What is the evidence that sound travels asrlwbf/i. ljjpo 5 k,hz.n 47(x a wave?

What is the evidence that sound is a form of ener .;w bq 8 +nb h.hk37cgs-vrcdqrx)jv.gy?

Children sometimes play k:6 qg)ozax3uohooc, m4i j(r)h xi- 1with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched anmq ) 4:ii(rxj3ooxgc ka o1z,-hh6ou)d 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 from air into water, do you +( cip cb;h7a:w 2zaveexpect the frequency or wavelczv cw i2(e:ha;+a7p bength to change?

What evidence can you give that the spe +svq/3;e5lys dcmk fkkw1a*,ed of sound in air does not depend significantly on frequenvd,fk/m yl3s ke1q5ac s *k+;wcy?

The voice of a person who has inhaled helium sou4zvt y+x+,x : i**q sp ibw /)ok-.rlnfizd*eunds very high-pitched. Why?

How will the air temperature j qb/ucgl4y,3 in a room affect the pitch of organ pipes?

Explain how a tube might be used as wu7; 0o m3 emfv.uduq)a filter to reduce the amplitude of sounds in various frequency ranges. (An exampdm0mw ; u o3v)fuueq.7le is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as ydx9dscvxl,8 1b+zbx )z ,vlp +ou move up the f1 )lslvbzx89 v,xcpb+,zdd+xingerboard toward the bridge?

A noisy truck approaches you f) njh5m*kge47( ;lapcj (i abqrom behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffractq a(j5* b jcpgealhm4i)(n k7;ion.]

Standing waves can be said to be due to “ hdih:zte)2 b*interference in space,” whereas beats can b *zidthb:e h)2e said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, sh1i: kiy6j9encu:;z+z 5 *tsb k .oulwould the points D and C (where destructive and constructive interferencec;5bs:t e 1k+nh9si:.u*k lz6yzo jui occur) move farther apart or closer together?

Traditional methods of p p+wwzasu6 .z8y y7.cirotecting 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 ip8s+yz.6.ywa uiw7cz t 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 though:nc0p 4zl254csp8 bb ndtczx9 t of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (az9ncp2 4c8l0dtp:bx5b nc4 sz ) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observ9k ja 3nfmwcd9l4tt- )er move in the same direction, wit )awt j9l9mn43ck-dtfh the same velocity? Explain.

If a wind is blowing, will t efs;*yfbcs-umro99+t t: *gqhis alter the frequency of the sound heard by a person at rest with respect to the source? Is the tte -bgofsuyq*f c*r ;m:+s9 9wavelength or velocity changed?

Figure 12–32 shows various positions of a child in 2an d6dz 5pvz/8yz x3smotion 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 the whistle? Explain your reasonin3/pysx6 z z5d8 avndz2g.

  A hiker determines the lengqqi is.,8r r,3-ghql rth of a 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. Estimate the length l38 r-s,iqh,qriq. grof the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side h+ u* igqewps6v6vcau 5/+as* of his ship 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+suuv epv/a wia56+qcg6s**h 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wave c rd0nu0o1 1oq*lv(xtlengths 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 a school of tuna on a foggy dayd5n: i)f o:spk,pgyj4 . Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapsydjoskn5p 4:f:,g)i p es before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cli .a(.3;qoh0jfdyprvl;i s.q sff. The splash it makes when striking the water boi dj; s.qv fqp;.sa.rhl0 (y3elow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to th-wk 0 7r79gbhi 6akwdxe ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and gwkix9-dr07 wbk76a hthey 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 overe j) 9qxva :drh6+rty4 one mile of distance by the “5-second rule” for estimating the disjr xqyvh+d96 tar:e 4)tance 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 lev06* t 6wrpkf(pgwsj0 nel 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 q7p tv) h(;klu0+rnqa whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when f 2,rjihf: c gjdsdw4:8ired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities:w:4j,8 dd2 irfghjc s, not dB’s.]    dB

  A person standing a c:tfuc40hc 4xxertain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. Whaccxu4 :0t xfh4t 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 ssmue 7* 4:wvhd98fs c,jsn7r fignal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of s94:v unf*s7cj me,87r hsfdwthe signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conver6 s1) k)kraoshsation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere ceno1 s )rka6sh)ktered 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 sfk:9w2kz.lrzs 6ii7 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: -cahdoyh2c+ c5nuh* 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sounuhn- odc2h*h ycc5a +:d level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 9* rbz dovo.n12.8 m in front of a loudspea*b.o1n9 ov dzrker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. What is3rffd-h ez/:tyfh o n ;n)(4a0sw7hcw the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 1cwazyfh7h0 (nrdtn) f: -o ;4w/shef3 1–9.]$\approx$   

  If the amplitude of a*5 +*bia s cetkeaj80(a5icm u sound wave is tripled, (a) by what factor will the intensity incre 8e0tc( *i ca*mai5as5j+bukease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemenyeve.il+ qy*d yv 121oyv9/p dt amplitudes, but one has twice the frequency of the other. What is the ratio of thei*v y yvveddo pq./1iy 1e92+ylr intensities?   

  What would be the sound lea0jr+y6qf e3z. h,fr bvel (in dB) of a sound wave in air that corresponds to a displacementj+b60,3eay hfr .q rzf amplitude of vibrating 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 3 ewp)yzb7(wi0an-gb 100-Hz tone that has zwnb(bae3 -g) wiy70p a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the s8..7ju4ot qa aapwqt:rg r -,aound level aa4-r ,tq.oraj:wp7gtq.a u 8 is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of so quefl5m; o3j)und levels. What is the ratio of highest to lowestf 5 oue3)m;lqj 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 funda(rk ld6dy4/gky*bk zld5b72zltd 3 sn2b ;tx3mental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g (yb6xb 2z;td/tdsy r32 d 5* 34k7lnbdkzkllg. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are c4vlgeuemn4 sb/: i/1the fundamental and first three audible overtones if the pipe iss/4eiu4 be1c:vgmln /
(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 (y rmqdvayupp57v3s e: ;+r53bfz: qzexpect from blowing across the top of an empty soda bottle that is 18 cm deep, if beus 57appyrq+zfzr 5(::y3 m; v3vdqyou assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of jft6 e x1 h*l46kcyy4zhuman hearing (20 Hz to 20 kHz), what6 jh6c14yzykx* e 4tlf 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 .,byod/431xqbjx y w oHz as its third harmonic. What will be i,xyyo/qd.4b1wb j3oxts fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m)j9rzg vk* 0sfnjelir*cy/ () long and is tuned to play E above middle C (330 Hvrfz 0ync**sg jrjel/ k (9))iz).
(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 emits middle C (262pnopvssp6wk:f4 5( n / Hz) when the onpp/(k45wp6: fsn sv 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 atv2+:plnrxq v , 6pxb5vp2 u6bc 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 Example 12–10 should the holrt;.tm 3)wntr1a/so lzgn 7ucxj r/;-qwr-z0e be that musto.z wr1tx;c;q0r/7 gmnt-szn)/ rt-auw j l3r be uncovered 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 pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but no.zex) e 8zrysnb5d92it at any other frequencies in between. (a) Show why this is an open or a bry8.i z edeszn2)9x5 closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m i 3p:*yxitmsvl4r ro,wf00;aay,my 6long is open at both ends. It resonates at two successive h miy,apxliw6yo0fa403mr :rt, v ;* syarmonics of frequencies 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 iyv nze3ie2/a5g2c m 9$^{\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 range for a 28gfc)6 gilgg* .14-m-long organ pipe at 20 )l6c8ig*fg gg$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxim,nt 3 thmh v*lw/o6)7ulgyf9wately 2.5 cm long. It is open to the outside and is closed at the other endy)hw mf/,7n6t *9uowh vgl3 lt by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat evea6umcfo5xzilw:l 9m( 6-lybd*4 0wm l ry 2.0 s when trying to adjust two strings, one of which is sounding 440 bwxw4z9oa(:-lly l05 muc*f 66dimlm Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency ifozo:9ttc ma 1i8dwxz l+z2)4a 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 operateiu.uw45l7 fva9o b0 rrs at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultra9bol5rf.4 7 v iuuw0aneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a9k. u9 4wiu,xy5ykf n4 ip0h3qva0hak 350-Hz tuning fork and 9 beats/s whe5,k 90hy.fiia90yv4wn k a3k4uxh upqn sounded 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 e h3z.j*rbu(rsame frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard w jhr.3b*uz(re hen the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes e )xc:;*shgoznoo+ + atbrk )c6ach try to play middle C (262 H+sc*xozcogrh) :k;)ao6 t+ bnz), 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 C. Fork B hapx4ka.4)h*kuu ej7ppr7 ke05:exbu ps a frequency of 441 Hz; when A and B are sounded t xjp7r p*e:4hux7 u) kubpp4 k.05eakeogether, 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 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 apar0ikq tjulek5 c*tm 1*3t. A person stands 3.00 m from one speaker and 3.5*lkt 10c5kijtmq*u 3 e0 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 vibratjm:sa gru-3v 5i86 /ac l;apozing at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?gaps;acu /a6j3im v:5zo l- 8r   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.+evk6 rgvmk)yyc/ s.:64 m and 2.76 m in air. How many beats per second will be k .:gv/sekc y6+ry)mvheard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engi*dtv4y 8gv5e,r. 9 oljbxj1vane’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 drt x jo8 evlg,9vj14.a5y*v bm/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Whasouwb/q3g o6vr m9k7 *imu7+p t frequency do you detect if a fire engine whose siren emits at 1550 Hz mi6+omo g9svr7/*q3m up ub7wkoves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequ0-gg o:fb9xzl 5yl *ksency 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? Are * zs xl 9fk:ybglog-05they 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 sinkk p/(38p7n dkr1j ffygle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears kyr7j1(dpf/f 3 n8kk pa 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 them egl+qrc:kaj3gp 1 yae6 q)d-- returned from an object mecga3q ge-dr )+:lj a-q1k6py oving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall as 6er ;s1(mq ddx/us4kt a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0mud(qkx s 1rsse/4;6d kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimezx yli+r) ,b9ants, 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 i b+lzxi r)ya9,f the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to mf7iq ud0a . ns;duhpc ,:8baz4easure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is tak;:dsdi p8u4bhuqzfn.,c07 a aen 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 frequencyoq xc6ufl7bpl nh8 q2 i 0hz2/82t0klc $2.25 \times10^{ 6}$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 )qq4 tv8kxz,7nztdot ac)+9x 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are loczcat9 ndtv78qxq) )k,x+z4o tated, 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 land if its speed at ,ki sytzz(rsfv5 +i-; 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 oz 2vshn: cim.3ksf 7*vf sound is 310 m/s (a) What is the angle the shock wave makes with the direction of thesvs7vci2 .m:f 3zk*hn 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 speed oa m+z84qr3ltj c7az5iscl d*5f sound is only about 35 mlaq 48c57itjsz ld3c maz+ 5r*/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. Determ: ybf(:8qniht ine the shock wave angle i:if(t8hbq n:y t 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 x+v5yg,esk 0: ca fc/nn08su d$/theta$ 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 exac2)xiaa 3fknq4 tly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plana)3a k2nxqif 4e 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 pulsbe c4sfe.4q 4zes 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,bs.f e 4z4q4ec what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are t dst/ntbk4onv 0nw;7/here in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display yr;g-pqauc1x knatc 7/5hnd *k ,kn/;called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are k5 7/nh ;-kaa*uct, npxk y1dcrgqn /;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 threshold ofp:u*wplk4tekr 70-a j human hearing (0 dB). What will be the sound level of 1000 such mosquitoespja kk:* r0l7 tp-e4wu?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are haceuh.o.t m 90eard simul0ua.t h. oem9ctaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dz0vvne/1 )lou.- gc :z-blxmnyks+y3 B. What is the acoustic power output (W) of the speaker, assuming it s1z)zy l o3.l: b-gm/ne-cv v x0kuy+nradiates equally in all directions?    W

  A stereo amplifier is 3+uhufxzlxj r:o/. e7 rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output ir+xjuoeu lfzh :x./73n watts at 15 kHz?    dB

  Workers around jet aircraft typically weam00xt:7;p a,uf gryjur protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and tha0up:t jgam, 7uxr ;0fyt 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, the gainh o3( gbm90lvbmnd0 c0o3 pd+.e7hcfz, $\beta$ 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 teiqn9tm og; t lc2+m5)o 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 cmsq3r b g0si/ * gxd2;fnvg93*6azctdf long between fixed points with a fundamental frequency of 440 Hz and6xgva3z f0 d *92b;i sgsngt3qf*r/cd a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with w1 x7ig:lyci5 1lpn zg4ater (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 heanixi741gc :p 1 5lzlygrd 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 s.r:/ slkeh*qbji6kce* +m 5vmtring 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 strmjbrc.+/ h5*lkeie:* m ks6vqing if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loho+q ch ,d4xg 1re1rt;op ($\frac{1}{2}\lambda$) 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 sol9/n;vrh8vdxpu8 c9zwwl:j +5v d *ny9s;fu durces. 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 than the other. Whatuy vvj8:+ nz lddx*rudn ;959v;f p cwh/l9s8w is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One trab,krl o2w8jnbe75g5m1zm qrs ,l9y *pin is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the sp1,wmksb eo2zlp8r57n *g ql5ry jb9, meed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches youfor* 4hxb9hf9b 3ny5r is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fastofr 9bfx n59hy3hrb4* was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lism)zej2u : :teytening to the difference in pitch of the engy)2j zuem:e: tine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. nd.g,m- .naa)qt v9nsThe shorter one is 2.40 m long. How lon ,)s-nqnag..dnv 9 tmag is the other?    m

Two loudspeakers are a x pw(y7r/;ogft opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, fwx p7;/or(gyin front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aor8 *q58qc,u32m:bzd vlkqecpa ta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the f 2p*bqz 8m,v:k lcd385e acqqulow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while t,l,fg vzfc sd-b/* -siw- j7pphe moth is flying 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,-g,f-wj/ dzif s7 pbvc-s* lp the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it appro5wcth/w( l:d;jfrerx 9k)1,iiap,o jaches 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 from one chirp returns c, l19 orkr5jtwpi:wjfe)i ; (xhd,a/before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once p,lsrmlyvsro) x9/ ht; 5f3/ - ope,sdused to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundalmrsop5yhp rl 93,sf/o /tevd s;-,)xmental 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 lih:e3a65fx vswstening 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 w 5exh vwsf6:3aide, 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,” innjln)+ p 9 -b0ars; q:cvq/ubr)ddt-evolves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. bj0/ elrd nd+c;qt--pn) 9)sq :b vruaFor 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 asx0fny q 9 qcv8zay* ;la ,7ygfv0;tl- frequency of about 1000 Hz is lq 7 aqx;y n,8-0 *ayfz9yvtgslf 0c;v$I_0$ = $1 \times10^{12 } W / m^2$ 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 Ma 8hvprk1db) 5nec9(qlga11 ej ch 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the pl1gal qr5b1 )dc1h98njkv(ee pane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isdgx: gwvr,6)v,o s p7k 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