What is the evidence that sound t wc.oklt+ +vc:nzmxk(ki w5/ 5.f,xus ravels as a wave?

What is the evidence that sound is agz/0s7okc: .:eh c qapzp8;zc form of energy?

Children sometimes play with a homemd s z9sw0mc/:eade “telephone” by 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 the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to ths: ws/9 cde0zme other.

When a sound wave passes from air into water, do you exhfg4s pf+h +h;pect the frequency or wavelength to chh;+hs4h p+fgfange?

What evidence can you give that the speed of sound in air does not d:b wo:01d 14iu.oqinrbur yd.q thx+. epend signific .o10 4 .q1o.rtdiyi:u :bx dhbw+nurqantly on frequency?

The voice of a person who has inhaled helium sounds very hi)0esb:aq6 uz jgh-pitched. Why?

How will the air temperature in a room affe5d i *c/ovio+eiejlg 0kq a9//ct the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce thya-v)fzis 58t. w8yxw;km- uwe amplitude of sounds in various frequency ranges. (An example is a car muffla8;-wk if.ums -yzyw)v wx58ter.)

Why are the frets on a gbbw: o:-*(-qdshxrfa+ oqji .uitar (Fig. 12–30) spaced closer together as you move up tahis* +q:-bro:( wbx j o.d-qfhe fingerboard toward the bridge?

A noisy truck approaches you from behind a building.v6 cuka 1*2fav Initially you hear it but cannot see it. When it emerges and you do see it, its vaf1uk2*c6 avsound 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 “interference oxj7,e3mfz0 sh: su p/in space,” whereas beats can be said to be due to “p jx uze,ho f73m:/ss0interference in time.” Explain.

In Fig. 12–16, if the frequm2 2wu7w3iqmcn3 ew y(ency of the speakers were lowered, would the points D and2(y 3imwu encm2 73qww C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas pig7 nqyo4j ,v0;eau/b8dtj 1 with very hin1 d eabguqji 8;j0y,/7to4pvgh 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 ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 1kuu z.bq75ea2f olo+82–31. Each wave can be thought of as a superposition of two sound waves with slightly di kfe+5.728bu oaq zolufferent 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 observer move in the s . 6lzod22qcg*t tu-zyame direction, with the scyugqz d2tt z-2.6 *loame velocity? Explain.

If a wind is blowing, will this alter the frequency of t:r veto;jtr mor/*) ,zhe sound heard by a person at res)r*et;zj /ro, to:mrvt with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various position 1j8z90fpql 4cx:esaqs of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reap:8c91jfxlsqa04 e zqsoning.

  A hiker determines the hui ljk1 znu23l*4 xv4length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shoutiu k31jxn4 i2hlu4lv*z ng. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hea bh( k+hn0+ ,zoya)gsyrs the echo of the sound reflected from the ocean floor directly be sog+(k ya,)hz+ 0nbhylow 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 atjf f, k)e sbk4vf6xx6( 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 su nhk9 rdm+:,odlm9 ru2rt u;4chool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is he:+,mrtrh294ddo lmkn9; u ruu ard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The 1dr q //f tvynj(,vo9nsplash it makes when striking the water below is heard 3.5 s layqnfjor, 9vv(t/n /1dter. How high is the cliff?    m

  A person, with his ear to the grounfjt.z bc*,;fe9e 2tcw d, sees a 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 did9.,e2f z ftecj* bct;w the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5l4wfb7p/n6 s.*ey fjx-second rule” for estimating the distance from a lightning strike if the temly 46x7j /nse.f pw*bfperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pb/i um7,/ *h cm jifh+.f2ghqeain 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 lev(0r2yel;vhood/ i :vp;vea*o g-ah4vel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired-a rukp,e8 )*2umrg db simultaneously at a certain place, what will be the sound level if onlyu8pgb er -)kd* mu2ra, one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplanef r6fzh-1eoi 7 /e3t* q:oieqg with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would tfzo/i qth*e7 ofg e16 :q3i-erhis 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 si e o+3j71tzwuuu yfz3:gnal-to-noise ratio of 58 dB, whereas for a CDyw zjt 1+37ouze3:u fu player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound frmwhc:ys-q f1 d9y1 x,rom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. 1rsymq:fwc 1h9y-x ,d$\approx$    $ \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 0zf.m/syqhd:+ gke9h 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 rt95yy*+chfwj ated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level iw9tyfc*yh +j5 n 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 pl(bks13sluh8( jde: y eaced 2.8 m in front of a loudspeaker on the stasyk dl( 3eb( :eu1j8hsge.
(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 f;dwsjhx (t ofs2.4 l:)yn*xsdB. What is the ratio of the amplitudes of two sounds whose levels differ by this a2ndxsf):ylfo sw s( .;4hxt* jmount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the ing67 j-re wfx3ntensity inc6eg-wrn j3x 7frease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement g;)w t *o6uoxig/ 7qdm5zie+ camplitudes, but one has twice the frequency of the other. What is the z7oq;dux gto m5gec +)/6*iwi ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds too*br)p*mg8mhhnmbx 1ny ; +*r a displmnr*ob p+8h*xmn1);bgmyhr *acement 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 kn:1gzd-94xgfp yke y,x13 zra 100-Hz tone that has a 50-dB sound level? (See Fig. 124kkgf1 ,gxr9 1dez :y yx3-pzn–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the7 8oulkc4c q)u sound level is 30 dB? (See Fig. 12–6.)luou)q8 4 c7kc

  Your auditory system can accommj 15y1ift9u7zn/umc9j7e qqf odate a huge range of sound levels. What is the ratio ofi/7uqe1fn 75jz tc qf1 y9ju9m 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 has a f swv(gmhf(*fy,yzvo 5rq;. 2tundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string bs qw,mz2( .fyv yfv;rh*o5t(ge placed?    N

  An organ pipe is 112 cm long.x4vmbn:3 wh k-wmx9 7s What are the fundamental and first three audible overton3-vx: whk 7xmmsw4 9bnes 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 yo:nv uwemf/sdo+s;/b 0u expect from blowing across the top of an empty soda bottle that is 18 /be / dwf;0 u+smsnv:ocm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning te9+ i 6rsguv5f7fgh;idjaj0 3 97o lcthe range of human hearing (20 Hz tri v9fjhcaj+ 6g e77ts ;l0uo d5fgi93o 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 t.k d6 ,hzkw+5cs9kho a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it zdk9wk kho+sct 65.h,is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 mnmf)dxb q6v 8. long and is tuned to play E above middle C (330 Hz). x6)m8f.nbdvq
(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 r4h w9o e:4m70o bmliymiddle C (262 Hz) when the temperat 4wb79yr ooe40:milhmure 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 2 j0ik4w.joduk48c7 xe0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute inn wjbik4l 2;qvyn,x)(8iw52 4mu iega Example 12–10 should the hole be that must be uncovered to play D above middle C at 2 jm(vxiw825nq ;4ni,e)by2uil awg4 k94 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 fa-,cf-9giwnli7hgkko;:s k, +6ncy Hz, but not at any other frequencsy,l+9n,;c- no7 igffkhki-c akg6w :ies in between. (a) Show 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 reso/+tvy1xq q-f gnates at two successive harmonics of frequencies 275 Hz and 330 g -/tfq yv1+xqHz. 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 *tqca q29*d 1q2 euzga$^{\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 the audible range for a c m d13oi,rk 0oimo 2n9m.6tnj2.14-m-long organ pipe at 2n12 iio ,r c09ko.mmo mnt36dj0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately6qzth o0 )-lrpn+, 0gmsh3cli 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 tl hp0-3l +)sic6, ongm0htrq zhe 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 adjust two strings,oj0ds- q*mus0 one of which is sounding 440 Hz. How far off in frequens0os0j qudm *-cy is the other string? ±    Hz

  What is the beat fre--ix0y e d4wnaquency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHf :l q l;6niv(:y9bmtpz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating fr(q9 mvl;blp6 :tn:y fiequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hx-)oso2 zmbk9z tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the stringokxzs2) o9- bm? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensi w rpfj) kz6jbw/w ti9hi*o2 (/s.ji,pon in one string is then ib.j,hww 9k sr j z)jpof2*pw i/6(/tidecreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard iv z f+bzio9m5:(7():( xstbhgb2zunfrmj9 qmf two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at7 nsb:h j m) t2mmx(z9 r g(z+zo(9bfbf:v5iuq 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forr-vx +ji( e+qv s0q+bw-6w7 a2 razqraks, 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 possible when A and C are sounded togethe va+j7b+6a-qs w wi0x v+rq2errqaz-(r?$f_A$ =    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 speaker geffvg3 e*:u 27e(mbn and 3.50 3u7*e(: bfge nm2 gevfm from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano k pbg8m.vdy4jl 2lxvw9:x3v,tuner hears three beatsmvyd 9 wjk23 lp:8xvlgv.b,x4 every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.7vv a/t+ff4 tsz+ 8 -)n4bje(hxmox t /yv1qs7f6 m in air. How many beats per second will be heard? (Assum qtao(7)msnet vtbv8fx + -+/s yff1hx4/zjv4e T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whekge6, wr0*u mw9 av ;mkrp,y0nn at rest. What frequency do you detect if you mover,p9 gr0m6 ; ay umkw,e*vn0kw 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 yz(zieksyrh3rmh zn;, /ks0s,w6* n s4ou detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m 0r k (h;z,wyz,4sennzi*/smk6h3 s rs/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward yo7a 8bx-b-ui y n-)kwv5gz.r-cjo6z rlu at 15 m/s versus you moving towarz-xn87rgi5 jzrk--o.b vy)b w-alcu6d 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 frequen )v vco-yyua*km ;+:8c4nxncfcy horn. When one is at rest and the other is moving toward the first at )m ck-nv*fcux4:aync +yv;8 o15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonif7 l 1 v7 nj7-qhf- ttb2kkqbh)(jjnd;c sound waves at 50.0 kHz and receives them returned from an object moviv72b h qtt7d)hn f;nb(fl7j- 1-qjjk kng directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flr lxg,abvc/ g84:dfe 9ies, the bat emits an ultrasonic sound wave with freqlg,xfv 8 /ge9:da4rb cuency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimi: x2tj,o(q tgents, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same toxgj2tqt:o (,i ne 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 ultrasound waves to measurew;p7 pah fe2z xi4l (lqs0,i6v 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 aq6x02pep,v;7(ifzhw4 li slarteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using u7i4wm c;rv.wz--l-f64 nolq7dswo-- oak wtt ltrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emi.m 6qiav;zi3i8yc/ b yts sound of frequency 570 Hz. When the wind velocity is 12 i icv;ayy z/i.q8m63bm/s 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 on land if its speed at 20 ,53pprg9)2hng q eod b$^{\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 bjq85 i(h(aqb j h+:sxat Mach 2.3 where the speed of sound is 310 m/s (a) What is ((s 5i+qa8b xj h:bhjqthe angle 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 atmospher(x uu2)w8fdrk0der ws7 md-(hzg7fc2 e of a planet where the speed of sound is zefm( h2du2wxf (d7rd8w7 k-sc)gr 0uonly about 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 83d6i kq.avmd 6500 m/s strikes the ocean. Determine the shock wave angle it produc dakd3.mv 6qi6es
(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 0v- , y;wkmf1nvw5g ic$/theta$ 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 exactl-fxyr6y ec9;yy 1.5 km above the ground flying faster than the speed of soun9 y;6x ercy-fyd. 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 tp.trwasq9 h(w;i 7ax7d2wf x4hat sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (xa qw pr92(7wdt.;hax4 s7i wfin fresh water)?    s

  Approximately how many oct yq-xqv 86z.ayaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonyrnq v3:3zx zz((6*.retxhv xt . It consists of many plastic pipes of z(:xn*etqvx6 hxz( v r3r. tz3various 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 tox)q yt kqz-hc j3kx+a 8l(:xgy+;aoy4 the threshold of human hearing (0 dB). What will be the souny );htk +3qaxqy +a(j-:gxz8ycxklo4 d level of 1000 such mosquitoes?    dB

  What is the resultant 0r-ucb17 z55zzso nly sound level when an 82-dB sound and an 87-dB sound are heard simultaneb 7nzuz sz05 cr5ol1y-ously?    dB

  The sound level 12.0 m fr 8x yn2d85fpl9yc +/slbotak :om a loudspeaker, placed in the open, is 105 dB. What is the acolpyxld5nykf88os :/bat2 c+ 9 ustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W)mqa;rklekh +n 0h70x output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the pow ml0 xhk+7nha;)rk0 eqer output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ovezn h0 6rh9*5ip aiibni92u/ asr 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 intercin6iahz*ahs 29rui np 90 /bi5epted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatl,el9xy tme; guo 1:d7ions systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to tf7w47qj)yhksf5 6y g 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 r:icmxfx mb*54* ;mk opoints with a fundamental frequency of 44mr*4x oi ;m5xbck*fm: 0 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical openewo5j4pcb88v 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 wa8bp ecvwj4o58ter 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 that is opeu f uu*mdc o 6w*af+m-jdf:e:;z m8-yyn at one end and also 75 cm long. How much tension should be in the string if cz*uf emyd6 : :-mmu*uawyo+8-fd;fj 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 resona/4 a(x x-)tyvo7zh sorte 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 ranw8c8s xqt4-b d.,ywolge coming from two sources. The sound is loudest at points equidistant fby8cs 4 8.wod-q, xwtlrom 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 sound?   Hz

  Two trains emit 424-Hz whistles. One t0s.+4-yso ta gkb -8vkzul. unrain is stationary. The conductor on the stationary train hears a 3.0-Hz beat+gy4ukvo nl.ztb-a- s 8ku0.s frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam tra poih mbc1b51fbzw n8-n3 ta w5sht1:/in whistle as it approaches you is 538 Hz. After it passes you, its :b-1fm8it znw1bo5hs p/ tw3an1bch5 frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimax7 ;9sxd* yjv9mepp0 nte 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 certain car drops by a full octave (frequency halved) as it goes by on thee99;s pd07jx* xny mvp straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, p2vaz1y3hkt45l(r zs);ci m6wbv gnh.roduce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How bzmst( 2kc6h3w;nv.4 riy)va5 g h lz1long is the other?    m

Two loudspeakers are at o9n ov3+ad qbx7pposite 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 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 bn 9d3o x7q+avhim, at C?

  If the velocity of blood fljhv kzjr t(+5-ow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-5rjt v( hkj-+zMHz 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 w2h )zsc 5jeu;;6niuuxlh+8 t6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the batz85ucjuh)xhl 6wnius;e t2 + ; after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sounz, /hxlr3 us14qn 2empmmjfq 2 bi71 g)*cgqr0d pulses as it approaches a moth. The pulses are approximately fej2xp0rqbhn z4ismg*3 r2 /cl1)mmg7u qq1, 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 is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vi*.y z7 pwt10z ccqr0vellage 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 frequen01c cr7tq 0vwyz p*.ezcy of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of st6vzota5 j5z.wanding 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 v az.o5 5tjw6zin this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invo8)en wdu j kbj2o.efj5(ux 46vlves 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, loud, ringing sound. ufjoj4 8 (b5w2.6jne xduk)veFor 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 thresholhl mu-*fgt59x;z dte,d of hearing for the human ear at a frequency of about 1000 9lmftdg 5x-hz; t*,eu 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 heard9z9+gd 2arrher+*l r)3vm rv s the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitr+err 2h +mvrlrav9 9dd)g3z*ude?    $ \times10^{4 }$ m

  The wake of a speedboat isg dj+m495r,1ro-nivw8a pyf w 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