What is the evidence that souys:mtz + 39qovnd travels as a wave?

What is the evidence that sound is a form of ene roiu2.m*e wnx 8zw1,v i/-pgprgy?

Children sometimes play d p22n fnk96w(7n3:r ;oyg kogmwauji1 nf:t ,with a homemade “telephone” by attaching a string to the bottoms of uj 31kwg2: ,n d9niwgam76;rtynfp n2(fkoo: 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 the other.

When a sound wave passes frov +e-ma ye2pv*p 94uo ieg.cz/m air into water, do you expect the frequency or wavelength to change?.ve -vip*4/uzgeapc om e+92y

What evidence can you give that the speed of sound in air does nolj1 f dv*cae)4t depend significan a*)ve lf4cjd1tly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why?va7/, nl7,tu a6i 7 3 :wzuhltppo/qkl

How will the air temperature in a room affkw fg ,(,l8urq.zkf+k ect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soun;i1mtvbpp f;f,*n u 1kds in various frequency ranges. (An example is a car muffp;u ,vi;*1npm 1tbkffler.)

Why are the frets on a guitar (Fig. 12–30) spacvzu -b:piq 1se0u 0bm1tx6o( ded closer together as you move up the fingerboard toward x su 1 b-mq6tio00(upe :1dbvzthe bridge?

A noisy truck approaches you from behind a building. Initially you hear it i2ex s5gp6i*l )2wfsacoqjw9uc-66obut cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the hc6csog)5oplq 2w2f*6j e6s-9 a uxwii igh-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spaceip3vxe/,7b6 p tx -1rnn*ceyb,” whereas beats can 1xc3 ybb ni-r7e/,6v et*pnp xbe said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the sp+7d oaw8(q/j-nf fra seakers were lowered, would the points D and C (where destruct-+rn/oa7fdq aws j(8five and constructive interference occur) move farther apart or closer together?

Traditional methods of protectinq1bkal6nl:1 qev q9orke.2h ds3j1 b)g the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones ib)k 1d.solqnv a3hq jl1kbq1:r69 e2en 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 wavev7ekiklwk) 23y 5pbx+beze*) can be thought of as a superposition of two sound waves with slightly different frequencies, as ilwbb k k+pee)x2 )y*zk3ev5i7n Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same d79 pt6 h.a0pk2dn qy/l o*pt. kvtztd5irection, with the same tapl0.7/ y.hd*ptdt zo2 nk6k t5pqv9velocity? Explain.

If a wind is blowing, will this alter cfqssze 59 qlsd 79(d5kgf2556qjnj i the frequency of the sound heard by a person at rest with respect to 2n feqfz5ds5 9 q9(sscdi5j5lk6j7qgthe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motionhl-y)9w aif: ,cnd g0v on a swing. A monitor is bloyh: 0a-l,v ig w9dcnf)wing 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 the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of:aw (l i)aopn*zkcr-3 her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimateo *a)i3zan:w l-(kpc r the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship j(dtb,61oly zw ust below the waterline. He hears the echo of the sound reflected from the ocean floor db(zw6l1 tdyo, irectly 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 wa2 3 :0g8 ixkjs6 4vtjsrmcml4svelengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above m*yf8mc 2f777dz zhfx.tb .u5hm4nqj 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 elap cn 875y jzdbq.*f7u2.4xzhtmhf7mmfses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a 3azey g5b.,q,bn:zrk8wh oh.f01 pkt cliff. The splash it makes when striking the water below is heard 3.5 s pkhek5h.1a zb8f.n bwgz,3to0yr: q, later. How high is the cliff?    m

  A person, with his ear to the ground, sees -fwwnm0(e9i sa v36d idt5u9v: 9ydmca huge stone strike the concrete pavement. A moment later two sounds are heard from the impa5f c dw90 m9vniim6:w9-d(dt3 vys ueact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-seco/q2ix;.ninlsm,m 8 yand rule” for estimating the distance from a lightning strike if the temperature is i. 8 nya;,qnsx imm2l/(a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thoi8otn3lxj;o- e.u,u .6b bgfe 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 ofkt89/ l1g jyof a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneous*eb2 zg2 k6-n *wfutuagd oy*1zi*h1sly at a certain place, what will be the sound level if only oneianw 1ku6zu g2doeh1fb*-2zs*ty** g is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equallf:( o9p9jbkn jyskawo hr)2 7304 ckruy noisy jet engines is experiencing a sound level bordering on pain,nk3kb2r h: oajw suf79j)py4k 0(roc9 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereaszv5aqfl x:g 34n6a5 3lz)brm g for a CD player it is 95 dB. What is the ratio of intensities of v bx3 a zn)m6 345:lglq5grzafthe signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a p njm+pee2o cg42vtbi l2x1::x erson speaking in normal conversation. Use Table 12–2. Assume the sound spiemobnepcl4j2+:tg2 :1x xv2 reads 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 strik:)h guh5kq( zwes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 2bpw8 ,hm*z-0(jj y6bi7qw vxz50 W, while the more modest amplifier B is rated at 40 W. (a) Estimab*w0,-6jix(7mvhbj wqzy zp8te the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter rk/gssgpd192 iszd ,q ;egistered 130 dB when placed 2.8 m in front of a loudspeaker on t1q dsz /ggd29pssi, ;khe 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 differencap ,x+ dsm*qu2eq8squ0bf- 6 5 xff5oie 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 6f iq0bum8,qfsps -uaxfo25e d+qx5* Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) b9*yp77:dspgfjv j (k by what factor will the intensity increase? Increase by a factor ofsyfj:pd7 j*9p7g (bvk    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the frequeion:tbxx: sk*;m3) jfdr5 q(e ncy of the other. What is the ratio of tni 3bdeoq:rk xfjs(: )5*mt ;xheir intensities?   

  What would be the sound level (in dB) of a sound wave in air that z-hsj vq8o (hp l1zcxx.2h1w:corresponds to a displacement amplitude of vibratingwj hc zqz:-8s.xph(v xh1l o21 air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone thatqdr787-ha6n 8ix aody has a 50-haa8rqd67idy7 no 8 -xdB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can dete :yjj)fa. s5/dbk .nbcr;viks* :n5hqct when the sound level is 30 dB? (See Figvnydbsi: 5q j)nfa; .* skjh5b.rc k:/. 12–6.)

  Your auditory system can accommodate a huge range of soun ;qptg/rhzlkfo3,( :q-oun 3nd levels. What is the ratio of highest to uqt;o,orl gh/n pzq3- n(3:kflowest 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 freq+ (hfu0 +x:rngoi0 0zkuy .qfzuency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.x.(o 0n 0g zfui+uyh kq+z0fr:35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Whah9xycyyse .2f c7jn7 ,t are the fundamental and first three audible overtones if the pipe icjsh2.,yy e 7nfxy97cs
(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 fr9wy +a0d an;e1buza q2om blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a cl ue0+azy2 baa;qwn9d1osed 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 open-tube pipes tb2)je/-zbd ye c*mjpes 73n2spanning the range of hume bm-s / 3e2)pnc*bdtz2je jy7an hearing (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 Hz as its third har2hjx4 zpi eo6k6/ lf(amonic. What will be its fundamental frequency if it is fingered at a length of only 6fpha64iok(lj2 zx6e/ 0% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to pydqei:9 w o.:flay E above middle C (330 Hz:ify.qw :o9e d).
(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 thav i;i vvp1 8)u*zc3awyu x,ep;* mgm/ut emits middle C (262 Hz) when the temperaturyzae/pvw;im1;3mcvu*v u )*g uix ,8pe 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 agc-6jvah/s *+grlak.za1+n 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of r bltowax zp-*k6-(h+the flute in Example 12–10 should the hole be that must be uncovx*+zhpk 6wr-ob (tl-aered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipikl2. ai:v.bh e can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betweebah . 2lvk.i:in. (a) Show 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. Il-d-.slk;52g oe+ tq7tr b*t5jqay w jt resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What ist.d ta-jjoqb5e5ts7 lq*gr-k; w2+ly
(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 4+74g, vu0 zkpx(yy:y dgdq hr$^{\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 wiwav/zd 53* artrw/)f3vd m:)- ktowmuthin the audible range for a 2.14-m-long organ pipe at 20 -w mart 3w)/u:rft*/odv vawk md)z53$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately hxs4r koq i.5s-tax(z v:q i4+2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your ansx xi45iqoa:(rs k4z -hts+vq .wer 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 every 2j4xj/gpj: sci27s s h j s4w8yp1xb09l.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the otw79j0:i c xjs8jxy44g psb /sslh12pjher string? ±    Hz

  What is the beat frequency if middle C (262 Hz) av at/w(k./ q*,rtc( obn)visnnd $C^＃$ (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, w 8aw0kp5ao z 7kkv,:t4y 3npelhv+:gohile 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 occu gakv:o4 t:7ek+l8po 5w3k0a pvh,yznrs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded w1lu8m 3: y6tqor ac hehy*.re-ith a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the stcy-* h.1:rlaq3y6e tu8oer mhring? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The gsc52:3o z ofypk5ul+ s -pmq5tension in one string is then decrelc 5z+o ysp5ps5fo2- :3kuqgmased 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 hem*t--rj0rv 7 l/nnze iard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°rnr iv/70emt-zn-j l *C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of px);n- zy0u3tsi nt3rlxx 3 0f441 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 are possible when A and C are3 ;n3 yptfxxrts-003x)iun zl 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 onxmt n( y15oc.14vus fee speaker and 3.50 m4 e5x fo1ysv. (ctun1m 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 aijo35wfxjpz ,b i+-j ;mjs7w3 piano tuner hears three beats every 2ij+xbwfw3;5 p,j3s-iz jm 7j o.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wad :b c c:x2zyk. t tbu4+vd0p*vdf(r8yvelengths 2.64 m and 2.76 m in air. How many beats per secv:z2x.b4 bf+yrd 8* d cuttyd cv(k:p0ond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certa +r)zo1 a;eeoyin fire engine’s siren is 1550 Hz when at rest. ) 1zaoy+roee; What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if ami :7f;llsb osz m-i.gp7p 4:a fire engine whose siren .: mgoslsziafm plbi7p-:4 ;7emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in f9 dwax9(w20:qrn1 m umsv9cvxbf*k w+requency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are2x wsqx m9w9afw:v9ur ndc+ v(1kmb*0 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. Whr5 tw79e ma5vpvbrx*7 en one is at rest and the other is moving toward the first at 15 m/s the driver atr7x59*vw m 7pae5bvrt 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 ana3bo6 1b6z awtfd/5ool74x end receives them returned from an object moving o/wlzf5bxa t1n66doo437baedirectly 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 of1rz7q9h e9j l:rs.n zo 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does:j9q ozrh 79 s.zenr1l the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original D6l v)rjl2i/,5gy95kecz y oz9ti i.izoppler 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 station. What beat frequency was heard if theii glr, o5lzvyzye59c k2i)jt6z9/. i train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves bor6q .+)i r7d oo;xq+wxjii) to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat freque+) +or.wqjirx ;7booi6q)dx incy 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 f rw 0wm8 d5 7sewm1hkfe1*e+dwrequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wigbw0 zzvj. mdmxn:z -y,k*a8g8t* ei+nd velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest,m* k0-gx8bjg vza *+.zzeyd: mwnt, 8i
(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,3 +qnan9 hh v.x9wvzi)-wq me 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 Machwdmef(90ecdko : :-oxnuqb *0 2.3 where the speed of sound is 310 m/s (a) What is the angle th-co d dx:f(q9eb: kune0o *0wme 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 znsy wf 30)6e16z4b+ vtwkuddatmosphere of a planet where the speed of sound is only aboutzyd f 16)+w63vne ubswd 0kzt4 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 milb7p*-aj;f i:lk1u.d:aijyn4 d)fs /s strikes the ocean. Determine the shock wave angle itbjidf4s)li- knf 7li*:1j:ya. dp; ua 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 inq+metl 5 g+-5q ugbv3 u0hg/$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plat1n-6)0u.zin dkg 3zi (z vlvvne exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear tvtzg -1)i. n(l z0vdkuv6n3 zihe 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- 6f5.qydxxq 7d ch3u0bHz sound pulses downward from the bottom of the boat65 c d0qhxfx.uydbq73, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range qczjh0 9/vgf*yw gz/9? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dirf ok.f n/0(qpsplay called a sewer pipe symphony. It consists of many plastp/o(k .frnq0fic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshol .tjypd)c0zr 3d of human hearing (0 dB). What will be the sound level of 1000 szt y)cj3pd0 .ruch mosquitoes?    dB

  What is the resultant sound le8ncv /w gc z+rc--qlb*vel when an 82-dB sound and an 87-dB sound are heard simultanez+b8c -*/cncg w-rq lvously?    dB

  The sound level 12.0 m from a loudspeakerzrdxg :a*nxvz: s03:k , placed in the open, is 105 dB. What is the acouz:r0n a:x xdkgs v3*z:stic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dro4as -fmi j93vgps by 10 dB at 15 kHz. Wha gm a3-fijvs94t is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective dev 4(mjixvc otk+z (rg*.zu1v8 jices 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 r v.t+(g(xjozkv 1c m8zui *4jear 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 communicat)pz4ltr e 69*qm igoz/ions 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 tuned to a frequency 3jko0*jw:v/e)r-- cjd vrxtsx, z:eg1$\frac{1}{2}$ 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 virmme;:+ jxz: m3 bqt(uolin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit e :3m: brxq;t(m+mj zulength 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 vibravjr;vvgv 9ls*b- vb s+m3- .pa5oj*sdtion above a vertical open tube filled with water (Fig. 12–35). The water level is allowd vvjb .bsgvjo+r5-s vvp9-*3s*alm ; ed 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 stringnk7hw; c4r5nj7be m 58r9a uib 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 7r9nbh5rw8 5uia je km47; bcn(in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as onl.g)u .yzpvce )z /ssjgsq9zk) 5lz,,e 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 range coming from two source.1r5cruu* -aiihluvr,wi0c( s. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequenchi( a.uuiivrr *0-wc,1r5u cly is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whi do*8k s5. y-/phiihlustles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when theskp-h5.i/i8 ly do*hu other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistt;ubl z pfm s5qdvwhx99/0p3. le as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the traplz b muwpsh3. 5;0txq9 /d9vfin moving (assume constant velocity)?    m/s

  At a race track, you w 7 encxg2g445t4jysccan estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequys4e47c2 cg j5n4gtxwency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounjf bpxshpcj;/6,* df1ding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How lpc ,jsj *;xf1h6p /fdbong is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stati+a;f xr)uot jd8+ ckg 7asd1g-onary observer at 10 m/s as shown in Fig. 12–37. d8rf-d atag1x 7 ;su +o)gk+jcIf the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood x. *cnzy8 ;*ibfn*x9 tvyq+fl * /bpgsflow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume th. s+*t bzl/ i*yg;fxfv*p 8qn9c bx*ynat the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towardva; xo1jsp(w r.t683d*vwi x s 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 after tha;x o*tj pwvx(83w 6i1s rvd.ast wave reflects off the moth?    kHz

  A bat emits a series of high7,h5e:psia zc p2 o51s-ojmmn frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apai:s zo5a,7o12j-nmpemc s5p hrt, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villal0ye8.oib3 nl ge 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 nb.o3 lyile80overtones 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 stereo listening can be compromisess+u)o: x;dvwd 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, ando;s:vsd +wxu ) 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 wk(w2l7 o:/ vfi/uzuv 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 soun7:/vou/kvluf 2 i zw(wd. 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 hag0q y 7sk67rthreshold of hearing for the human ear at a frequency of aboq7 a 67kg0shryut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic booefjcbs ,;c1gnq1v gen68uvd+z d m+16m 1.5 min after the plane passes directly overhead. What is the plane’s altitud6z cj1 6q ,+gdg; efu1 8+1dnvvmecsnbe?    $ \times10^{4 }$ m

  The wake of a speedboat isakwrky8i*2: x-vp6 ,ai.gc+ hbp7jkyul3x7 f 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