What is the evidence :5j.gyv9m pet that sound travels as a wave?

What is the evidence that sound i7 .,gwnpbq /5a8,uhv qsno: 7k2kj ssas a form of energy?

Children sometimes play with a homemade “telephone” by attachin9 )j o*uyhqo8bg a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to)8juo oy*q9hb the other.

When a sound wave passes from air into water, d)xtu+s htit7(n/pxk dwm.4 5 so you expect the frequency or wavelengxx.spw7u tikt)d h(/t4 5mns+ th to change?

What evidence can you give that the speed of sound in air does not depend signiqtfjzgo:2 852-jlywx9k aj zjo6, ya5ficantly on 6ao59- g ,xzlkyjwy2 jt5 oqjz:82jfafrequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why?:9c hjf7:/qpjefs n g3

How will the air temperature in a room affect the pitch of organ piporcb6+cywodt5ltj/7 2d w;a 5es?

Explain how a tube might be used as a filter to reduce the amplitude of sounds*8;h u8wtxmf i in various frequency ranges. (An example ix; umh*tw88fis a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move uz zm1.u.v+ uu ,pr /j:o6ftobbp the fingerboard toward the b/.b zo.rou1zmufupv +j,:6 tbridge?

A noisy truck approaches you from behind a building. Initially you hea9 (2tbq, b8:qithyvebns 4: etr 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: Seeqyt:t ibt:e b2 4(qbsn, hv8e9 Section 11–15 on diffraction.]

Standing waves can be said to be dueh,wc-0) hrlx/, x mwo2rr4 enx y:vh1q to “interference in space,” whereas beats can be said to be due to “interference in tim/exm-lvrx)w4wx 1c,qny o r h0,hrh:2e.” Explain.

In Fig. 12–16, if the zu8,yryh:al. frequency of the speakers were lowered, would the points D an yza:lu8r.h,y d C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who fvu ji)ci5)3gwork in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new tvf5u)) i3icgj echnology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wap-3lxfvjz)g 6 hikvg lb;+ ,p2ve can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component fx3p j;v-2fk lgp,bg+v)h6zl irequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the samen1dm7k es,puox/:)nh6z g sh5 direction, with the same velocity? z:houn dm p6e h1ng5/,)7sks xExplain.

If a wind is blowing, will this alter the frequmujvpt6lzhdo npw9s1 :-u824 ency of the sound heard by a person at rest with respect to the so-psu vpnj:9u2h 48twmz 6o1ldurce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions ofvb6/ h-smh /zw 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 throughhvm6w bs /z-/h E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lenmss ng;f 1+-pope+vb3gth of a lake by listening for the echo of her shout reflected by a clie- +vg snp3 +b;o1spmfff 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. 4vx3,hhggrst + *dxau*ba sp; c4w.9a He hears the echo of the sound reflected from the oceaash p.43dtag;9,x gcx*whu b* 4+srv an 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 aiwgf(wfl21 o x7r 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 a school of tho b.pohl 8sg4ft6;;e una on a foggy day. Without warning, an engine backf46 eofth ho.;;lps8bgire 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 s: p m1)y 1wmejbar 1mtj6;7gzxplash it makes when striking the water below is heard 3.5 s later. How high is the cliff? z 11e6r awtj1);j mgpm7my:bx   m

  A person, with his ear to the ground, sees a hugema,gkxv( wm,ek,6l)r stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far aw l),, g,mvkw(eax mk6ray 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 rcga ji: h*4d4pule” for estimating the dista4j*:dih pg4acnce from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of 0b(/pnvxw* xca 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 intensit/lc8qhw0z9 *dwl j g+6hriwqz58ic b, y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired suxnh9i5q9j f7b(z5hj imultaneously at a certain place, what will be the sound zh 5 7uqbi9jh5jnx9(flevel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from anlgsm-8x9wrt k i, y6s0bwn9p: y87yjg4tgqg ) airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound le 9b48w76il-ryssjgk8qtg9 w tg: m,n0 g)y yxpvel 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-noisebes5 4fec:x zhj f7:y+ ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each de:s+cz ee4:fh7f5 jyx bvice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking f5)uqr;qpx8rcv s) )r in normal conversation. Use Table 12–2. Assume the sound qfrqvs xr)c5 pr ;))8uspreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum ef2-1sj yjuj) 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 thdq rwx(oge6 :v4d )(nhe more modest amplifier B is rated at 40 W. (a) Estimate the soue6g:qdo ndvx ((4rw) hnd 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 wheioo)mcf1 lw32n placed 2.8 m in front of a loudspi m)2oc ol3wf1eaker 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 detect a difference in sound level of 2.0 dB.c yz ytr.ddsw f,v*n1 n,o8cc3st8m- 2 What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Secti.cn sm 3yf8,dd* 8zc2vtwo-,1 syn rtcon 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will qgu 16oqea9e 6the intensity increasee1 e6q6a uo9qg? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the fre :x:n;v7thh(b(of) k x)w3(rv brg8vkdnyqy ; quency of the other. Whao3rf qynx yr b8(nvd: bxg) ;:vh)whk;k((vt7t is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thh bc:d;;0h bzaat corresponds to a displacement amplitude of vibr;a: 0cbz; bdhhating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to ser+vd;q2 u/yj/ap /o*) lquqys1gs l-fem as loud as a 100-Hz tone that has a 50-dB qs+ u)vlu;j 1dl/ g y2f*/qoa/qsrpy- sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies tha*v7.xm 6musu et an ear can detect when the sound level ismu*m7esvx 6. u 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rku5llbe)rk olol. q4+/w x2 :oange of sound levels. What is the ratio of highest to lowest intensity at bx /lll 4ko.l 2rou:5owk e+)q
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 4fgtpc u7 5i9u) a,ol3eynpc6 640 Hz. The length of the vibrating portion is 32 cm, and it has )c6tp76il,f 3un95a cop yg uea mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are 9;pi (8:;hedcmzax u pthe fundamental and first three audible overtones ma9x( ipzud;:cp;8e hif 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 you expect from blowing across the top of an h)fp2i x te4+0hnh i4aempty soda bottle that is 18 cm deep, if you as)hit 04en2ixpa+hfh 4sumed 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 ope q6 mc)pf-a ugo02lsg*n-tube pipes spanning the range of human hs6ag-* 2mgpful) qco 0earing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string h k6eo y+aoc2 c1yhb,d5as a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its o5c6cy d1ao2oy keh,+briginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above miw0)fddf 2 tv1*c jafsy-gf +0bddle C (330 Hz). by0f+fd1 sdf*j0a-t )fv w2cg
(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 p;nwo jrqmmn1ru a+; 08ipe that emits middle C (262 Hz) when the temperatun;wmu1a80 rmr qn ;o+jre 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 206t*.xvkg kr 8g9 qew:f $^{\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 12–1y7lh3s9 e4xhv v -0gsvzgr1mte y/;+ g0 should the hole be that must be uncovered to play D abovzleh13r-g yx s/;hs4 90 t+ v7gmvyevge 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,sae c3pe9nis :try:rqm7 j hd 4+6vb34 and 616 Hz, but not at any other frequencies in between. (a) Show why thp r c hqt:dj6m7bv 43e9n+ es3a:ysri4is is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both end o7q)f; l0cxaws. It resonates at two successive harmonics of frequ) qx ;0wfal7ocencies 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 0 ct2x qh- w.hghor.(v$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audifb5u :fz cmv b :w:kudle.em:xe-g994 ble range for a 2.14-m-long organ pil:b94mckb9xvd- :5. e: fzguem: wufepe at 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 and ho 7) 17hsfdmfd8r7d10 kbf:gs ukow 2is 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 infor)ku2rf:70 f 8kb7wodshgf m1h1os7d dmation 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 striu,5jdp)qz2v v2 z *j30 ybpowv)-kjonngs, one of which y32 -oopvq5k bnvzjwuj*2v z)dp0j) ,is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if mg-o.w u. w/u (g5hynjp0 +twn/qvp a5middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.kbh 7 np;-7d lt.(rtiy5 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 played simultaneously, estimate the operatin7 rhp(.ndybt7 t;l -kig frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded withva2x8yyx p2t+ d-o 35tv:p jks a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational fre :5j2pyxka8x-+vt dot3ps2 vyquency of the string? Explain your reasoning.    Hz

  Two violin strings are 9v+c: b:ngthekhyf)5 tuned to the same frequency, 294 Hz. The tension in one string is then decreasedcyk :+b59ehf:vg tn)h by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle-m6wpk:q+:k,c8 og h8msi ian C (262 Hz), but one is at 5.0°C and tm 8mnc8gk i,q +p:w -s6a:oihkhe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequenu.h ylk b1z t16uze.i)cy of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are s1z1yzl b6ukieh..) tuounded 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 .o--* flhxvcmspeaker and 3.50 m from the ot.m o-hlc* x-vfher.
(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 s lpl +vn/f+ ,zcczp1h6upposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be16,z ppclf lnv ++c/zh 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 an:xwt 0zlx 4w0ed 2.76 m in air. How many beats per second will be heard? (Ass 4xwlw xt0ze0:ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certa zw;qs2)vilhxxmk,3r.6 wjq-, cp)c jin fire engine’s siren is 1550 Hz when at rest. What frequency do you ,qzx; k2s wc63jq-.cwrvlx h, i)pmj)detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do q0vsaqw a0 a,s(a. j*dyou detect if a fire engine whose siren emits at 1550 Hz movajaswd*(qqav,a0 0s .es at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a pf). og/eyzq*v-b zv c47noi 32000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the og i. qv)p4ycnf-7b v zez/o3*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 equippedh8n;* 4fj4xlxii1pce:7 hsd o with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the hor* np hoxflex 4;i8cj1id47 hs:ns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wav u49*(-luou pi- r-giue3jf fdes at 50.0 kHz and receives them returned from an object moving directuf-i g*3fuir (4el9u pd--o july away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s o+rsm43e nf5 08yfm fsAs it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in3+fnms8m 05r f4fsoey the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a:fg1tylmn;8i3l d7wl moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at7 1l f m;n:tllig3yd8w 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 mefujr;q m;ek9:bi12 jr asure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is2;;jqfi rmbe1 kj:ur9 taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencyc ie9tnq; )cyo/(owq; $2.25 \times10^{ 6}$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 frequenl rtt qiax3-m:7:s hm0cy 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, 0 -hrx :a7im :qttls3mat 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 speedfuy25rob f,;l 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. e8 p(5lqtegb13 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s moti 1beq(tg58e lpon?    $^{\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 u 2pw1tm* wsr* eg)y/oplanet where the speed of sound isowty sr/m)*u1w*epg 2 only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Deterx: b2;fu2s(u 9rs/e hhvc6bhfvygr6 0 /lm/aomine the shock wave angle it vyubf6/( u;lr/h9eg6hs cxf2o0a:rb sh / v2mproduces
(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 uv: sjppu:ih0( ;/b cq$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and shupk3+-tnq 4:,syl mx ee 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 traveled ax tlp, nmqk4+-y us3h: 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 i5d8m q8nz*g 2av(weypulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between p8d2(w 5gni vazme8 y*qulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range?u8akqw :d k5ej/x /oa, $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe s: c4 8ule73xu4ddepgrw :i giwp180zgymphony. It consists of many plastic pipes of various lengths, which are open on both 8dw ulrcdwp :1:7i4 0zipge eg4xu3 g8ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound5ussur +6za gh 7qp +w:lo+ku. close to the threshold of human hearing (0 dB). What will be the sound level of 100z 56 ks.s+up+owuu:+ larhqg70 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB so:lov a oq,a*/xund and an 87-dB sound are heard simulxl:/vqoo* aa,taneously?    dB

  The sound level 12.09co 5iw0 0tqhz5fst5d m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power ou5s dqf0hci9t ot w505ztput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. sr -5r6 b9i dl1rd6sqqThe power output drops by 10 dB at 15 kHz. s9 sql1did rqr-566brWhat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft l24 m(k 9u.6auftv5skawrr1r 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 effectiut(l2r9w vr ksk4ama.5r61 ufve radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, t- mtj-*ef*w aphe 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 frequency 1i b9xwx3j*b1 g$\frac{1}{2}$ 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 bet9t:zjw l/ 6e 9iaz0vnaween fixed points with a fundamental frequency of 440 Hz and awije09n/zlzv6:ta 9a 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 o3 -inpl baswejt6, 63cpen 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 heard6 3jlbw,ts3ac e-6ipn to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is opt)v :k0. n xstnb5k iim:gv-(qen at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (svimvngq )xkt . ibtk:n0: -5(in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed t-h1 m.a)vmn0 l,xq gjzo resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range4/njpo y;u6:yvf n3.un:fepd coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a pointnp o.3f yduny:unfpe;j :/ v64 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 stationaqggygi81 vny8 7v9r 4yry. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train ap 9g7148yryg gny8iqvvproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 5j7qwnd p* o:v xenr0-(38 Hz. After it (pe:qwx7d0jo-n * vrn passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimatech4l:k-83zt lf6ehj q8 r-l7uoin 0wn the speed of cars just by listening to the difference in pitch of the engine noise between approachizt:8- 0wc -ijq r llenf87o n6k4lhh3ung 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, sounding together, produce a beaa3qt4t v ,3o)oza3w;zcb o je:t frequency of 11 Hz. The shorter one is 2.oj3ea tvz4z3 b;qawoo,) 3:tc40 m long. How long is the other?    m

Two loudspeakers are atakgmed8hm-i 5y/ kni.2u;vm: opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they hav dymku82 :kmmi;na/ ie-.5gv he passed him, at C?

  If the velocity of blood flow in t:bed ( e ayqg2b20aik9he aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50eg2b a9 a ykqbi2:(e0d-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flyingut drq)1 bcc2 m--n51lpz1 pek sz+j6g toward the bat at speed 5 m/s The batlcdt 1b2c-6+sue51p qgj 1rzp-nkmz) emits a sound wave of 51.35 kHz. What 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 sound pulses as it approx o 8*0cr+k-afy )bdxdaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away ydc )k80r*f-bo +ax dxcan 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 sent.4 mkob30y2thq( cpkua7 )g-q0wwond signals 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 most popular al )y oq 2.(a 7ukcnt- o4300wqgpwtkbhmpenhorn 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 u v4l-*mo7rui oxju /.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 wa4m l/.ou riv-uo ju7*xves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstrati cg6dck4jpf,*on, called “singing 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 clear, loud, ringing sound.6pcd*, 4gjcf k 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 atjl-8hbvm fot c/ l57/y a frequency of about 10005cfm ytvb lh/8-l7oj/ Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the soniczvmp*6)8b 8;hgv.glwsod f3wkdj 5q . boom 1.5 min after the plan8sjb* oz6wld ) .vpm3d;kw8 .hvf g5gqe passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is0vis/+nhnoog *x3 8dx 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