What is the evidence that sound travels as (coz*f9fwb98rrmh nxrv/ i48a wave?

What is the evidence that sound is a form of energy? lo2 )4e1/laixh xrg2q

Children sometimes play with a homemade “telephone” by attag5qk 2row-r bdo i hx8:ecm;q(4(xjn9ching 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 cun;rxw-m (5ie2 xh(9 gqorb :ko4qcjd8p to the other.

When a sound wave passes from air into water, do you expect the t3, ufhrfc+p0 frequency or waveleurf f,tc0h+p 3ngth to change?

What evidence can you give that the speed of sound in air does not depend signifi7)m(yk,65s rsexetxicantly on frequ56 te(yis)7kxsem xr,ency?

The voice of a person who has inhaled helium sounds vee 0+vbpkmyz : 5nc8+q, thrux2ry high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipo 3qlt*o mk:4 yyhso:s6fcu+ (es?

Explain how a tube might be used as a filter to reduce the amplitude of sounds viy icj*.z-x qm, 8)/ijyng8j in various frequency ranges. (An exa/8qvj i8j)jn .,*-i y myzicxgmple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togetf ; fqfe6k;:9axjsbk+her as you move up the fingerboard toward tqkefb ;s f9k+; :6afxjhe bridge?

A noisy truck approaches you from behind a building. In1v03yiaxb 5blitially you hear it but cannot see it. When ilx 05b 1vab3yit emerges and 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 “interfer)4x sm * o*7ytjjdp*irence in space,” whereas beats can be said to be due to “interference in time.” Explains*pr jt* x)*dy4m7jio .

In Fig. 12–16, if the frequency of the sped f9vmduh. r*9akers were lowered, would the points D and C (where destructive and constructive interference occur)*mh v 9drdfu9. move farther apart or closer together?

Traditional methods of protecting the hearing of peoplei-tgaf2 op /1x)-lsyw 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 noyslw gta-i/)xf -21op t 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; 8*rhcdyuw1+ ob2 chy/ucv)b in Fig. 12–31. Each wave 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 frequencies farther apart? oh huy 1+b*r/)y;wc cduvbc28Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directi66u1y49dv5 hyvgjlej on, with the same velocit v ue59y1j646dvhy gjly? Explain.

If a wind is blowing, will this alter the frequency of the sound hf vfiy)vfm6w n:wbq,ap 06 /:qeard by a person at rest with respect to the source? Is the wavelength or velocity changed?b66)wn, y pfmv vq::/0wffqa i

Figure 12–32 shows various positions of a child icd4tt 4ls/2s we.qf u-xov8(pn motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the8tdo/424l q-psfs x c (.uewtv whistle? Explain your reasoning.

  A hiker determines the length of a( n-dn24n zoho lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimatenz hn2od4(on- the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his s;qirseh:d+*j 2 rfog-hip just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/qgo;id he+-jf2:*rs r s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in g;y(x zw:3/y :k+wyl1r virb c;a r(hvair 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 abovdr.ikt -/lo6f e 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 is hearf l6k /.iodt-rd (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 strisf scb/;qnq4y+. gmy .king the water below is hf/sgbm. cq4n+.ysq y;eard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees 2gdq (0j4cu fyz0xme 7amev,2a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in thfdq0v 7c0(eyja g,x memuz22 4e 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 idff8i79 5mzhtx 5cltf 2 z8, h17zucpby the “5-second rule” 8 7f8x dl9uzt5f 5izzh,tp7ch1f m2icfor 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 a sound at the pain level of r z. ih,qfiemy(43 (lr120 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 w(el1e+ u (umd uovfl2.q0k4 rj5e;prqhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouso8 kg8rm)) pqmly at a certain place, what will be the sound level if only o 8mmqk o)rg)p8ne is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equall+xln lb50ie1ry noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if x5r0+illenb 1 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* wgk4)v*jm2w l/dl4cjw 5a rg 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 device? 58 dB d2lrjkww 5 glg)*c4w* / vmj4a=    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal ctpb)8i6xlgv . onversation. Use Table 12–2. Assume the sound spreads roughly u8t x i.vlgb)6pniformly 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)5r/ jse pq6 4u0htx(wbln5 gb 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 ayx(r ()1z qi,xzs mqe/ 97klppmplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker cons z ymq/79(i1r)eklzqppx x(,nected 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 metervb+ q vkjz/o.; registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. k/bzq.v+o;v j
(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 levn qje m+;2gy-vel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: qjmvn;2y-eg+ See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the,7e - v6l ntwnpw *:ry)ra;vep intensity increaser;7vwn tew:pr-vyen l),a6p*? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, br/qcuor0+r (u ut one has twice the frequencq(uror/ ru0+cy of the other. What is the ratio of their intensities?   

  What would be the sound level (in)qx6r.aiw+fu u) yp0w dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules 6 wyfiuu q)+wp ).ar0xof 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as tzq0 ,jd 3ol( ,co6ietloud as a 100-Hz tone that has a 50-dB sound levdicq(0t,t 6eo,zo3l jel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detec(cbg(ot v- mg7t when the sound level is 30 dB? (v m7(-gg(o ctbSee Fig. 12–6.)

  Your auditory system can a.o zop,;(e4a 3y snf ywl4ib3pccommodate a huge range of sound levels. What is the ratio of hig3;woyps yli oba z4f(e,3n4p.hest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The l pu7 nuiz. zdcr(xknw(7 d+65o2.rnrsength of the vibrating portion is 32 cm, and it has a mass of 0.35 gc .uzpd7rkrz (sw.( 7nn+5 6n dxri2uo. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first cjs axd3;t6e 6three audible overtones cxa 6tsde ;j63if 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 o89 phsz(e pbx(:xx)h would you expect from blowing across the top of an empty soda bottle that is 8p )(x (z px9bhhxo:se18 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 wiyc9ireevbe 70n ( fu18th open-tube pipes spanning the range of human h0iv7 (8y be19eeunfrcearing (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 has a frequency of 540-b2nvbaghmz7: c b+x: w8dwq 2 Hz as its third harmonic. What will be its fundamental frw-+dxwg vnz b28:q7:c bhm2abequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunedvwoap /ck.6lt5, vr *u to play E above middle C (330 Hz). .rtw6vpcv *o/5,ual k
(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 pi f p/hwld/+7oqpe that emits middle C (262 Hz) whenf/lhq +pwd o7/ the temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at ou6p-sia2n *z20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be thatj76m) dzkjds:cdj 8u;ccq54 t must be uncovered to play D aq jz j)d:s4jdmt7c5c8;6kd ucbove 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 a3i)j2i9tpvnmgfywwxas i1 81 . uhs ;8t 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Sht98. 283 fwvju;siwiishanmp) xy1g1ow why this 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 ends. It resonates at tu 2d)da d1o8 pcnwltpe8f;y :9wkka6 ,wo successive harmonics of frequencies 275 Hz and 330 Ha pnu,l6w tad 1:8powd kd8eck;2y9f )z. 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 :tdmi2cyxee0:x 66vr$^{\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 audible. 5t ohmewsl3,j:y+ypwj d9:g range for a 2.14-m-long organ pipe at wo+myjhs,e.p5gl: : yw9d jt320 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm longghie(utdztd*+ 8 ( lk)4; bppu. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible rang (tpt; eidl4ubhdgkz8+)u(*pe) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beaen94v8kgtm-6r7stxa1 uq3czp 5 *oukt every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in freq n 8zuoe5xc tks94tq 1m3p76 -kuagrv*uency is the other string? ±    Hz

  What is the beat frequency if middle C (265(pfgwaa b+ k, skpbk e)zf 8f1v.1)tn2 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 n 6 s *mr6sk*fj3ys0fwkHz, 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 operatm*y r663s skf*jfws0ning frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuninpigx0v* zn 7zegxvxvd:4 k2v2 x-fo8;g fork and 9 beats/s when sounde 8vvge;xv2nzv2kx7 4ox0z - fx*:dpigd 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, p)58hhlp z ramifl/- jx6k9 ,z294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequenp5-8 fxal6i/)rhzj,hk l9 pz mcy 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 mid tym91b5ab4 5fwobh)f/ru*z fdle C (262 m rafob/1uzb) 5 wff49b5th *yHz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tunin- um -6usk t;xfxi+.oxg forks, A, B, and C. Fork B has 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 and C? What beat frequencies ares-t+u o i.6;xf umxkx- 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. y(i8+4w f2 poh-gx.m7: gn yo;lvfmh rA person stands 3.00 m from one speaker and 3.50 m from too4- g2.8whrf :;fpy (v+xymmigl hn 7he 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 y*zq1/(yk i zxsupposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together.z1xz(i yk /y*q (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. How many beats pem s b( :i 5s7o4x+)yj,vsbn5sb2u)tvn wq-swor sbbs,xv57o2ob m vu(-w)ys )+sw sjns: ti5nq4econd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engin qu6 ;gjs mxw1u(h2re goxl;+3e’s siren is 1550 Hz when at rest. What frequency do you j6123 q+;rwh;s eo mgu(x gxludetect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect ifdieg733xz n 4hd 4z8vu5es; dq a fire engine whose siren emits aden7e4 x8dz u;gsv5 43hd3qzit 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in anzfcb 8.6b lc+xq3q5frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are q5z.+6f8xncqlc b b3athe 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 sin8xu yxi- qnb96yfp2 9pht,d u7gle frequency horn. When one is at rest and the other is moving t x d9np9 pbxi-7qy68yutf ,uh2oward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives s1j 5hta 7wigq .bn01ethem ret57ni 1ase1 twjqb .hg0urned from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a waj6;k -+w1ce vqdh 4rlls(p5dzll at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What f6dp1qlwsve zdj;-4 c+hrl (k5 requency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopp ;,o.y9jjv goboe 86qfler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway stat9o.byoj;j6 e,ofqg v8ion. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter use*8jci p 3:opgjhx *fc0qcn(nm,p/ t1i1igu;ws ultrasound waves to measure blood-flow speeds. Suppose the dei3*0h g1*;:qx8micn1u (gn w,ocpcpf/jitp j vice 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 sound source?   Hz

  The Doppler effect using ultrasonic waves of frequenc8/tv0e z qg1a-s5qtig*glnsago+5(c y $2.25 \times10^{ 6}$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. W63 7 4fge21ke2 6bb+lsisjee(uljfyb hen the wind velocity is 12 m/s from the north, what frequency will observers hear who are los+yj6g2kls 6( e fb1e biele4b3uf7 2jcated, 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 movinpmj v7152vax;e fk;l ng 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/s (zx stna3, jj/0 phpx9kk2;j+sa) What is thss90z t2+jj xjp;p/khnx ka 3,e angle the shock 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 atmosphere of a planet where the 31(w l -x y i:/pzp)qkxfym4gvspeed of sound is onl )kxx qf/4z-ipymp3:wg1 (vyly 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. Determinevh koqb11/kv y7, d5d1 kbuvq6 the shock wave angle it produces ,1 vv 6db151bkqk7 qy/vhoduk
(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 ytmli0lbx0fsy /e; 4 .$/theta$ 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 xw3 cn8t+p9bj the ground flying faster than the speed of sound. By the time yxj ptw+8n3b9 cou hear the 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 dy jh.)gmk;8 pt9( mskiq:xh-h evice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between hp )m is k.h9h:q(gx8t;-kymj pulses (in fresh water)?    s

  Approximately how many octaves are t90 ubl;baidt5k pbr: 3here in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It; x o v3+oso+la;d l;hu/tv8zt consists of many plastic pipes of various lengths, which are open o vll/t ; +v3u;t+x;hoadzo8son both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close t.n47mkvr r4o n p6:wcgo the threshold of human hearing (0 dB). What will 4nvrow :nc6k4p7gr.mbe the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB souvg .f,q/ww 5otnd and an 87-dB sound are heard simultaneo5,w wqv/otf g.usly?    dB

  The sound level 12.0 m frum xx3 ,sjf;,qom a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in alu,3qxf;msx, jl directions?    W

  A stereo amplifier is rated at 150 W output athw5zyg yetnc1 5hs-4* 1000 Hz. The power output drops by 10 d5twyghn5 e shy-c*4z 1B at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective dev(nj3 dvhoq:k;ices 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 airj :v3dk;(noqhplane engine?    W

  In audio and communicationfxvs2lb( 8* (urx4/ hh mz+kous systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuneyzdfd ;b -m(a-;gs;qbd to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between-miilb x+ rw dces0*fh/7-u/e fixed points with a fundamental frequency of 440 Hz and a mass per unit xd ubim+0* /h-w/e e7ifc- lrslength 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 verticwx-.jd1me fku3ot , ,fal open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning foo f 3 w.edtjkm1xuf,,-rk?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at oie/ean sy; /x. uf1k9 lizne34 mi(m-ob,txc 2ne end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its funal-eucemim( kf oi 29x sibz. ,x1/;4ne/t 3nydamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to ) rh w1;n(pbmx4.ea vrfn1ue)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 ovo0 y* dp8j;,ff/vxnrange 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 point 0.34 m farther from one source v ,f xof /jno0;y*vd8pthan the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The condy *wym.raci1/ wa r5r99x pp4yyw(t.ysbeo-*uctor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. 5cy w* -1 yxwr w.9yreb /o9yty.ira(4pspam* What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aftem./d2d) iulwwg9(n eugyf 8 .ir it passes you, its frequency is measured as 486 Hz. How(e.d )u 2dinwwgg/fuil 9 my.8 fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just/ b+z do6svx8,wmj g o1yzohn1.ac 9:t by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound+1zzdcvsoo:h6 gaytn 8m9wx/o 1bj ., 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 beat frequency of 11 Hz. The fy-7)(j l ruuinh.z l:shorter one is 2.40 m long. How long is the other?j lnluuf r yzh.7i:)(-    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a sti.ne9qzgcm7x1no4 0 r ationary 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 1 emoxri qn90c4.n zg7between 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 normally ab)3h)b. ;caafkab ::gps 8weg; iwe 4tmout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflecte.ba:mwhg4 f)w i ae:t ekp)bgasc 8;3;d 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 flyitv wu e-um(,0umk-m/ kng toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat aku,0w mu/u m- ev(mt-kfter that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches on9f;rha l mt+0tm2t* a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo fro ohm 9+nr02t*mtaf lt;m one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once uorq3l -fp/8 f0e(ntkyw k9 9ovce:l-jsed to send signals from one Alpine village to another. Since lower fre9e/fv o-8:ntoc 9eq-0 3kkyjfpl lrw( quency 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 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 st0c3(k x -46h egh,8kdqcj tochereo 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 6d-3eh8ox0tj chkqc , 4 (gckhm high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singio, un9,w*mjw4iu k.wjng rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked wi4ou * kwnw,uimj. 9wj,th the other hand. With a little 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 threshold of hearing dj av+f ys,7 x/0f9xaufor the human ear at a frequency of about 1000 Hz iafx+, yj0vdfxa /79 sus $I_0$ = $1 \times10^{12 } W / m^2$ 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 observuj://ka-a(j 4u xhydy rm,r8ger on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s ,/ghaj4 k ur8: j/ya rm(yudx-altitude?    $ \times10^{4 }$ m

  The wake of a speedboc w7p, w:y7rmrat 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