What is the evidence that sound travels asn1u1o ; or.bvs a wave?

What is the evidence that soundb c90v. yrjb68jew,g a is a form of energy?

Children sometimes play with a krn,tz c34* qe kz0x,rhomemade “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 kxcke*,r,0zzq4 ntr 3(Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into wate5wfx9 6gd adr/r, do you expect the frequency or wavelength t/a59 6wgrdxdf o change?

What evidence can you give that the speed of soundnrmz +xrg jj5o4i40c * in air does not depend significantly4*gciomr40 jj z5rn+x on frequency?

The voice of a person who h*vb-x2eilrczf dn5 0 /as inhaled helium sounds very high-pitched. Why?

How will the air temperatur7u ay ees5pf/:e in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the aus+bb 3.u eaney w38)zmplitude of sounds in various frequency ranges. (An exa.esn)38e3u uwbyb a +zmple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as yoe2sp gh;,p-bru move up the fin;-sg r bphp2,egerboard toward the bridge?

A noisy truck approaches youjf0w c 3ev0u0)hqec l) from behind a building. 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 noise. Explain. [Hin 0qu0 j)wflc hee03cv)t: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference it6co 0()s-vypmq+g wcn space,” whereas beats can be said to be due tco s 06ypvq( wmc)+t-go “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were low q*ible2nv. a-ered, would the points D and C (where destructive and consteb-2 . *iqnlavructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with 8m7g)l .q8fguhf/yd a +3oe lavery 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,/ hd .ugef8llg q83f 7moay+a) 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. E sck (/3j5 hw39pido,e u9arffach wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in /9ohdp9ca r,j uw f(e fis53k3Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directy q0f4enl)aa:ion, with the same yeaf q: )0nl4avelocity? Explain.

If a wind is blowing, will this alter the frequency o ,3k;mec3qp ; w1nwmlhf the sound heard by a person at rest with respect to the source? Is the wavelength or velolwm3p3wnhc ,k;1em ;qcity changed?

Figure 12–32 shows various positions of al5*4j8o/q nn2zescj 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 whistle2 lz*5 ejnq48s/anojc ? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echorg)g-e*aoud3 .dqx w+(c9 y eknvo2y7 of her shout reflected by a cl9ndvuo*(e yy)a3gx-ow dg2q+c .rek7iff 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 waterline. *0p z-0x gzpm/hv3tvyHe hears the echo of the sound reflected from0-vx*3tpm v/0zh zpyg 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 at 20s9rq5na q i g84cg6w8s $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggnc hp-,j r75t6ejz9;bw pvk/d y day. Without warnie7c6p/dvr;5-n,zh ptj9 bwk jng, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes w:mjff 9zv jfwqw:; h57hen striking the water below is heard 3.5 s later. How high is the cliff? fmf:w5j;z qv9hw:7fj    m

  A person, with his ear to the ground, sees a huge stone strike the concrete p k/dyr7 xqw4*7tngb i2avement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impactqxktb7r*yg w d 742i/n occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-secon 73 ib:lg*k:b g;msjdnd rule” for estimating the distance fgm7 n:d:bsj i;k*b 3lgrom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the painrzd 1tin0u g;8 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 so (*j5u/ axk8thfn3.m/ bienkaund whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a.3/6r szq,,miirih z lm8rn1l sound level of 95 dB when fired simultaneously at a certainr izs mm/ qz,r6l1.hiinr,l83 place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain 8.3 4 ctlh(r5j r;ubibt kon,ydistance 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 okt( 48. n ;lirt3urbbhc ,j5ybut one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-v iaco)v0m/0r: 0qhn8r;th mdto-noise ratio of 58 dB, whereas for ah/8 v0t;qm ch0)i:dvma0 orn r CD 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 soundn yqo+wwm-2 )y from a person speaking in normal conversation. Use Table 2wmywoy)qn+ - 12–2. Assume the 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 eardrzmr oa29g.g ap:-,l l/ fr:aw-q ekc9sum 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 modest amplirpaly656 -o1 vx xk/r4k vfcw5fier B is rated at 40 W. (a) Estimate tv5p vyl1car6fr5ok/k 6x4 x-whe sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 d*e e46m2n-r(sprlj mjf;9f ,g0tlojph 7y b5eB when placed 2.8 m in front of a l;4nmjl 59p6 2msogjl rffeeb(jtr7pe,* 0h-youdspeaker 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 typic5 ,mtxgrha( jz/*4eaf8 aml2h ally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitemh 5/a*mr l axz,8j( hfa2g4tudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wh-b,n8;skgv6szbu mv8 at factor will the intensity incrvv mug nszk8-8b 6b;,sease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacementz v /sz::bl0gp amplitudes, but one has twice the frequency of th:/p zvb0z:glse other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a ;qy45muwv )v/, ormkr h0slc+sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hvr 4)w;rhc/y 0u+kms ,qm vlo5z?    dB

  A 6000-Hz tone must have what sound 06tj hm89yc6o.zf zu f j+m-bulevel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 18jyotubj m.669zmz f u+0-fhc2–6.)    dB

What are the lowest and highest freq v3z j ;4bw7jl(j e.q9h69kxfvaj+f3g ar( rlguencies that an ear can detect when the sound level is 30 dB (vljlj+fj9w x9(.4bkjeq ;37argz6av3 gf hr ? (See Fig. 12–6.)

  Your auditory system can accommodatm6jl dln;z z3+xtib( ,l cp.h+ )n0hbge a huge range of sound levels. What is the ratio of highest to lowest d,l 6;xmt+3lbz) njli( 0 nhhp .gz+bcintensity 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 fre fu+wet)uaz 1 k+fs qd*m:xmfa) 4:i(a(:nd ziquency of 440 Hz. The length of the vibrating portion is 32 cm, and it ha +az*dit)xf z (wm )(qffmdsak i:na: 14eu+u:s a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundex/ 7.k;b ketxsv+xz0 amental and first three audible overto.eb+/xks0k;tv exz7x nes 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 yosxkhby* zo 17mg )b7-eu expect from blowing across the top of an empty soda bottle that is 18 kb by7 o*xem7gz 1hs-)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 o70q 27umjh g-ztkdgd(rgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 ktd07hmg7 2gq d(jzuk-Hz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its t54uu w07sjerle)cen q yr3.4hhird harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original5ywh7u lju0 e)n rers3c44qe. length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abov/s wx/(dsxmy /y a8l3ae middle C (330 Hz).xdlm w8/y( //aayxss3
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (cr,illl g73 n+2/au li262 Hz) when the temperature is 2lilan7 gl ri,32 +ulc/1 $^{\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 2:8qtdrt/ /2q)ibhayk0t:v 92c weu ru0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shoulof1liz, s;b1-m 9 nsgud the hole be that must be uncovered to play D above ob 1i,uzm;f -slngs1 9middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616i,m4e) ykzyt/ Hz, but not at any other frequencies in between. (a) Show why this is an opy4/mzi), kyt een 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 endsrhhn 1c(9y+tor 5dt2 t. It resonates at two successive ht5(1trytr29 ohch+ nd armonics 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 1ns)w* z( lxdfdo7vp+$^{\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 /o3 )u+swzpr clw fq15present within the audible range for a 2.14-m-long organ pipe at 3)s1o5fu/pcwl zwq+r 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is lumf5/db 3x nx,z4b 5mapproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequenc 5z/mnb3f5um,4x l xbdies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two stre 4xx 1tr;mw(am) eu0rings, one of which is sounding 440 Hz. How far off in frexar41w)xe u0mmt(e r ;quency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) 8 9 hg l1rem-k r-oou.gfp:tlv6 nqf5)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 (brandcy swwg,:1tf ei+b 41t/zx)pr X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a +:, 4wsb)cyz tr/ptifw1ge1x 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 with a 3n6+/rtc j wgm:,ug 2ax50-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is :+utg6xrgm w 2,a/n jcthe vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension z8t rn i kam/v.hq 5u 8,inmk-959r yvqo6a4xain one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 1qa5inikzk 8mv4ax9nuyvt a5 m-. ,9 /q6h r8ro1–13.]    Hz

  How many beats will be heard if/ezzo8g pz 56o two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other 5pe zgz8o/6ozat 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a b0sk,hmeau o9 )+kyt6frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is )y6o,mb +sh9e at0kukheard. 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 speaker and cw5gr443e-ni eg.jd tgi 4em 83.50 geg-5e43m niiejw4tcr.d4g 8 m 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,nl9d.cy+uf) dw)v4 rq /g 7obk but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequencyrw b+7/yn qlfu. d)kg)do4vc9 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. H(3t tuj /4npy*qov;r s4bzah6 ow many beats per second will be hearnv;*/zt 6puja4y(h 4st r3oq bd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fiwx)v,z6 q,1wt0 vbrumre engine’s siren is 1550 Hz when at rest. What frequency do you detecq,v6v ,1ut xr0wwmzb )t 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 is d(rs0e*8 eupf a fire engine whose siren emits at 1550 Hz moves at a 8es r*p s(u0despeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frenioe 8jt6 *hd3quency if a 2000-Hz source is moving toward you at 15 t 8nj*die oh36m/s versus 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 sayu: n jc.2r,ntme single frequency horn. When one is at rest and the other is moving toward the first at :jynt.u cn2,r 15 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 ultrasonic sound waves at 50.0 kHz and buc(c5+m tfw; 6qhxy; receives them returned from an objectut wmbxy;+qc5 f(6;hc 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/upwip5vx l-8* s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in thei5p* wxuv- l8p reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flatz; 2emv2m..fqk cobc3 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 hearo.2qcc3e .k mvbf zm;2d if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to m0:- (ksh,q vvd3oxaj2 ml ;lgyeasure blood-flow speeds. Suppose the device emit;(3qxjlg vhd ,m:l-s0 v yok2as sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultras 2xl5flby t44donic 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 emits sound of frequency 570 Hz. When the wind velocb;2c e6n jc czdg1uf3p,eqx.+ity is 12 m/s from theegxb . ,z2fjq3 ;cc+d nuc6e1p 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 atbd4m au2j ))fcww(p) jmn 6gc au2s;:xf+cus* 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 the speed of soun;t )x*,3 tqe ns vtobkt9u-:bad is 310 m/s (a) What is the angle the shock wave makes with t9v,k t)t atbo3buen*-;xqts : he 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 ata: s lfs 45/b.yb d3cwen:mry4.lk7a planet where the speed of sound is only about 35 m/s: s 7lwkrmby afn.3e4:bt5d4yc s/.al
(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/s9r88 t8h 9w4r )x 1aipiowcfogi;vkw/e, o3 uu strikes the ocean. Determine the shock wave angle it r1488 )wo9hcw/p;ukfexogarvi3t uw9,i8o iproduces
(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 )9*mezg-75aorf yvxh$/theta$ 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 grodhf6wuog+y *ju)5sc b(; 3o ( (mykfhvund flying faster than the speed of sound. By the time you hear the sonic b 3hgud f (c;*hb6k)ow5su(vy+o yjm(foom, 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 k whtk29 ssb05x uinm;2a,w,xthat 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 tith20 5ksxm, u;aw9n,i bxs2wkme between pulses (in fresh water)?    s

  Approximately how many octaves sa7;8jg+x olg are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Itvdstgvv z3h:1i:t*vp 40ou9y consists of many p vh :*o0gpdv vs9vtit43uz1:y lastic 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 5.0jxmer(q b5-e*y6m f-b m from a person makes a sound close to the threshold of human hearing (0 dB). What w (m5efe -ybq* mx-j6brill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 8,voxv8w i ,v1up xku*37-dB sound are heard simultaukw 3x1ux,,v *vpiov8neously?    dB

  The sound level 12.0 m from a4bpwc0s0ht:i loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming i0:pc w4i0shbt t radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pow5jf-.(/u(y uwwwqaegml9w pe s 44ke8o 4den .er output drops by 10 /a458 g(4n kue9eu f4m qy.wlwwosee(wjp -d.dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft t njr4(a:in d3typically 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 radiusj:(a dtnnr3 i4 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 communirl.r;q a. eh-ew(cc k5cations 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 a frequency8o ign+4:4ic5sehaqpz6p mev-.v 3 he*to8cj 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with0uef,;1rctk,xs .jmy a fundamental freq0kf x1c;.y,tmru ,s jeuency of 440 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 verticu39 tyj 1qsx1n qraz00al 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 andu10jx1 nyq0 tqsa9r3z again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar nxqa8uk 3tj,:string of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the tq3njx 8u ,:ktahird harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full look/: zbx p2pu6jcpdc;. p ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming froi +0vftf9q-ljsc w5*lm two sources. The sound is loudest at points equidistant from the two souli*v jqctffl5-s 0+w 9rces. 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 train is stationary. The conductor on the s +smlj .7f0iuitationary train hears a 3.0-Hz beat frequency whenflu+j. m0isi 7 the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afte/bjt p3f 1)kfjdb*9ai r it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)? aj1p kd)t*fbb 3 9/ifj   m/s

  At a race track, you can estimate the speed of cars just by listenirqb/ufp0kj h n7(f yn1pny1q)wv2i81ng to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by1 ffpu ()vnq1k7y2ipnbqw1/8hy j 0n r 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, produce a beat frequency of 11 Hz.,kr1 7piu9spuzx 4r,c The sk4uxirp9,7rs 1zp, c uhorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite endswspxwt34 8x/vown-n. . 7qnlm of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig .wxot7.3 mw48xn nvwl-s npq/. 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 is nolszs+ qeh832u f2tz ;lrmally 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 the waves travel with a su+lqz2t sls8e2;f h z3peed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth lyz2xql t, uxyp-/xl :z2er 63at 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 kHz. What is the fr xlxt2ulq-e 3y/xl2 :6z,r pzyequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moizds m/ji2 l7yul5a yq.qe/i2 k0:qxa)mmz(2th. 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 5l7se2idyk )qaj i/2( m: a/uzq q m0x.yl2zimthe bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once tjj nzb4s+( o(used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep soj4o+sbj (znt(unds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised b (d svxz(:oh/c*u,-q.p oqzvxy the presence of standing 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.uz(d.vx q o- /oc: (,*zpxsvqh
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singihf 5;0lv te+j7hyyri/ng rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a cl+y5/ h;fl7t yi0ehrj vear, 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 ear at ah(nn2t;btb9zi o je+p 3;0 s-brbty +x frequency of ab-+bj;b 2x e90o ;y+tpnzn b(thist3brout 1000 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 th.z d9ow- xtqj.drzv8h/x u9bmmq-.*vez if71e sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitudeijz/x*d rmf9 m8. d1xtqw.qe9oh -7z vu-zvb.?    $ \times10^{4 }$ m

  The wake of a speedboat i9b -wz0o n, rvsv;c;bzs 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