What is the evidence that sound travel u(xh;qa3hf,d s as a wave?

What is the evidence that sound is a form of enermyb(xi-.6+g- fwwuf rgy?

Children sometimes play with a homemade “telephone”gvby3 a/*b. wf by attaching a string to the bottoms of two paper cups. When th b3a wg/fvy*b.e string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave paskys 9s-(b8 d mnwbju87ses from air into water, do you expect the frequency or wavelength to cm b8-9ksnuw y(7jsd8bhange?

What evidence can you give that the speed of soun 3 :bgjkv0m+xvd in air does not depend significantly on frequencyb0vxmkj3 v:+g ?

The voice of a person who a0c am0xgr5fv7j tz:19rgvj*has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a rj /5gdwozwh2i4qmb a +.s,7 tfoom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to rs.6vhe f- z) *s2cpabkeduce the amplitude of sounds in various frequency p6-hb* av)2sf.ks c zeranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced i* dvzx-:jy q*closer together as you move up the fingerboard tow*yx vi q:-zj*dard the bridge?

A noisy truck approaches you from behind a building. Iqt8t726+m- ouynmw;s jsq0mo7( s e brnitially 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. [Hint: See Section 11–18su 7+yq- 02m(w tqjr bnms7ootm6;es 5 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats cv4 6mfko1wz- 8 cua)xlan be said to be d6)kv ocwmx 8 zfa4ul-1ue to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the spehsh*s+ uv31zo*cl 9zrakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apartvz hz*9*3hsr+lc 1os u or closer together?

Traditional methods of prox muf4u., 5ue:nl gq tw:rlo.-ped)(x tecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient ndp-,.u(gm5tl fxo:eur:eunl.x4q w) oise. 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. Eac/to rmie65 hc6h wave can be thought of as a superposition of two sound waves with sligh 6mt6/ihr5coe tly 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 th1mag73jb;nkz9spb6b a;kq8;b pb7usroc:0 re source and observer move in the same direction, with the sameq0m; k r7pa pg7 ra;:bc81 j;6bbubz skosb93n velocity? Explain.

If a wind is blowing, wifp0txc ka jb69p9- gb4ll this alter the frequency of the sound heard by a person at rest with respect to the source? Is the6p gpa0bck f49t9jx-b wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a sw)/iu0xd pim *zing. A monitor is blowing a whistle in front of the child on the ground. At which position, A thro zmu*0i) id/pxugh E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lak+*( ddb;k +y/vau 7nufoarq,re by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hud,q/ u7kfr bn (y+od;a+*a vrears 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 waterlgl rmaapt o,273b z)i4ebj)+ yine. 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 seawater is 1560 m/s (Table at) y2pgm, iejo+3b a4 zl7)br12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths,vn jhgpwwwh0)w/ -j: 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 drifting just above/+p fz;oyvk6 t;ho* ziwnvz)5 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 fhp5too zv;)i z z+ykv6 ;n/w*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 when striking t h6 nr+2qxkv0s6mwo4ehe water below is heard 3.5 s later. How high is the cli66 oqvs +2rxnh4w0ek mff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrejo s6tdkqg.5w 8ye,v,te pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and ye8oqg5 .d6vk,w jts ,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 - - t1y4nsgzap“5-second rule” for estimating the distance from a lightning strike if the tempery gan p-t14-zsature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 pv8:mcx,e1:i. evlz f 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;/7ds2j8kr/bp o hezl is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levelzglb /jo/uj;3 of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitiesbgju3l /o;jz/ , not dB’s.]    dB

  A person standing a certain distance from an airplane with rtn ,c vz0woc /1;fbi:four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound levncb 1 ov:cfiwr/;,zt0el would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, w-7 g z+dgonkdcys21k;, 9hy d6.ccbgfhereas for a CD playen gccgc; ds +fh9k-7zk gyodb.2d ,y16r 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 s9,t (hhrt,eez0 eie/ltuq )ec:wj/ y:ound from a person speaking in normal conversatitehic:tl),e wh9jy r(eq0/:z tu ee/,on. Use Table 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 stp9ymhh d 5-kj7rikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplipe.3 tacmao. 3kp 0js1fier B is rated at pe t.sapj1k. 33m0oc a40 W. (a) Estimate the 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 dB when placed 2.8ee,djndft78u(zx (kz3i.2jg95 o /zn 7z c rzv m in front of a loudspeaker on thenk 9jrf72 (dz7ei gt5 czved(3xz /zj8,nuz .o stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference (z5 -b7nm)ux2a pe dwwx*6 spsin sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section -x ww *)2u5mepnp( sbsxa7 6zd11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by 4fods8m1+lde2*/msq sc p g-bwhat factor will the intensity increase? Increase c*f 1loms/-4bm + 8dgqd2sspeby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplil2osf8/p7hh f + hqhc/tudes, but one has twice the frequency of the other. h hhfp+oh7/cfql /2s8What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspondshgzj ;r k:);jeh*wfofd;3 pz+ to a displacement amp ;r* ;kdhhf:jef 3;o w)+zjpgzlitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to se/y enrox r5*v 22n9lhqem as loud as a 100-Hz tone that has a 50-dB sound level? enx*ry v92lhrq25o/n (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can deko +z- t)76o9szatify tect when the sound level is 30 dB? (See Fig. +-kt ti)ooz 6z9fsa7y 12–6.)

  Your auditory system can accommodate a huge range v+c9j,1 u pexj9f8z fnof sound levels. What is the ratio of highest to lowestj njeczx8f9, p9f+1uv intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violvi-, /):c**midzy*vk*xen4qkexx vu in has a fundamental frequency of 440 Hz. The length of the xvkinv*:,uxz / x*- 4 iyv )deemk*qc*vibrating portion is 32 cm, and it 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 th6s iw(pa63tf*h 9q;rtzp 9kite fundamental and first three audible overtonkspr(6at9h6wtpi3qi*; tzf 9es 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 freque*70 qz wg4nmqs2;b .pc:vqmovncy would you expect from blowing across the top of an empty soda bottc qq m:gbo w7.0zp;s*qvn2vm4 le 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 open3axrc pf( 9bj2kstna,ml ,qwv 9t8:/k+t gc 7x-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what 8w :b l2ac3,f(vtq/tcg kxa m kntx+rp 7,9sj9would 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 has (aqhpo/ :/bermonic. What will be its fundamental frequency if it is fingered s eb(ho/:/q paat a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle v31+q-ul :t jkoth+boC (1 q:l-ttj3bok+ohu v+ 330 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 ok3+kwrm(h o;wrm ) i6xf an open organ pipe that emits middle C (262 Hz) when the tk ;r6wh +m3wxo kimr()emperature 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 a0fpt*3pjfy2p c h3 )ott 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Ezne d;p;-3 ufr8 csa.bxample 12–10 should the hole be that must be uncovered to play;n ;3s rfzpcau.8db-e 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 20.9c31 zullmxgge/+xwaaka7 9* dq gf64 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed 0kxgdlw3ma l /fec g* 1.x97 qguaza9+pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is r knx(54f+gr 1+swfy(a/oymj;r z kj +open at both ends. It resonates at two successive harmonics of frequg;4k+ /(axs ozrjf j+rr(ny +mf51y kwencies 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 20 405 +jqpxuhfz$^{\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 mafk/ez-a6mxi.o uz:gb8 50z present within the audible range for a 2.14-m-long organ pipe ammebiko auz0x.za:8f5/ g- z6t 20 $^{\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 outside an4l7gpm 2+ qsgk ;k0yedxo5fd7d 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 ;ypsfe2k o+k5 d lqgxd7g 470mthe graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, ir0v8r7nj)m7. b:c cgx pp3mxulip 4k +g0:cmone of which is sounding 440 Hz. How far off in frequency im:7+m)l j 0kv r4:mxcurcb. gg0cnip8pxi 7p3 s the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andchi v:ig)n-;lk;0tgyn kpvk6 k 6x, x. $C^＃$ (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 operatesr ox ek4 .ukrdn7- ax5yq0*9ws at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by 5 k qo7 wxy.0sknau*r-ed9xr4humans when played 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 z57z2ca.st qd when sounded with a 350-Hz tuning fork and 9 beats/s when sounded wic5 qzs7d.2ztath 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 te/jvoa wu e9ein1 mo(x3r/ap*;l+w +rynsion in one string is then decreased by 2.0%. What will be t+nwveo13/ x a*yer+ip/(9mou lr aj;whe beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be tkg pi7ab:2+ lheard if two identical flutes each try to play middle C (262 Hz), but one is a b +lpgiak2t7:t 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hdvtoad9o 9 q49as a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A a94do q9 dvao9tnd 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 p2fl /yg)jnq 8+1 tjlxxerson stands 3.00 m from one speaker and 3.50xl8gj1jq/x ntly2+ ) f 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, but a piano t -)(uqvizo b j9rj0p:juner hears three beats every 2.0 s wu-i z )j(oj j0:brqp9vhen they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. u7q ,- 4( +cjdfv nk.yki*irbvHow many beats per second will be heard? (Asduc4 rjyvif+*qn(kbi.k,7v- sume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren q5itc 9ir67eoz7urlma/d,i( is 1550 Hz when at rest. What fretdie 59i/ qrzc 6limro ,7a(u7quency 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 m(ll;n g6d z5edo you detect if a fire engine whose siren emits atgllm56e(zdn; 1550 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 a 2000-Hz sou y/t, ask.-kcyjnyxm;g ;(da,rce is moving toward you at 15 m/s versus you moving toward it at 15 ; xn g-,ym ,k./(jya;aydtkcsm/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 freli2t:ts /q*pgqb+:ng pju 99oquency 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 /u*l+b g 2ttjspiq:o: 9n 9gpqhorns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receij nb es;,b tr7hqt:d9 z1,or7wves them returned from an object moving directly away from it at 25 m/s What is the received sound frequenct;h,r1b7w9,7ds rbqtj: en oz y?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed o- 8)j+g 6iwjcfrz4fc af 5 m/s As it flies, the bat emits an ultra) zc8+-rf if6gjwja4csonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originp/dv q pvlq+xjr(hup fy6,v0)6-f yd8al Doppler experiments, a tuba was played on a moving flat train car at a freque q0xvd-8(d ) lprph jf/yvuqp+f,6yv6ncy 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 blood-fcfk*dn4m( (lc low 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 blooddkcl c4nf*( (m is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic5 w tp;-zjiocq;be)y 5 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 velo:n t:9z:a) rr(o+tnaz;g q43pxcysab o2 gx*bcity is 12 m/s from the north, what frequency will observers hear who a+ t 4b(r z yx g;aao:p*3z 2o:rnxg9:qbtsca)nre 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 mo/ b2p -ft; hkw,dx lyhq;/u.cfving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m(n yy2x qq a hf5jr2ix2lp.hy(;2b3dn;y -ynr/s (a) What is the angle the shock3lp yyy 2ih2 (2(nxa2b 5 .;yxhydf-rjnrnqq ; wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmospherek3f )rbkcc upds+8+mf k g4+vd90bs s) of a planet where the speed of sound is only about 35 f m)bk830c ++c4fs+s dp)gdsrvukb9k m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes sdtz k-h(zy6: the ocean. Determine the shock wave angle it p yztzd-ksh6 (:roduces
(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 hyd1y:2l5 v2 fj qjg.c$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead andb(5h+l4j x kkx see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has trave5( lkx 4bxkh+jled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound byw3jmpoj-x:q -ejo(q v(4 s)pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work isbes -mj4x )w(v: (j3y o-qoqjp 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are thoe7v-pk1ce -b82dja bere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphtc0( fe :l/6zv -ozqbyony. It consists of many plastic pipes of various lengths, which are open onlqoyvzzet- f :0bc6/( 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 pers6v72*yu + -wqjunlhxf on makes a sound close to the threshold of human hearing (0 dB).fu *6xuj 7+ lq2hyw-nv What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultans*r kj *4xz1f ixu+of/( doi(;x1bbpvt sound level when an 82-dB sound and an 87-dB sound are heard simultaneosi d(;(b/zx +k4xxrf*ojp1fivu b 1*ously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whatha *+af(7qsfu is the acoustic 7af+ su (a*fqhpower output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 m2sr0n cklj3)9deus7l*efn(i pm 0 + xW output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watl f(+pr9i70u e2ksx scmjn ld)* m30nets at 15 kHz?    dB

  Workers around jet aagff4frp , mm0 74wq+nircraft 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 be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine fr +,f0mpnmqw4ga47f?    W

  In audio and communications systems, th1+14be8yjwumb2lwc dv 3wh6 de 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 frequencyo1fcqv;0imqm *-+du k 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 0 ;- 0 t1-fwieyfgnbmnbetween fixed points with a fundamental frequency of 440 Hz and a mass per unit ywt f;0bgie0 1mn-f-n 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 ts6 xp ais9.jhq+*z edawa /ci(fi8 ;n(ube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube8 +xqij wp9.ss ai/( d ca*6h;ez(nfia 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?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that i s2m/g(rt;/ac 5mwsj: gqas*js open at one end and al;c5 s*sjg (m/j wa2/aqrsgm:tso 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full l;wjudnm3t irvg8mgp5jphut, , ( 76u,oop ($\frac{1}{2}\lambda$) 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 comii o.pmh7r7wxn h6(qi4r tox.; ng from two sources. The sound is loudest at points equidistant from the two sources. To detrpxw; 7hio txm roh.i(4n7.6qermine 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. Thefkw ,.nul6rwfhjo*7 8-/,fqj :vqdr a conductor on the stationary qfrvufl w6ka, wh7df ,/.8nj:r-qo *jtrain hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steagddo h7lc z/:(pf r(fkq(wa3+m train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the h 3r :dqzp f/dwkcag lf+o((7(train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the ssr csc;4q xu)4peed 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 goe s4u;c4crx)q ss by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequmqmdfat ; 1z*wb-u;6 cency of 11 Hz. The shorter one is 2.40 m long. How ;-cbatu16 ;dzwmmfq* long is the other?    m

Two loudspeakers are at oppoe)ncrr4j6 sma1 /f5us site ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in)6enc s4u1r s/ m5arjf Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is nor +xc.j/ +cjh-vyd8k;xm1u tl4 m6gzqimally 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 ch1k4 i/u g -ctml.yd+qx8jv xj;6+zm red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward the nr,p xcgj5nqo / icf-bm5vrg.k4927 vbat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequr 457q5rp /og,gcv nf-. i2jx9 nkvmbcency 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 mo9 o,/kzbfkr6 vth. The pulses are approximately 70.0 ms apa9r vo,fk6zb/krt, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vi5xf y2s0 ru7tbllage to another. Since lower frequency sounds are less suscys52rb7 0 utxfeptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for sgwt*nvps4 has)(i0 3atereo listening can be compromised by 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.)30 htag(n ispva *ws4
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods1yh d:*h- nan t(6dh(emetjp-,” 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 emi((ete-j nphathhd *dn16 - my:t a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency of abmi-55q50 qa mnvxd f,dout 1000 5v5xqmdadn5qf i ,0 m-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 lj1h.) jl:x s cskp10mthe ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plall. 0s 1hkx:spmj)jc1ne’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ndk+;8u/ntq lj5 ryaccq:4 i nwd8,u*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