What is the evidence that sound travelnli8xf wy/r1 8s as a wave?

What is the evidence that so6et skp*1w5i kund is a form of energy?

Children sometimes play with /e;d::1l3zl hprg o-wxq9fhqq) zej+x.yfa-a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearyfx ogh:3w+l ez:z)-rjq9;fl/q 1pe d-hx.qa ly how the sound wave travels from one cup to the other.

When a sound wave passes m;pant dlyo :a+71 6mbfrom air into water, do you expect the frequency or wavelengt7;yn1+pt 6dmam o abl:h to change?

What evidence can you give that tkq adb/p0 9;pohe speed of sound in air does not depend significantly on frkd oppqa90/; bequency?

The voice of a person who has inhaled helium sound s/wbf3 u;++fx:ulwwb s very high-pitched. Why?

How will the air temperature in a room affect the pitch of n(sevfu75 a j:o.rjj6 organ pipes?

Explain how a tube might be used as a filter to reduc bkkq/edah u5*wvc;-fhds +0 /1-sdcee the amplitude of sounds in various frequency ranges. (An example ic*eu0fd-we/+hk vk1h5 q sdc / dba-s;s a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mw z/e v wbvhzba*j6v;u((w rm d/,:9smove up the fingerboard toward the svw9uz/: jvr(mwe,vdz/a* m w b6h;(bbridge?

A noisy truck approaches you from behind a building. Initially you hear it (fhm(x/yvi)6cjy39 ysb. kdk but cannot see it. When it emerges and you do see it, its sound mhk (b36ik / v.)yyds j9fyxc(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 “interfqv4wu mb/v19pyg*lyo9+ 3f 4 l le(uleerence in space,” whereas beats can be 9 f* v3e y4(uwveoqlugy+l9b 14mp /llsaid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woul(k8o2 )b/ojernroz 9td the points D and C (where dest rt2(nr okoe8 )b/zjo9ructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people ) -xcjbc .k(:-jq;hxo7jkdk swho work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a r(7xko;bdk. kjq- j)jxh: c-cselatively 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 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 tho) --l) amk+3vv uespwcught of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or +se al--)mwpkc u)vv 3(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/1-b8 azaja4 slev;we same direction, with the same velocil / ;v18zab4aee- jwasty? Explain.

If a wind is blowing, will this alter the frequency of the po))- f r, djmxp8k8cbsound heard by a person at rest with reso fp-x,dj8r)kbc) mp 8pect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child beh1z* -idv4n ;-pswsin motion on a swing. A monitor is blowing a whistle in front of the child on theh z;41b --sswn*vepdi 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 lisxub i742qef,b a-nj- jtening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s afte2bq,f74-j xjin ba- uer shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship fm*+ja.m( h gxjust 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 (Table 12–1) and does not vary s+x.m(*fg mhj aignificantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveli d6nj 9nq4ho-engths 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 tn/dbz // cnq0s2 qzz7zgb+9j just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is hearz/ /znn9zbb+z2q q /d7j0gstcd (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clz (sz91) ywpe.fjcr q8iff. The splash it makes when striking thew j(z y1ec8pr.zq9)fs water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grom eyg7rr)1s+js6wy7 rund, 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 they are 1.1 s apart. How far away did the impact occu )s6 mwrjg+7se yyr71rr? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over on+zv*y(cftu al* bz(/+fmbgu *e mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperatura +bgzz(f (**v mlb+*t/uuycfe is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soun4io cksd,lfy59-ql w )d at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of 4nl7g;ml wfng 36 )epla sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level o(s76 eb7)n3upag o h cpqq;3pmf 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exeo7p ;q6 ga7nu3 (spcbh3pmq)ploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distigqw-(c8h i t(ance from an airplane 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 shuiw-( tcqg i(h8t 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, whkyc2o;(t 0b1/vj xc whereas for a CD player it is 95 dB. What is the ratio of intensities of2yo;v/jct c10hxbw( k the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound n)jvi (dk7 -yrfrom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered o7dyvrik(j n)-n 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 p -n.(/knn)f8pw i n9: olervvwhose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B isr t*qc37sfj bz81nnbz u.-g4l rated at 40 W. (a) Estimate the sound level in de n.u7 gbj3*f8nz 4l1rc-bt zsqcibels 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 2.8 m in front opi oaz9zw mr-4+; r5gvf a loudspeaker on5;p ria4zv +r- mw9ozg 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 o jc8zsnx)v (,ei -0ak*( jtytcf 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–)ti, kvjct cn*(ya z (jxe0s-89.]$\approx$   

  If the amplitude of a sound wave is tripled, (a)w0ob42t se g8l by what factor will the intensity increaswbs8ogtl02 e4e? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacesqg; (kus64xhg b)3 slment amplitudes, but one has twice the frequency of the other. What is xub)shq(s ;sk 3l4 gg6the ratio of their intensities?   

  What would be the sound level (in dB) z2s7mcc:w w w5of a sound wave in air that corresponds to a displacement amplitudz57wc2w:cm wse of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seemxxw7pnf/ d;(ri,c cb ,e:vi6d as loud as a 100-Hz tone that has a 5wfc e d, (p 7v/,i:dncrx6xbi;0-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies ,xya i9 -hmgs:that an ear can detect when the sound li:, -hxsy9gma evel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hu1k2b /* wuitdnaunj +:/q+dxk ge range of sound levels. What is the rati *jqduik /++/kw1n tx2b :udnao of 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 f.j/u+ rei.euj 7hr4r qrequency of 440 Hz. The length of the vibrating portion is 32 cm, and ituj 7r.. ejhi+r4qr /eu has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long.6 mni n.i*iccin1w,(x What are the fundamental and first three audible o i1nw.mi c n*ni(c6,ixvertones 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 daux 0kkibp6p)fm e0/(h p+ +sacross the top of an e s 0kfphmux60epa+dpb+i )k( /mpty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of hn3jz k+k4kf) buman hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes reqk+)nf 4zbjkk3 uired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thirv11 zq5aazyk9ts e 7b2d harmonic. What will be its fundamental frequency if it isqkvst 529 azyze1b1a7 fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to pla5+s;n.dc b1yry vv0kemt6n7(8p xi jby E above middle C (k 6y87+vv(cbn ij s 0yxerpt;n 5.db1m330 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 emits u9 -;qp7 ;d6fzt qjqbcmiddle C (262 Hz) when the temperaqc-6q7ut bq;9p d;fjz ture 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 201wg azs4xbwx* :s -:l. smcf+mx,4wx d $^{\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 bfxp;yb xcyq*uu a-5706f(ab hole be that must be uncovered to play D above middle C at 294 H7a5(6byybu0 p qfxcufa;-x* bz?    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 pipej uo)w8m-vt- n can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other freqw)m vjunot-8- uencies in between. (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 1.2e1 zegf2,e /h *64t)y /y,zyhnxqv mae6ddyt80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz andyzde, 2e,zet6ydn1 6ax2mh f)/*4h g /etv yyq 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 95x )nz)6 cnh+gbubksy o3m7q$^{\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 audiqp;mp+6bvr 8bble range for a 2.14-m-long organ 8rm bp6pb ;vq+pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the ou x5:lt,x6fg7z /i+ r6pzdmgxgtside and is closed at the othex:tgzix 6pg/+md6r5x fl z7,gr end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two striec6d3v v8:pvxzr3 54h3*ovm ly r 6sibngs, one of which is sounding 440 Hz. How far off in frequency is the othervry3*shcleprbv5d3 o:4 6i86z mx vv3 string? ±    Hz

  What is the beat frequency if middle C (2 3qybrz bfd+81j h82jz kn7,www-z9u e62 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 (brand X) operates awfe:1n z26bh0e g9lyhbg3nc* t an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs hg 03f :z12nlnb9 gb*6ceyehwwhen they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s 6cyf*p0n +y x: inc-sowhen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of theys:iyn0n-+ pfx6c o c* string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same f- s2 jyeu)hvu;-jc/ier 6ppl*j4xp0n requency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together26 xurphejj v *i/-neu4l-s p)c;y0jp ? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hean:u2pp, ska b5rd if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 2usb,pp:ka n255.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and szk p+3u89lavC. 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 s8+p zl9v3kuaand 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 person stands 3.00 m from o4gtgb i2na/7 one speaker and 3.50 m fgt7g 4/i bona2rom 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 9oix, c nn1c3ihg1-dj1 5ur agat 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is - idgchn,5a un 1icorxjg3119vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m z 0es c1sjmb*v(3,zd qand 2.76 m in air. How many beats per second will be b, z*s ec3qm(d1v0jz sheard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certa ;qnr6 mcea6tgzu;3j-in fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with;cg6e qmz; 3nu j6-tra 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 .2 lk lbqkg2n8a fire engine whose siren emits at 1550 Hz qnl228 g.k kblmoves 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-Hz source is moving toeajnplik rra639f1 -n;j,no (ward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exa3 ar-jk6(jpn iron9,;elnf1actly 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 singl(.+nprd9oi ;eixebl 5e frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. .d; e 9rieo+npxib5l( What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out52gegsiqa,( o ultrasonic sound waves at 50.0 kHz and receives them returned from an oe , q(5giog2sabject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fliesvfig*t:m kktds8*m +x(,+e kv, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the kvt+i*,:fmsdekkv x *( gtm+8reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movio cw6b :rbmx(*ls :sa(ng flat train car at a frequency of 75 Hz, and a seba sr:c x(6*o :lmb(wscond identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spepp 5( eb3z4entvd9wy+ skw w(3eds. Suppose the device emits sound at 3.5 MHz, and the speed of sound iy+nsv (t bk4pwdp9w we5e(3z 3n 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 oc2mg-3 :;fnkzk5layd f 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 sou br2gjtn+cy5 /8gah; und of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequetbgyh;5a8c +/2 ur jngncy 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 land if its speed ato)n86y4tk+,h - nxr5asjtkd p 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 *ff w7g-vqrn6.h v /vxrgi+o*where the speed of sound is 310 m/s (a) What is the angle the shock wave makeiv*g r wo6-vf+*qxfnr7.vh/gs with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of u5t o skwk 13m2i,ouuu8 +dz*ya planet where the speed of sound is only ak3dtuouk2* ,51i8mosz+ yuwubout 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 85-aa3mq:boz mjuy6 gw(,8 cds,00 m/s strikes the ocean. Determine the shock wave angle it produceswag uj-yc s3,6 mqm(d o8,zba:
(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 / w*0pu in1vzwz56hqk$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the,yis ymr-*: gy ground flying faster 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*igm: r- yy,sy 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 devic c2l:essnu8 ovs6u bbbh59i97e that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses ( nlebcu87vshs b2s:699ob 5u iin fresh water)?    s

  Approximately how many obtu 96 - dsljiu8djmjs)z2q2/ctaves 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 many3w tzvk a2*kqo2, l;sz plastic pipes of various lengths, which are open on both ends.k qw t ;k*oz2slza2,v3
(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 fromd )l9fck3o km,;r..;sxrxcwx a person makes a sound close to the threshold of human hearing (0 dB). What will be tw crxx kmkol.;;sd.3,)9 r xcfhe sound level of 1000 such mosquitoes?    dB

  What is the resultant sound l z*xpic 7 b,e6r9kihlvj. /qj9evel when an 82-dB sound and an 87-dB sound are heard simulta.q i9l*/kb9zj7 iprvjh,cx 6eneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whatz/v q(biy5vkmn/ tc: ) is the acoustic pnm5 c:k /v(y/ zt)bqviower output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated atcwwz skbejd463q 0 )b: 150 W output at 1000 Hz. The power output drops by 10 dB4bw3jc0s wzdkbq 6:e) at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aioemzl qitp m/w2;96,ko8 z cx)rcraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB,9c/m6zw;kzoexilpmt o2 8q ,) 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, the)nz16. 8dod+e ava98mb2-tqq bwoi wx 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 2df9xoa to/*u1$\frac{1}{2}$ 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 points wi ,qtllb ;yyq05th a fundamental frequency of 440 Hly5q,qy bl;t0z and 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 filledu1m)i+, -o m:dfl bpc;wpc d)x with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the d f,1;upli+)c)bwxmd- pm:oc distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near:.zqf -ziwgpwo9) 8) vp hj;fa a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is tof z)vagipp) wh9:.q -fwj8 z;o produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obse wp d.1e, rz6t6xufqd8rved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sourc.:t:v j mrc:ofq.ddn;4 pn,ctes. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds thatntpc.d;fdjr.qv :c:m t4n:o, 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 stationary. The conductovzx,82fe8p/ hp0 gvrg r on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. /8ev8,xz rh gv0p gf2pWhat is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you2i8 qr*1y ob jicqag-5 is 538 Hz. After it passes you, its frequency is measured cq-ry25biqi1aj8 g *oas 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the sx g3tf:xwea *oj1,i5pdp ;0nq peed of cars just by listening to the difference in *oigxen q;pftx1a3dj5p:w0 , pitch of the engine 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, soundingw(.jv j fyc-q7 together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m lv.-cy7f jw (jqong. How long is the other?    m

Two loudspeakers are at opposite ends of-q/( pei6qzdx7 ajq+j a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he ip7 (6- aeq /iqzj+jqxds 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 aorta is normally about 0.32 m/s wha62ab:n)c+inx,uiv -uwsf 3a yt beat frequency would you expect if 5.50-MHz 6unf 2x-asnv wua+y i:,ic3b)ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flhlh6*e sofa,;hn( a./e 1bzwlying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects offboe/nsa1 l.efzhw h (hl;a6,* the moth?    kHz

  A bat emits a series of high frequency sound pulses as it 2ao:e0ytz bm u 0g/br(approaches a moth. The pulses are ab0/m t:z g o(0rbeu2yapproximately 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 before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villson1m,iudjjjj* +b9 x:.k m5g pb6f4wage 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 mosd+6pkbj1j o,bjni*5u f4: ws g.xm9j mt 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 com js;b-ogb353lsvw0,.y;v d5k bla mjppromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room. yakwl3;5 p;-s .5djsg3lbb, bv 0 mjov
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, c0do n )jpw,)htalled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stton wh) j,)d0proked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a fruk-qwl3crf67xzb wp;6h dn(6equency of aboul6n-;7k (bfrc 3dpu6w 6 zhqwxt 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 thew g(a*uevn n o)hafd89- gwk/;,q r4yt sonic boom 1.5 min after the p nd*og4wy;nf9u(w ehakv a /rtg)-q,8lane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 1)noib i ,i.7:hmykng $^{\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