg /:mjr cul7sd9 ooves 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. One train is stationary. The conductorav l9* ymwc,cb1y e42a on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the ,*vy9ebc41l ay2 a cmwspeed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yopqqj(;1pr/:e2zcg sb u is 538 Hz. After it passes you, its frequency is measured as 486 Hz. Ho; jzpcre2pb1q/s:(q gw fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can 2/jpu8 +axcwcq sye/ 5* ex8fgestimate the speed of cars just by listening to the difference in pitch of the engine noise/q2awc*esx c5 uje /y8xgpf8+ between 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 together;urlwoy4d02+ jfvm a8, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long ijd+lv2um;4owyf a8r 0 s the other?    m

Two loudspeakers are at oph 86+vt*tgcqm(7*qnu3ua heq ;)f vfmposite ends of a railroad car as it moves past a stationary obs 3mt8(6 qv*t uqh+ nmu7)cvfhf;ga*qe erver 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 aorta.wj3v4e6 w sw5 j.b4 t4ey h1do.lvkw1 fn6fuf is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that t j43vwsnlt6of4 5 hb4 .ky1fjw.61ed vfwu.ewhe waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a / 9;.kk3p9s opko y 6yqonks/fmoth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 k f9o y36/o kq;ykk9.npop/sksHz. 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 fr3y.co g0:ifzf equency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp isg 3cyifo0.:zf emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one , tf9lh+dvf7u,pva doqm;:iv : 6n(vcAlpine 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 h( v u96,nct:m7+ dl pvav qdvffoi,;: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 ster(2 kawyjx7u9 g2qldm a 27a;rzeo listening can be compromised by the presence of standinw(jmaq7y2ku;lr297d g2za x ag waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calleplb 1)./nop lld “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. Theop lb.1n )/pll rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human evi4y0gei.4e5 uu,bdh4 h aitb4ln:l* ar at a frequency of about 1000 Hutbnh 4*4i0gy.dvi45e,hl4ablui e: z 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 h5c7m agbg6 o,1s6scx fears the sonic boom 1.5 min after the plane passes directly oc,fg5xc6 ssa176 g mboverhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboaqhmbw fbv-lri ,jq*7v7j:8v6 (jc2 dtt is 15 $^{\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