What is the evidence o/d izcucozul;t )8ke 8b)r64 that sound travels as a wave?

What is the evidence that sound 1dscq*wjn94x is a form of energy?

Children sometimes play with a hor*/ c2b/0aoiy g6u bxwmemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stre*ayugiw/xo2 b b/6cr 0tched 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 the other.

When a sound wave passes from air into water, do you expect the frequency or 8h.p+axz/ gnhwavelength to chhng/8 azhx+p.ange?

What evidence can you give that the speed of sound in aio uyb/9zlw o.5r does not depend significantly oool9yw5/b z .un frequency?

The voice of a person who has inhaled i6(/xd82 gu.xnuvzztc.7x j c helium sounds very high-pitched. Why?

How will the air temperature in a room affect thu r;qv3jbx. 4ye pitch of organ pipes?

Explain how a tube mih(p8 8owgercbnl32 ij p(q+ 7lght be used as a filter to reduce the amplitude of sounds in various frequ ll2 oq (bcpj+3h87pngi8r(weency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 120 hro 0a.vp3an.uxox2 –30) spaced closer together as you move up the fingerboard toward th o r32xp ..naoh0avu0xe bridge?

A noisy truck approaches you from behind a p o .7njt ldqg; -uiya (q24osi;2ogx8building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound 2o4n8 7 ;iulo agq-og;.qps2xiyj(d tis suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to bz1ufsuv;ho/// m ia, n:orag(e due to “interference in space,” whereas beats can be said to be due to “interference in time.” Ex/gfn1/a i hzso u a/u,;:(omrvplain.

In Fig. 12–16, if the frequenw0del 2ey9qo:cy of the speakers were lowered, would the points D and C (where e2l q9:wd0yoedestructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work- o5hr l4o*koh in areas with very high noise levels have ro*lh5-ohok4consisted 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. 12–31. Each wave can be thought of a)pj hx 9i5m8jlts -cxb*jaq:,s a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), ajla-9i)m pjtj,x q5c:8hxs * bre the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mouqjy *k ns.i3zwe.; - v-c6xah:hy* ssve in the same direction, with the sxvawn*y u .3ecqjs 6y.zh-:i; h*-k ssame velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard b;bh o q(dpgr;;y a person at rest with respech;dgqr pb(;; ot to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a /q ni:7xlf1 j yvj5q3eswing. 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 frequencq:ex ifv n5731jq y/jly for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of 7 8,):x 6xlusa jt an6l9s ,wkamao.lda lake by listening for the echo of her shout reflected by a cliff at the far end oa9o) l :x7lsdal,68u njaw,6m .kaxtsf 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 k h6 agzhg6qq an,3y9)waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater3q9g6,ag h nhzqa )ky6 is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng;g::lt u )kwzdxg,b1i7t2k lrths 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 drifgh6.ss .6v dj2) eotziting just above a school 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 elapssszh 62i.jvo.dg)t6 e es 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 splaskjchf2ish81u 4) 7je ah it makes when striking the water below is jcj sf) 8ha uhi24e7k1heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the groundl3:xiz+ :dbii-5py ks, 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 k+ iy:lz idx:bi3s5 p-they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent entx)ec t24/ t zjbv.)srror made over one mile of distance by the “5-second rule” for estimat2bct)v.n jt4s)x /zteing the distance 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 xax5b i9 hal82q0 xk*zat 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 b+pyu p8x)fu s2nb)fp26li9jintensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produc : nuafs+u tx)cu6su,k7asa0 ar1s*t 9e a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one iss ukt t9axf7a , 1a60unuu*:) ascr+ss exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane w xu 2pvqtl9ud(s0qe9 1ith four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience iqtd92lx vse9u(pu 0q1f the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is :as,o5d/ znnbsaid to have a signal-to-noise ratio of 58 dB, whereas for a CD plays5d:n b ,o/nazer 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 from a person speaking in normal conveids+s+kepirf 3 + h(9qrsation. Use Table 12–2. Assume kifis9ed +( hpr+s+3qthe sound spreads roughly 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 strikes an eardrum whose ar a(i;82 gfr)mlxc)uuq ea 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 meje p89- e(djwodest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudsp(e8pew jdj9e-eaker 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 metera jmh.5:vm3xt registered 130 dB when placed 2.8 m in front of a loudspeaker on the 5mx.h: j 3vamtstage.
(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 differenc d,ktpp9ad(o 1v2k5hge in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds wh95 ,dakd1opph(k2gtv ose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wili7f6dl2 8(gvh7j, isb1e xzxtl the intensity ij(,liitvx2f1sgxz7bh 8 d6 7 encrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitude1 3tt1sl7vhk-rc)rnr s, but one has twice the frequency of the other. What is shr1n1tv kl7tr) cr-3the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wavecdh*npl,e*9 k3 qs r)h in air that corresponds to a displacement amplitude of vibrating adq*9p ,hhc n)r3lesk*ir molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound leqy;b a gcg1q 3 t.nud63pz.e+svel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) dp ca3q.gtsb n+u.e z1y3g; 6q   dB

What are the lowest and highest frequencies that an ear can ;j.n6kb cka0idetect when the sound level is 30 dB? (See Fibc.ij;nk a06kg. 12–6.)

  Your auditory system can accomqqvg6an7rg3wf9 . rgb k7,l.m modate a huge range of sound levels. What is the ratio 93qlqv grw7f. b6,.ng7mkg ra 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 has a fundamental frequency of 44ont8z2bq8dd 3.s p*rz0 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0o nd8z.zr3s p*8qt2 db.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the cuztus r0,vzi,,1i a* fundamental and first three audible overtones if the pipe is i v,zz c0, 1su,tauir*
(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 fre1c,ee a,ezev ,quency would you expect from blowing across the top of an empa1ze ,, ceev,ety soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning ty/)amh ./e) zv;eppbt he range of human hearing (20 Hz to 20 kHz), whatbe/pe/yzmv ;h .t ))ap would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. e8,4m aoa*cndWhat will be its fundamental frequency if it is fingered at a 8c an ma4,deo*length of only 60% of its original length?   Hz

  An unfingered guitar string is 0 c8az49pqpu )9eom+ts.73 m long and is tuned to play E above middle C (3 +eca8q9ous) ppm9z4t30 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 middltz9 mroc y2vh(ik;d5 :/eup /fe C (262 Hz) when 5vfty2(ohueiz/r d; p 9k /c:mthe temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 gj0iz6 d77k;7b..thpue ztp g$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in E, 6 ;qxl-gui/irg7oeqnp7/ek xample 12–10 should the hole be that must be uncovlx 7en-qo 6 gi,/igr/7ep;qukered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can reso)km ft++lya 0odw).cnd4g )nbnate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closedo4 f)c0)+.lbmd agkyt+)dwnn 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 po*;8 gb3yx8 i9 d trq+pvtoq9at both ends. It resonates at two successive harmoni9 t*p p 8g+v yx9q3i8ordq;btocs 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 9ck:e;3h w s* rhh3drz$^{\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 th r7s-h4 8v7w9xyzuy ufe audible range for a 2.14-m-long organ pipe at 20 r-u wsuf7879 xvzhy4y$^{\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 outside84,uj2s7kz mr hdlok0 and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the z0d ro 74 kks2hujm8,lear 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 adjzg8qsoyb42umse 6-a -ust two strings, one of which is sqba2gu mez8-s- 6 o4ysounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat fre bcfb;148gurd9j- gdiv);askquency 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 kHz, while another (brand X) opg4ifg7 wqlv y3) 2-qv7ozheb.erates at an unknown frequency. If neither whistle can be heard by humans when playegiy7l 3qzqf42w7)v- gb oh v.ed 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 sounded wizbhe4t idsx ti7dy1 ;40tu2u*th a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning ftibz2 *eyu 0sx1tdt4dh4u ; 7iork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequencadc4f /t: goo+0yknx 1y, 294 Hz. The tension in one string is then decreased by 2.0%. What wig od:4ykto1+x n f0/acll be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to pwcw8 * erus( cji0a52flay middle C (262 Hz), but one is at 5.0°C and thefaue w8( rc2s *5jwci0 other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; gor.o,j*v 9 o(,c-bkrkda odr)5-eoxdta i58 when A and B are sounded together, a beat frequency of 3 Hz is5r(r kdb-,)oce oo5,kd- r ax.o atig8* dvj9o 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 together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one s 9v7m3tsfnz7b)9j44 vx lixtl peaker and 3.50 m from the other9z74 fi74 vtl9s3bmtlx) jnvx .
(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 ip6z/wgq0j7oiof lm0g *t:( s 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, zo0gmwsg/7:*op6( ij tq fl0iwhat 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 ulsz94 u)2xrynot)c( and 2.76 m in air. How many beats per second will be hlz)t42crn( ou9s )uyxeard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sirencjecim+ c2)c smxc,6 u::nmr4 is 1550 Hz when at rest. What frei )c :6emxr+2su nc,ccj:m4mcquency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sire7bcqx- jw81ar cix4p .n emits at 1550 Hz moves at a speed of 3pw.xb7-r4 qcj a8ix c12 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000hdgw (bc l-g47b1e.np-Hz source is moving toward you at 15 m/s vers 1d.c b-lw pnge4b7(ghus you moving toward 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 lk3-2jairb z 1givr/6iy)6 k ysingle 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 frequency the horns emit? Assume T = 2 z l6/)r6rkav-i 1ygkjb23iyi0 $^{\circ} $C    Hz

  A bat at rest sends +v u (ipgz))gbout ultrasonic sound waves at 50.0 kHz and receives them returned from an o v+ bi))gu(gpzbject moving 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 flies, the bat emits an gif9tmzb+1x16j n c8yultrasonic i6jm+8t1gy9xb 1cf zn sound 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 moving flan5++ahkly,oh wl( ) apl +t+trt 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 +tlhp)(,lh+5o w a+nyt+kr a lapproached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wavk8gr+: fqti)oor ir 1sk g;k)9es to measure blood-flow speeds. Suppose the device emits s 1kf;q9 gk)r) sgtirko+i:ro8ound 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 directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves o6g f/-nlf41 -wyrdsfdf frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When ttvxzdi: 5f 3n+he wind velocity is 12 m/s from the nortx53 : nvfdz+ith, 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 ita+kr)sy0 djfc0s3kirzvoba8 k (,+ ,gs speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where t9d y,p,m (m o:ue8vo )akf+tcmhe speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mom9u,)t:ov p+(yc,ea m kofmd8 tion?    $^{\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 tu155fweahh wl*j; l /d8hsij +hin atmosphere of a planet where the speed of sound is only about 35 m/w lwa5dsl;uh+1/fj*e h hi58js
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave anp t;(lwq0 z/6jyg-vaby ef8m-gle it producefev w0/;ztyg6pq lj m (aby-8-s
(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 wxjaxbal 0 m)o17rc29$/theta$ 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.kesqi+jax 978if7b 0j 5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 kmia b9s07jf+x8k 7qjei. 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 sends1lpk4bdr:,wu wdj.4m 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for whb:4l d pkwm1w,j4rud.ich it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the3fknyzo9 12fe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dis,glaba/yv / 9b ;b6ckxxb*g p(play called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open opabb bva6;lx y,b k*c/g gx(/9n 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 of hu+ch 2m0 )rj fdbj,)xndman hearing (0 dB). What will be the sound level of 1000 such mosquitoes?xrjdbjc+d)hf 20, nm)    dB

  What is the resultant sound level whfq tu;i;r5d3bf7j3 hqen an 82-dB sound and an 87-dB sound are heard rtqh3 fujb53 f;7iq d;simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opeiiz,tr6gg(ta n88 4tmn, is 105 dB. What is the acoustic power output (W) of maii8z t4n6 grtg,( t8the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 H l u,gijcdr733z. The power output drops by 10 dB at 15 kHz. What is the power output in watu r,jg c7ld3i3ts at 15 kHz?    dB

  Workers around jet aircr66ax cu0: nq +yt7dhfl:hyexo+rt ;b ,aft typically wear protective devices over their ears. Assume that the sound level of a jet airp ht760: untx dlbeyxry :hc,+ao; q6f+lane 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?    W

  In audio and communications systems, the ga7ut ehsr+il skss-*k8oy v/8 :in, $\beta$ 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 tuned8 b+obw..lebr +6ox*q sl f7ok 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 lonq85nj tclgd+ip8jw 6sa 8d 7;wg between fixed points with a fundamental frequency of 440 Hz a7+dsc nt6 8lagwp5qd w8ji;8jnd 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 abji +reftyj.;e/s kuus2 3s,c4ove 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 fk2sr+t3,.su ecsjfjye4 i/u;ork 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 ma,wm bj; tb5wk5n o(w7 qm ctuxed59:;bss 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension shouldq,mj d5b exo5(w:ub b57tmwwk;9 nt; c 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 yd hi:p.0)hn coas(xb 1x tf*2to resonate 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 rang. s 3k xmaqid,lckhx ws48;8w8e 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 ml 8i3xcw . d,qhk4wx; sksa88minimal 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 3f ipaw4s+ )a :ut1ddvtrain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving t3add)pts1f +ua4ivw :rain?   m/s

  The frequency of a steam train whistle as it approaches you is 538 uv 0+ v9osp2/gn: +5llbxd2 , xmgdiolHz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocitygl2ob d d+u0,mxi5: vplxsv+l/g9n2o )?    m/s

  At a race track, you can estimate the f)c ,3/ tt 9:/ska1alx2hu kv*lhh*p r zauf9dspeed 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 the straizda*cth//fhtv*r93k,u 2 ls)9a 1u ax h k:fplghtaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, prod gg5v;d fmr*l+2oic d lfpqa10bz-/o5uce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is tham;0cl +pvf/zfdb5*l12do5r gi qg-o e other?    m

Two loudspeakers are at opposite ends ofn7tl .;l.bckh*i;u 5phhp7gt 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 freqtnhgplh hbplku .; i7.57tc*;uencies 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 is n1ciwodeiw;fceh,m. * 5tl/+pormally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflect5+hdce; e1wcilipf/,.tw mo*ed 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 spe:m7 gpl 1+bhgfmlb.tp95z9a ded 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 kHz. What is the frequency of the wave detected by thelg t9+dbbam9p:mh 7lf 5g.pz1 bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth.-yy aw hbs0l;brl3: jk(j,cl3 k2w 5km 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 cryc lj2ysbk;w: 0jb3- a5 w3hklm,lk(hirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send si3-z 0qt 3w;iit j(pnfmhs./imgnals 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 atzptm 3ins./iwj;f 0- q3m(h i way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening ca)esk, k 3ddi8in be compromised by the presence of standing ids)83ke ,kd iwaves, 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, called “singing rf k838vmud:hb+sjwp7svg-vg9 )hgb -ods,” 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 prgm-sj gbv vv88s)buhhg 3d wk-9f+p :7actice, 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 t*55f9j*w6t7e avq ub qnnv*w 8 dgos5ahe human ear at a frequency of about 1b 8q dn6*evfatvn5wa*s* 579wo5qju g000 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 hears the sonic boo b9avzbuj.x:5 m 1.5 min v5. 9auxjb:z bafter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is . ins-)opa )qq15 $^{\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