What is the evidence that sound travelt sapnf-z ; 1e,+e5xxzs as a wave?

What is the evidence that sou;iu f fizx3/pzvs*)10ch xj 5snd is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a strz62mz *fc9.5oled jysing 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 otherf.scd *ze65oljzym 92 cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes mb( k3ic,1 oc1gyvr c+from air into water, do you expect the frequency or wavelength ti1yvc or(, c g3b+k1cmo change?

What evidence can you give that the speed of sound in air does not depend sign opksaxe fw64r ab3.mz8q23( eificantly on frequen6bza3p8mfqw3 axs2.o(k4e e rcy?

The voice of a person who has inhaled helium sounds very high-pitched. Why w-k+bw 55ds+dvf 4,ebxu:osal o ,(ob?

How will the air temperature in a room affect the pitch of organ p fh7ixl n2m/eof;a/r; ipes?

Explain how a tube mighqc 94i:qcn;5n- l(bc5z jlm rb26 bhtrt be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An emrb- n;(ccqnq bj:5i9 l6 bzt452lhr cxample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) space il;cvfgq9n4fi.m q27. cut r(d closer together as you move up the fingerboard c.g n72r iff m;qt9cvlu. (qi4toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it butsfo cz(+lf5f:c (w um8 cannot see it. When it emergzlf mo:f(+w8ccs5u( fes 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 “interference qrlov62i :,. kvy zarxk4:/ bpin space,” whereas beats can be said to be due to “interference in time,vp4 rk vi. kr:z:ol 6q/2yxba.” Explain.

In Fig. 12–16, if the frequency of tr,9p2 d yuvmu9he speakers were lowered, would the points D and C (where destructive and constructive interfer pdv 9yr,2uum9ence occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peoa rh:czev r .xys9v+/1 gcb-c3ple who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts c3b.+ s zegaxvcy19/r-c v: hrit 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 wave can be thought of as a3vr l(r ga169 3zeewscea*zx0-3xdkzg 2m-zn superposition of two sound waves with slightly di3ev e rz-eagz(9 wz 3mxn6r23cs- l*kdz1 0xagfferent frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source -z*xs0c:q c t9cdxs/.v yv gahlx4+ (cand observer move in the same direction, with +d v4q/ x:gcyh.0xls cst*ccv(9z-a x the same velocity? Explain.

If a wind is blowingdz2rwmde 1p)zyw6 3/z+z )mvv, will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength o mz rd)/ 3w2v)zpzey6zdwmv1+r velocity changed?

Figure 12–32 shows various positions of a child in j b0,/; q+edb0tqtyr; m .mienmotion 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 chiemi;+db.r 0j/bt0nqm eyt;, q ld hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by zmddnc7* 9+,cdo 8kj alistening for the echo of her shout reflected by a cliff at the far end of the lake. She hc m oa7,*n9jdzc+dd k8ears 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 jusc ,vhfxi0vew1dgz*bru+ f nx )-+u/8ut 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/s-w0xzbrfcxfv* i+)v 81/u+ud,e uhng (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavele o ,c5xljx+tx-bsr h8-ngths 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 driftingli c;imr)1h7q75vz; oj5e80b dfeii7 gi4snf just above a school of tuna on a foggy day. Witho4si 81e7q 5b7frmi l vez;gi5if;7d n)0icojhut warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking tn)ynv 04okc88(fs0-gpgq yty6,mz)t s u u6tk he water belowkg)c0gt0y,-4znmtofu8 )yu8 6 vnk( qsy t6 ps is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stm7q m1tlo3.mgjm8npo;g8c g , qsmo6/one strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concogjqonmol 7pmg /,8ct 1 mq.m;gm86s 3rete, 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 /.dfra /xe7 bs6d-wj kof distance by the “5-second rule” for estimating the distance from a ligh kf -r.xbsd/wad 67ej/tning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at 1:lye n26xrgkyi mc tu4245fhthe 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 afhl;in6dsm,(uxu27)mc m o*whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when flqhqxy)u lltrp ;, h-9tvq03 5ired simultaneously at a certain place, what will be tlxylqqh )0 v-u,;httq 53rl p9he sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an 5x.*vj k6, yu xzsxwv8 vl,.rlairplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shutv , 6,.xv*sk8 5vyxlwxrlzuj. down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hi4b; yo xc;3a:lxb wd*ave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and t :xcbl;x 4 ;*dio3ybwahe background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output ofcte:r98n,ofgyj3 ; dh k-.ypx sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on th-kgnj.;yy: r,cpd3x oh89 tef e 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 u.imv* git ,*uwhose 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 nb oqr(3 hr3t vbtv3p jn9z+glg:*a56b+6rg trated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a p+ztv36vbg pt36lrnt( h9+g3a*ron b5qrbg : joint 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of aimvat4 -ct9t 5 loudspeaker -vmt9 i4cat5 ton 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 differencew e9 ,nk cpq27ky+v*la in 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 1n,+v lae 29qwy*pk k7c1–9.]$\approx$   

  If the amplitude of whwc 9.y)3zsd a sound wave is tripled, (a) by what factor will the intensity increase? Increase by a factor ofh ) 3.wcswzd9y    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice thew*0cmyk 53 r ilz,zkj;dmec/2 frequency of the other. What is the ratio of theid2m c 0rzl5jk,ewzc k;3iym/*r intensities?   

  What would be the sound level (in dB) of a sound wave i9 o )msmj:6owmn air that corresponds to a displacement amplitude of vibrating air molecules of 0.ojmw9 6: s)omm13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz , r stk 1uw0huw3ur4*htone that has a 50-dB sound level? (See Fw4r uuhsr1tu3,0k*hw ig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the cwb osxr8;(wo9 heey+o6 q;(a sound level is 30 dB?(eqb6;;ar 9o(xow e 8hcosw+y (See Fig. 12–6.)

  Your auditory system can accommodate zy7lj,(fd6s( m o+zwz99vk f*qsh) p ra huge range of sound levels. What is the ratio fyo)fzkjvs9 9rp+zdqzsw,m*h((l 67of highest 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*drs6wvi* w o6 of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.dwvs6 r6w* oi*35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundx()m,m p+e xz7 3xdc+fwvi su;amental and first three audible overtp,e+ m;()fx xwcu3i+zdvxs7m ones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the toq:nyxjf uh 3/rxz-lz s9c9k*3p of an empty soda bottle that is 18 cm dehs9 y3znfxl 3k*zc-:j/q9r x uep, 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+n ,()omtwwmmv oo0/ a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of/vomm(m+ao,o n0 )ww t pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency ofpxc nwo67 iovcz 0d) ko9xw45fv- *wh8 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of onlz9o4oxhn w6w* pcxcviwk-v)d05o7f8y 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tune pexl czafq5hk m4qe 1:21)m0md to play E above middle C (330 : am4ef05mqpq)x1khecl mz12 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 of an open organ pipe that emitsc2.0dww ;wqzf middle C (262 Hz) when the temperature isw2zd0fq .w wc; 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 ate( d)fnhgpmz tku6pj5: j;g7qyb6+g. 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 Examppqw 21tt5ai46dfr0b p8dcov 7le 12–10 should the hole be that must be uncovered to play D above middle C atq wb2i1 f4t65 p0odpv7rd8act 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, anfjs(3kqb o)7i *zs1+o qgh3omd 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed qs j1 ozkbq3f*gmo o(si37h+) 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. It9d9 znwbx6bor diu-gq79w12b resonates at two successive harmonics of frequz 1odwr-q b9gw nb u2x9b9d76iencies 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 tl a aaex8c;r j4z;2/q$^{\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 8b1j n5dhe)mf(g h8pi4c iy6x within the audible range for a 2.14-m-long organ pipe at 20b n(45 fid8gj61pe imxcy8)hh $^{\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 andnm)s k8 wefal1i2s0,n is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the e8w1s)m 0iae,fs nknl2ar canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat c1g(8q kl z:7un0 yr,vwyzvm ta14,dh every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency ismnvqh1 v, 1:y,gzt( kyr4 w8zcdlu 7a0 the other string? ±    Hz

  What is the beat frequency iff lao gy1tl8r+ l1j0;x middle 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 23.5 kHz, while another.i okcd;;darjq( 0mvwux, v,) (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a s(;cjr ku,d q;vw) 0id.a, mvxohrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded 3fzxb ,0hhg cn-lbe +fnu, 82gwith a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explf,ugebznh cfnx3-b0 h+8 l,g2ain your reasoning.    Hz

  Two violin strings are tuned to the same frequency,d1-rp tbo0ak( 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat freqoa( -rp1d0 btkuency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if t-)p qyrf4 sb j4zt.e4awo identical flutes each try to play middle C (262 Hz-.a) e4bptfsyq4j rz4 ), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and /u9kpwefh;v ab( d1a,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 e(h1av ufdkpb/; aw9,and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A prxh 13x7sp(tcerson stands 3.00 m from one speaker and 3t731x (xrscp h.50 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 tuner hea4jc*7 u 7lvgqn 3wm8n4z4 mldyrs three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other*q4 l8mum443cv jn dw7l n7zyg ?   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 2.7ys1-2 w hi6n npimpqp/:.eov+6 m in air. How many beats per second will be heard? (p6n : si on-2vp+ye/1h mwip.qAssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at rew st m0(4lo le2ru2m2 vro)bz-0zp /jjst. What frequency do you detect if you move with a speed of (e0 vu-2ltr4o2m0rjb/ sm ljzwp2oz )30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency l7ls aru.av0 /yi*3)k)dq -aqdx7zjw do you detect if a fire engine whose siren emits at 1550 Hz movesqd/ur)*ja-yi)l7 x3aksz . w7 alv0q d 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--l7 4i0lqoo swHz source is moving toward you at 15 m/s versus you movin q4l 70lswoi-og toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is (cx;kjh0 g88znz yn4 vat 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 frequency8hgy4j nz(; n8 vkxzc0 the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves awa* gaf0 kv (zr4g*;qwt 50.0 kHz and receives them returned from an object moving directly away from it at4a ;rgzkwwqa0** ( vgf 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 As it fo rcb59lrxceug49,0pu3r qr tn m-q:zj;z 2 b1lies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear ij1q39pzt,;4:cqbe- 2ro5 rxg9 bmuc0lrrz nu n the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler exg; jfs+7hwst; t,/mu xperiments, 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 station. What beat frequency was heard if the train car approachw, / +ftshs7 ;ux;jgtmed the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suxmyt3*62lbf;ou aao0at5rl3a3( dn kdvr*f7ppose the device emits sound at 3.5 MHz, and tt3vda5x(uo a* 72o6r r*m;aa3lby 3dflt nkf0he 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 otlib- :j/rnl 2f 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 freque2sg vt. 7f 4lm5otwvvqgqe*g20 (m*sency 570 Hz. When the wind velocity is 12 m/s from the north, what 02gqvemt( gsq54elm*7o vf vtwg2*s.frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on lans e jn6svvz2+n. (jmr+d 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 q ox1q1tjjv+ v+9(ipkis 310 m/s (a) What is the angle the shock wave makes with the dpj+q1t1 qi j vxo(+9vkirection 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 j*/novxc k54 ypmb/;ehs/(fhj 6 0jab thin atmosphere of a planet where the speed of sound is only about 35 m/sob4spaxkn0jjh(5v6h f/ c e;my /*j/ b
(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. Determine o* f zd6hcdc-t0e n7/zrll :2vf7teopk,u4p-the shock wave anglep*t6,ocpn0hl-:/e72dlf k- uo 74dc fvr ze zt it produces
(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 +zlqm6ifj4je7 4 r p4n$/theta$ 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. o8/px/xoo *h+j ;oidr5 km above the ground flying xj*o;+opdho/8i / xorfaster than the speed of sound. By the time you 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 device that sends 20,000-Hz sound pulsesgrsjb(uc9r 7 * 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 g7 u* jsrcbr(9time between pulses (in fresh water)?    s

  Approximately how man:9,gm1ibbbhc dnd ) r:y octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of mazktj- - u lze9+3ujuj;;+xpvnny plastic pipes of vari-ejuj t3lzj+;9u; vp+-kunxzous lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound tw,rj0e4ne.u tq/3kx close to the threshold of human hearing (0 dB). What will be the sound level .k/qex r3tut0,we n4 jof 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB e1 ,avrrj;sw (sound are heard simultaneoua1es(j ;,rvr wsly?    dB

  The sound level 12.0 m from a loudspeaker, placed in*qw qppan 068i the open, is 105 dB. What is the acoustic power output (W) of the speaker, as wp q6paq8i0*nsuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hzt-y/q w-d p:zqvmb/h6 . The power output drops by 10 dB at 15 kHz. What is the power output in watts at 1b-6wvyz/qh-p/qd m:t 5 kHz?    dB

  Workers around jet aircraft typically wear protective devices ovkvbpp qg:g *3+er their ears. Assume that the sound level of a jet airplane engi:qvbgp+ *gkp3ne, 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?    W

  In audio and communications systems, tg*mahxt.xr1jr (z zzp 3 s56,yhe 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 violink83uwhb/f pzm- oy+d*k23p sg is tuned 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 fixed pointsqjx2ddmnrz71w 7j k: 0 with a fundamental frequency of 440 Hz and a mass per unitk2d 7 jw1dq7zj 0rmxn: 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 vibratiowrqw ,c * cl.wgvx8b::5 yeb,y-phv-b slj9h;n above a vertical open tube filled with water (Fig. 12–3 c bwsvyhb;*,h.eby p:gj x w vl58-:,wlr9cq-5). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar s6:vw l 7;wxcea2hducp ,c2dyjv +8 fg9tring of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) cvyjx 6c dgdv+e,2f ;wlc92u78:hwp a with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full llyy2q- pk5 v+fox2)x joop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sondhylz3mb4u/v : wl )+urces. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person mov /mbnwz4:ud)h+yl3 vles 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 stationara(hozku .(a- r h nrv+re*a+p6b:8wkhy. The conductor on the stationary train hears a 3.0-Hz beat frequency when the ot ra:+w naeak6 *z8. r(k+(uphvbhhr o-her train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whi) )cewa/az +tv(ijg se8vrw7 9stle as it approaches you is 538 Hz. After it pa+sge t7 zr))e 9w(/vvw8ac iajsses 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 estimate the speed of cars just by listening to the diod)-l a9;qkagfference in pitch of the engine noise between approaching and receding carsa9k o-alqg; d). 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 togethertvn7 3/byd(re oz :h/f, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other? 37y tebzr/o n/f:hd(v   m

Two loudspeakers are at opposite ends of a railroad car as it moves past a 0jcl.(ahxe ox9 *wp/jstationary 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 freque0 *jexjlahp9.o(/xw c ncy 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 therb6k2nj/ yut *y -v9z1iy ri:u aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a r26bunyyjuizt :9v i yr k/1-*speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a o.y,-+.lpv r jjgqf4q moth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHl.+ pj4q,jv . yoq-frgz. 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 hi.ke8 vqqaq4z u)63s szhrsx8b 1i9sd /gh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 mssxe8kz3 b4/usisv8qsq9dqh a. )zr61 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 signafl-45pn4ghd )p 2jlq hls 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 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, ang-p4 2d p)n5fh ljq4hld which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo9q()7e mc w2ayye.,i1aokx u i listening can be compromised by the presence of standing waves, which can cause acou,y im )oe eakiu2qwa7c.y1x 9(stic “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.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, -v4awtjmc 8 n6slender 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 6wt8 ajmc v4-n“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 for the human ear at a frequency of ab b-osrk z3xb/i;eb/(yobo0oz 810bs dout 1000 Hz b 0zyo; b be sk/rd /ob1sbxi-z3o(80ois $I_0$ = $1 \times10^{12 } W / m^2$ 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 g4eff(xmx, h,x 98uhvMach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plan(u8x hg,f4v9efmh xx,e’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ic wg/x0f7zf rlck8 dr.(-lo,h s 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