What is the evidence th )z +82n mx1m*xysyygxat sound travels as a wave?

What is the evidence that sound is a form5q(gr:6ez 0 uo.v esue of energy?

Children sometimes play with a homemade “telephone” by (xn36om2ft mhx; xs*-xnsm 3gkqh, )gattaching 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 hearmg 3mmsxx26), hxnsxokf (-q; nt3*hgd 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 wav t38ufxy;i fr*q+pdr*elength to ch q8t3xy;d +r* fr*fuipange?

What evidence can you give th4ao9 wch3- uc4 zk:loiat the speed of sound in air does not depend significantly onw oic4azc-9 l :uh4k3o frequency?

The voice of a person who6k mo7gv;z8 ns has inhaled helium sounds very high-pitched. Why?

How will the air temperatup2 yd mg y.u7uri0v9uub)wv:) re in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the;tzt hv) ulhd z*,ue:pr 2k5b4k -gm57 y/qmwl amplitude of sounds in varioue55l;uzt7:b md lzgv)qkyu*4p/ -hthr 2w, mks frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar yfo:b)hlenual-. 7ab8i 3d8(xux( nu (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridge:-n d83eu (7)a.a (nhx8llbboufuyxi ?

A noisy truck approaches you from bma,6+m urooo7n b .k0hehind a building. Initially you hear it but cannot see it. When it emerges a u .mamooh+b6k 7n,o0rnd you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas jc bc,kg(;k9rbeats ckk;(9j,rc g bcan be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of thedjspc w 5de+,4 speakers were lowered, would the points D and C (w dcs+5j 4pdw,ehere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearinrn6xl)gk+xgdo)m+ 3 l g of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sxk l3nm dlgr+gx+o)6) ound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a( 8fvd*mpps 0a superposition of two sound waves with sls dma*p0(fp v8ightly different 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 same diu+gbsv5 rk dfu* iy,bug5)r,h3i6 1sqrection, with the same velocity? Explain.hvkr*busif u g igbq r)+563, s1y,5du

If a wind is blowing, will this alter the frequency of the sv 0qa5 /t3e*oley3ce1e;mp gcound heard by a person at rest with respect to the source? Is the waveleng vme lee/c3*3 yqo;egt51ap0 cth or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swine6jx8o442;ggiixs h a+ f4yc zg. A monitor is blowing a whistlesh6 y44i ox;iga e2jzfgcx+84 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 reasoning.

  A hiker determines the length of a lake by listening for gi1pw( ejb 1tl t(f52wthe echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of th 5g1pt wj( we2b1il(fte lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He lru45zl f2 + din06m-iyk.bn dhears the echo of the smif n-dd+i.bln 654rk zl0u2 yound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air atjsvfyo8 qig; 9f65- fu 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 a/4(zh et/vkht bove 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 elapses before the backfire ist 4kvz h/the(/ 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 when stskw: j9bsh,jsw5v7r xm3s8 c0riking the water below is wrjjs: v3ssxcs9 5 bwh,m80k 7heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strikn nmbd gskly4 7)54dd9e the concrete pavement. A m9 7d lnk4d)m yg54sbndoment 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 impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rulavq qb8f:, 0 hm:;c,xp) fcyane”pya qa:c v;fc,n0fb hx8q:)m, for estimating 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 aywtv d .s,iz5xg5m -ngn) -/uqepa0d( sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity p+la6a6 fcv-l is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneoussoi5xr-ym 5 5bly at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitieybx r-5 sm5oi5s, not dB’s.]    dB

  A person standing a certl2/ovaep -hrxg 4s 8jeto769lw0r ej:ain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, noweo87l2 l h4ve0e /9r:pjt-a oj 6xsgrt dB’s.]    dB

  A cassette player is sa)ef;eapp+ik3r hp +h s+,ljx +id to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitiesk+ras e,i+h pf;+xh)p pjel3+ of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sounu:(qes)1k6/bibpz7 ga fnv 3 od from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly unifo1gz6(: sun 3v fbo7p aieqb)/krmly 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 area isd2urlm52.sp ;l+k bv:nozd6w $5 \times10^{ -5} m^2$ (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 am ,g9i3j(p0d im hccpe( s.p+qtplifier B is rated at 40 W. (a) Estimate the sound level in decibels you p(.ci0mt phqi+( g3sd jpe9,cwould 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 placed 2.8 m in froq2etd :: +ghrqum6y.v .b) soznt of a u g)6:.zv tqh 2:+ys.modreqb loudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically d7iwy*j:vk ) ldetect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose leve lyw*:kdij)v7ls differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wavw/p6ekq 2 0bybe is tripled, (a) by what factor will the intensit2 ybk6q0/pw bey increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplipdchxch .s0;c4 sa)oy4vc4-i tudes, but one has twice the frequency of the other. What is the ratio of their intensities?chcyc-i 0 .s4s4cd;p4oh)axv   

  What would be the sound level (in dB) of a sound wave in air that corresponbcgla1 m4go3/bwp12 lvo qcn4(x 8in)ds to a displace(v 8 )2gxm4aq 1wp34/ib1ng lccoolnbment amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must han,yop63w k2j lve what sound level to seem as loud as a 100-Hz tone that o6k ,p2ywn3lj has a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear cjq+*7ic:ybnyc// bh nan detect when the sound level is 30 dB? (See Fig. 12–6.)c/h:ny b* n7/j+qiycb

  Your auditory system can accomfds q*qr7gltwn*/ /-lmodate a huge range of sound levels. What is the ratio of highest *l tlw*/ fdn/r7qs-qg 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 fp+ qvhq7 l,*4 salaht.s zx9c4undamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and +p4x *all7cq s.49hv,stahq zit has 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 fundamental af2-* siwkt8c bnd first three audible overtones if thecti-2fs8 kb* w pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across th/epjz9)o,g jhhi:v6jd g l(r +e top of an empty sodg9j/jzo)6vjhlihde( : , r+pg a 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 with257tozea ;b yr open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of p; 2tryobz5e 7aipes 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. Whan/ld dnpsa55yh,x )j3t will be its fundamental frequency if it is fingered a5la5n dn / )jyxd3ps,ht a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lo c7ys t n r(kdd2qsm6xbu7*1v0ng and is tuned to play E above middle C (330 dny0kt mu2ssd 7v*xq7r b( 16cHz).
(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 ope gi9bg9qvr :e1n organ pipe that emits middle C (262 Hz) when the teg9b1 qg vr:i9emperature 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 2lnd16a 4pgdt:k,ad2 q0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiecb sn2: zqsfx ;eqc8c):e of the flute in Example 12–10 should the hole be that must be uncovere;ccq:e8q)xfs bn2 sz: d 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 resonate at 264 Hz, 440 Hz, and 616 H(q iz*p +2d 77x.mb -bnokelhfca2 o7qz, but not at any other frequencies in between. (a) Show why thisid(+-p o bxq7ezqbhkomf 27n *l27 c.a 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 :xk ytlja45 9rw3ez3aboth ends. It resonates at two successiv w 5:tyalk439za3erxje harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 r1h -h5t;o bfy$^{\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 wih-sva5qbov 1zs/dh.fe +.*t v thin the audible range for a 2.14-m-long organ pipe at 20h-/*t. sz.obdvqsh 1 v+vfe5a $^{\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. z./pkbxar1ru3 xo0 r 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 the g r1 .0.3ox/pzrbaxkurraph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when 0mb0bksad .. e qc0p- lg6;wgntrying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency isgg.; dm0 pkbs0wecn6la-.0q b the other string? ±    Hz

  What is the beat frequency if middlasd(o1t+acuegngq* + * +kdf-e 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 2d gg.6)8 55dlkgoerzh3.5 kHz, 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 playedl8 r h g5)gg5okzd.6ed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a ayao(k zrt5 / 3c6xki(;o sn,z350-Hz tuning fork and 9 beats/s wheno5xo irk ( ;/z( 6anazctk3sy, sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one xmy8bb kk 393hstring is then decreased by 2.0%. What will be the beat frequeby xm833k9hbkncy 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 * n+ hy+/znuvqto play middle C (262 Hz), but one is at qhnvz nu* y++/5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork i5veb+e5a x8kB has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is he5eiexv+ b a8k5ard. 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 speakemcy 3:dtryt23 r and 3.50y c :2r3mdyt3t 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 138jxj.1lhy8rj 2 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is v1 8hyl x.rjjj8ibrating 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 soundu/s:h6gixsfe8kz-9 y of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 2 6 -hs/:u8zseyg i9kfx0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’;l- g7h zr cjqbp9)opp)0b/ie s siren is 1550 Hz when at rest. What frequency do you detect if you move with;o hb/ 9 egz0)qrj i-)ppcl7pb a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What f7us 5jn ly4zp6wfyq+s5 +nm4frequency do you detect if a fire engine whose siren emits at 1 7f6+pfqm4z ywn5s5 sj4ylnu+550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if pnp w2bouc81tc7u4inm 0nj (;a 2000-Hz source is moving toward you at 15 m/s versus you moving toward iwn8inumco c 0u1np(724pb tj ;t at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency j mz+ 7,ed q*q0ok/mpahorn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequenc pqadm/*q,z+o0e 7kmjy 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 r4elg+r/hla kk 68n;kdeceives them returned fr +h/klr4nk8ld6 age;k om an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward ayrro.0tdl78j pe /s;h wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wartdjyeo7h /;l 0s8.r pve?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played v rhv,vur;4t f1,iom* -gtldl3+m y 4von a moving flat train car at a frequet4l +guyfl1r mv34,;t m*rv -,dhvvio ncy 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 approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blotj+/ g6dcg9nzu7wv m w)+ry:yod-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the s zm/ ncd9w+utg g:7wrjyvy)+6ound source?   Hz

  The Doppler effect using ultrasonic wavesfit9u a,) b1r-kuad8b 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 thniqxc 9ngt-n;8 os6w. 2o lv(be wind velocity is 12 m/s from the north, what frequency will ob6b n8 .-w(ocvtg nos i92;nqxlservers 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 l0y.-* hfznzxcand if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a3no 6x(zg 6jvtid6 xh4) What is the angle the shock wave makes with the direh(6xnto gi z36vxdj6 4ction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a plane(sh .97ae9rfibny 1nm e(krm 2 cjp0s5t where the speed of sound is only about 35 m/s ms. 9kren i5bcs(y( 7jef19pmr0n 2ha
(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 8-h3e6d*n-enh el5 f ed/wj* or500 m/s strikes the ocean. Determine the shock wave angle it prodh6nw5rd o3 -*dj * -ehl/feneeuces
(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 *n)3da jox .wxr+yp 6()dhlo i$/theta$ 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 tq+k(fzq8 ff eded)/am77 zfd:he ground flying faster than the speed of sound. By the time you hear t/z ()fa: kq7+qdfmd7e 8zdfef he sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz-hnrkjzw,j /w( 82zfo sound pulses downward from tohjn(k2r zf, -wjw/8 zhe 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 (in fresh water)?    s

  Approximately how many octastn nja5le .km)fi;*1ves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cay njdlp,*k,l 1lled a sewer pipe symphony. It consists of many plastic p,1pn jl,dy kl*ipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person gu 5c*hhscm wi/ te25 qh,:a7,fn)pommakes a sound close to the threshold of human hearing (0 dB). What will be )*7m2p ef s hhoagu:hin 5qcw5m ,c,t/the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound avom b(;hls4eod/b/0 j re heard simultaneously? omelb jhsov;( 0/b4d /   dB

  The sound level 12.0 m from a loudspeaker, placed in thhblx+w3*w-+ tl ay phkyhf6 -+e open, is 105 dB. What is the acoustic power output (W) of the speaker, ab+p* +-htwxlh+-3lhw yya6f kssuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output d qn3g7pe fng1; nqp9l5rops by 10 dB at 15 kHz. Whatn51lgqq pp9;nngf3 7e is the power output in watts at 15 kHz?    dB

  Workers around jet air/o 4 dns1f0u47dktib/mb j 2q,plnuj9 craft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would p u1j bbtkd449i/nldjq/ 7s f0on2u,mbe 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 gm./b y7ght -rmain, $\beta$ 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 frequencynp 8hadkg8 1y,:x:sdk 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed po; /rqyxx90oa8 da*cgfints with a fundamental frequency of 440 Hz an /ofr9*gdxcxq0 ya8a;d 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 open te- jtfpxcs z*32su(x3 ube 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 and again at 0.395 m. What is the frequency of the tuning fork?js st( u2c*3epxfzx-3   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one en rjm *bcg,*bunus vaw4j2u95;d and also 75 cm long. How much tension should beuaur94 2 bs5*cjnwv,jb ;m*ug 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 observekleafj:zvv5do4 w,(c 9o( baen 1; e*kd to 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 ,gg/ o,7ssicee(f)u1ey pr8.iz x8cq tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is,7giz/ ecqey1 g, .urs,fi )(8oe 8sxcp 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 station6c0-u;qv) i4 poqekijary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speeq pi)ju -0v oi6ke4;qcd of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After it o bqh*3ru,d6f passes you, its frequency is measured as 486 Hz. How fast was the train moving (assfb 6or 3u,q*dhume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listedom,k;v+ py4rqk*8il8 vqfft2/ z /jqning to the difference in pitch of the engine noise between approach8f/mpzj koi8*rq2ty /4dlq fvq,v+ ;king and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soundingi8wran,uxi.9a -fdy71bmhi 4 together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. w-1fi. 4a yi7 mdh8 axurb9ni,How long is the other?    m

Two loudspeakers are at opposite ends of a railr4plxaz +wtzlek gp*s2 *(98jqoad 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 qjp49p s zz* kgw*l(2ex+lt8a) 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 blooso2s9 3l pagd8d flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blool2gs 9o8aps 3dd cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while w dx+)rm-qts7 the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Wha-msq7 xrt+)w dt is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency q g:w2t+a9kdyp9 k1casound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 9 yca w1+pdtka9k2gq: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 siy.12id3d;mia 9p6a r6i bvzan gnals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The dvyz3 m19ni66i ab2 ra.pa;dimost 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 by the presence of stabwlt5,63i 58 n a-dg5rm melxnnding 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 nmib3 5dmxe5l-rga,5nl 8 t6wfrequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves ai 6m/nm mj6s)y,d9nna long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a littles9in,6)6ay mmjn n/dm practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the m t0-b3c:aptfah cn ( yx:j7a09)rbuythreshold of hearing for the human ear at a frequency of ab 3jcat- p0aub 0rht9a m) fy:cn:b(yx7out 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 ,,w iow;gy fh-hears the sonic boom 1.5 min after the plane passes,ih ;wfwoy- ,g directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat fz 5.5l olm1tlb6q-wx is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h