What is the evidence that sound travels as a wavjk 6c( x8t i-cw2jb5rve?

What is the evidence that sound ishzm ov2mm:8 uqazk*y:29do 7y a form of energy?

Children sometimes play with a homemade “telephone” by attachin:ohgiq26i-dw o9qy4q (4ft e mg a string to the bottoms of two paper cups. When the stri (6t yq94qoq i-omwdf4i: 2eghng 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 from air intoj t8g :dryt,c6 water, do you expect the frequency or wavele6,:ty8 rcdjgtngth to change?

What evidence can you give that izo-m-e 1 7rkvthe speed of sound in air does not depend significantly on frequencyez k-1-7rivmo?

The voice of a person wh++mcrrk-vgi6ke7 l * (vsh*9f02f(taugfpvno has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of az7 pkj6ki47dil i+8 gorgan pipes?

Explain how a tube might be used as a filter to reduce o- om36nfbgd.tm-c3e;jv6 l ubplme/ q e3+i4the amplitude of sounds in various frequency ranges. (An example is a cogmd fee3q/m-- o+i;tbl.pecn m l vujb36436 ar muffler.)

Why are the frets on a guitar (Fig. 12–30) space,tx4ge rihba 4k k330cd closer together as you move up the fingerboard towarkig, cbt33h4aek0x4rd the bridge?

A noisy truck approaches you from behind a building. Initially yx 0onou6)csb: ou hear it but cannot see it. When inoo 0cu:6b x)st emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can b*lt am0v hq5-re said to be due to “interference in space,” whereas beats can be said to be due to “interference in timemqhav tlr5-0*.” Explain.

In Fig. 12–16, if the frequency of tc(+v bsqk z20ohe speakers were lowered, would the points D and C (where destructi(kbzqvsc + o02ve and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in 9j. 0rtx ( k n.bc0+xpyx,gnfsareas with very +tx0nb s j,9nxx(kfcp..rg y0high 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 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 hehw:h;aa h++–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, :hhhhe;a wa+ +(a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and : m(4uv0x-o/2byelb-s s*o b*gb2fgkl n g,ec observer move in the same direction, with the same velocity? Explain.k2b bxoeo(-2s:e 0 lyg/ bg* 4, m*-vflsgbncu

If a wind is blowing, will this alter the freque *wat(d)qsbk: llim, 4 b .9d/jzslw*hncy of the sound heard by a person at rest with respect to the source? Is the wavw,(w:t jdl a/l9q bh*msi s z4b.*kl)delength or velocity changed?

Figure 12–32 shows various positions of a chsphg); 6p6qosus zpqp*zn2uel37f6/ ild in motion on a swing. A monitor is blowing a whistlgu7l hne u36op)pq6/q;z2pps6z fss*e 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 forwp6u evw9q39esl u)5 .po *nnw the echo of her shout reflected by a cliff at thwwu3pe vnuo56 *p)nw.eq9ls9e far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship juc-6j y;q r1arsst 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? Assumrcsyqj a-1 6r;e 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 wavelengths in air at 20 p3f/ 1- /rdm xbmh0lnj$^{\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 tunam l8 em*vf ,ilaj4/zvq.6hu) f t-d*pl on a foggy day. Without warning6m,. )*tpjllf/84f- qavd emizu*hvl , an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it ma wq;ywxp 2s:rj0 t-c cjg;jjy+ b;*n:qkes when striking the water below is heard 3.5 s latercp+ 0q qwjw*rjy-;cxg::njjb;s;2 ty . How high is the cliff?    m

  A person, with his ear to the ground, sees oe1x jef29( am.0jrgn a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in thj0x.2 mj ae( egorf1n9e 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-svz.s3ui 4 b0kvecond rule” for estimating the distance from a lightning strike if the tev4zi0u k3.bv smperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the paino.u; nveuzq07: i+ wrf9vpib. level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensitu45 baq*tmpxd ta ;+x) kmean+v3( tb)y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultgcwsoaheo39p3 .y 8s ,aneously at a certain place, what will be the sound level if only one is explodywoc.gs3sp oeh9a ,38ed? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane withk za-sq7; epj1 four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. Whsj- zeq 1pka;7at 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, wherea9eh2/ syjqt;x l w6u +jqp3.() sue)b)ylijfps for l/qesi.+t;jfyl h36)(bu9ujy qpj )2 w x pes)a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power obk:e1 d*ebnk9utput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound 1dkbken b:e* 9spreads 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 s.vg :rodvn7l 06.5lxvjfm ,f rr;xj s*trikes 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 250 W, whill ta*d30scu6(mo1 apy e the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels ymp1 aa s*63 0d(uotcylou 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 regis )tf*p/zi,c6m tyk8m vtered 130 dB when placed 2.8 m in front of a loudspeake8/ m)mfyv iktc6 ,ptz*r 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 is v*p- wk sq9s0fp(qzj+ the ratio of the amplitudes of two sounds whose levels -spq j09 s*kvzq fpw+(differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factohmges s22ys, 2i+ :w0yp fub:er will the intensity increase? Increase by a fac 0 sweef2ysgpu+::2ibm 2hy,stor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has e * r++.kk.9qqdub lm9la, ifitwice the frequency of the other. What is the ratio of their intensitie*b, qri de. am9 +.kl+ilqukf9s?   

  What would be the sound level (in dB) of a sound wave in air that corresponddh1 ge 3:wg4k 7dat8tfs to fda 3t8 g4gw:17hkdet a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to see 93 u qzdix.cq:z8ecz6m as loud as a 100-Hz tone that has a 50-dB sound level? (Se9.6iz3q u:cd8z qze cxe Fig. 12–6.)    dB

What are the lowest and highest frefss/7 ,0-hn 9gxobyyvinn 7x; quencies that an ear can detect when the sound level is 30 dB?-h9yg0 oy7v,i fnsb snx7xn/; (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound level)4 )7 kb 7itcls7lq chybi)b0as. What is the ratio of highest to lowest intensity at cb ya0 h)4t s7bi) 7icbl)7qlk
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fun1xmo8yb tvph 0:cq1: ndamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placedmpq11:xn v8y:c 0tboh?    N

  An organ pipe is 112 cm long. What are the fundamenta:t 54uhdpd h/rl and first three audible ovp4dh hd:t/u5 rertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the t.bq5cecn8ds,dl ry +,ack( ;xop of an empty soda bottle that is 18 cm deep, if you assumen8 a(;xr +sc5 ,q.bdkcecl,ydd 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-tubezykq l 7 9,vt+bgjjo:x(+lnz 0 pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? z gzlqoxkn 9 b,07jyj+:t+vl($L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string g q+kr6d a+4q2-e7dha+d qsmfhas a frequency of 540 Hz as its third harmonic. What will be its fundamental fr a -7d4e rk2 mgh++sqdq6aqf+dequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned towgwo1qm7.12 t elm x, zupj,2r play E above middle C (330 Hz)7e.q21um1w, 2wmor,pzlt gjx .
(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 middld9cu v c+s69vke C (262 Hz) when the tem6c +k9uvsc 9dvperature 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 7t ubt,;-9s4c q ,zu -nzzwgemat 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 hole be0r gdzgp.c4* i8xja;3if1ax r that must be uncovered to pla3gijrfx pd0. g4z1ai rxc8a; *y 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 264kvh.exo p9- ug5l y+;o Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why thisg +pu; lheo-5o9xv.k y 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 lon9dwmv 79dc s6hdm;8kz g is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz.8cdwmk6 s7mhdzd 99v; 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 izkw+ 88hx9yx. z zabd50h+ud1nb+z g $^{\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 2.14-m-long 8 2zls;p5rnyz6 sy1zdorgan pzzy5nys1zdr ;l62 8psipe 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 outs9se-m. lsk v:-se8gp oide 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 answer to the information in ths8-9 m.e os-e slv:kgpe 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 strinswwjql-1.m/j 1i c25j.mot lkgs, one of which is sounding 440 Hz. How far off in frequency is the other stringo-ml5m1j s w 2jktcq.l1./iwj? ±    Hz

  What is the beat frequency 3a*3: fgk)sveiqvlhvt(u 3( h if 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 operatw1:hbq a2t 5tywm6q r7m;n da3es 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 simultaneousa:t3q6ytwbh1 5mw7 q ;dr nm2aly, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fore8 9 a p 0wbov(kkgm2*7jy0cyyk and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the strinak obw2*eg8cp70jy9v mkyy(0g? Explain your reasoning.    Hz

  Two violin strings are tuned to t ;q auzr5mrrc4 l8a(l5he same frequency, 294 Hz. The tension in one string z5rrrllc(m; u8 q54 aais then decreased 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 heard if two identical flutes* 42jo k pamfml22g,;tth np0g each try to play middle C (262 Hz), but one is at lgp*o mgf;t2 mkn02 hjp24t,a5.0°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 t;ln 3tx-rf)ma 5sdn,441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are xlt-3 d)nr;n f,t asm5sounded 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 odig ( bauxw26 *++tyustands 3.00 m from one speaker and 3.50 m from the other au+yx+uoi( 6td*g2w b.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner he;0 (h,s (q q g73xft,douhnbwqars three beats every 2.0 s when they are playegdbt(woh,qhqs 0 (7 , u;fnxq3d 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 wavelengrwjtu6d m3 lw7)1 e/smths 2.64 m and 2.76 m in air. How many beats per3) m1rtu7j6 w /wedlms second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz vip a5.0n rp4c0zbx0nwhen at rest. What frequency do you detect in0cb.z aip rp4 50x0vnf 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 a fire engine whose s c:pgru24xfyzm: 5fe2iren emits at 1550ucefr2 4: gpz yx5f:2m Hz moves 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 y6ht i 0aaf o):uty4tq0kza.9source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are9at)4u.t00y :iyaz6 o tk fhaq they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one l2 b8it3.dfizw)b .3cnm tf7 yis at rest and the om i y2fznic 37wldbbft8.) t.3ther is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and rvbis5ea(09ja ml+z e3 op24fmeceives them returned from an object moving directly away from it at 25 m/s What is tho 043m(m v9il azb5eps+2ejfae received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 sv11d rluzy 8q1u:a t8ngnne5dc( ( w6m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the r(dna68(unu1 8l nvs: wq5d11zget yc bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopplezv)m0uqlvpw x m: kdb 3s,* uj3f:d42dr experiments, a tuba was played on a moving flat train car at a frequency ofmu d42md)3 0:,fks:*vpdj3 quzv xbwl 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. walc+d.-i4agu+d 7tmd he 85z Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken toaazw 84 md.c t+hdu-5d+g7lie 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 ultrasoniys2)2 n+ zu5n hyss;fsc waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of o/htx wik8 sm(icps ;v5w5v02frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observwx0/5cviw528v(km ; ih otsspers 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 ,/ejuln.s :ys on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 x k2f 26-gfn gm; rp4adr-szk0gp2: qhm/s (a) What is the angle the shock wav2nfr:m gk- dpks6 2qf -2xh0gapr4g;ze makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where a6 e6g72ji c31zo.lxh g/k 5dmjcw)ne the speed of sound is only about 35cg6) z3cwje7 lgk5di1/ e6 .2ohjnamx m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determjl7i:zcj hi. -ta-p, +cr* mn b)jwd wuxk-.6cine the shock wave angle it pr nd)ut-l7-h+wj.r.c:k zc*-, cb6 mjapjw xiioduces
(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 (k-5m b)dizjm $/theta$ 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 a);rmbure5qp mq z 3:p0bove the ground flying faster than the speed of sound. By the time you hear the so3qr:br qmp 0ep m5u);znic 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 son d)*xg1nr+yzq ar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then deteg+ z n1yrdq*)xcts 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 i/nfbr/w6-ewf ,ggp d0n the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a seeq p6n+)2ecw1n1 o(vo twmjm 7wer pipe symphony. It consists of many plastic pipes2pmv (e1otw qcow+n )jne1 m76 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 permuez 2t/rz2 2dson makes a sound close to the threshold of human hearing (0 dB). What will 2urzme2 z/t2d be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 8n2bt 5zz* hzx; ih*(jz2-dB sound and an 87-dB sound are heard 5z;jx *z(th 2zhznb *isimultaneously?    dB

  The sound level 12.0 m from a loudsp yb1f itecr;:r*.x0n /q) lswteaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaketr0li* .ye:;w qnst rc/b)xf1r, assuming it radiates equally in all directions?    W

  A stereo amplifier is ratedw,rd39 eiiz 5u at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What i5w3r9 uz, dieis the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typ m9zzy,pv 72khd7 319ec ykidwically 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, 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? c1e w ki9zvz, y73y 2p79kdhdm   W

  In audio and communicf t+8 n(3 ca2hcppfw,cations 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 viouwrca 6b2hmp dl:ta *tx 5./m,lin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed poingfe0k ,khz/ hc) q5a4kfn 9h+il+ coz5ts with a fundamental frequency of 440 Hz and fclg),i 5hh qz+9kezhankk c/ 45 of0+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 wfo* h*q8+bptrith water (Fig. 12–35). The water level is allowed to drop slowly. As it +*qhfot 8p* brdoes 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 string of mass 2.10 g is near a tube that is -lxqmjq j( wi(t7 e-8fo h7v7iopen at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the tex7(h7l7w-fq-8v qi i tmo jj(hird harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obseryzn)8h 3b ,9 3socvr6q/f joexved 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 rax+b(mrdtc0 :8z8 ag.c4khw s hnge coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the soun d rtc zs84x:80wc+bka.hhgm(d?   Hz

  Two trains emit 424-Hz 3gi ki0f oum 3(tb;k)qwhistles. One train is stationary. The conductor on the stationary tribuf3;03t ki m( o)gqkain hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistlbmd;p 1bkd9 ,me as it approaches you is 538 Hz. After it passeb d,;p91dkbm ms you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can,2 ps*qj9h ;dppvsc; j estimate the speed of cars just by listening to the difference in pitch of the engine noise between9d; ,pppcj*;s2s vqhj 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 togeth5rep* mt6livx m5d(k*b n6x4fer, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. *6 m5*xf6itlm(d4v bkxr n 5epHow long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it h nlr06e 8crw98; f.s/tskga+jci;d mmoves past a stationary observer at 10 m/s as shown in Fig 8c kn;lraft. cwh d8i;rmj9g0sse+ 6/. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flown:n* judo3tw9n6a0 ie 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 blj0ntina nw:e do*693u ood 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 sp5pqy;jny 7)vpc kn/ p5eed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the m5;qy cnpvnp/jy7 k 5)poth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches wz/ +to;rygk zw5)7mw:wys*p a moth. The pulses are approximately 70.0 ms apart, and each is ab75wy/:z ; twy*)k+ rzpmsgw owout 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 7edxw5 zbv,dpzj;g0 + village to another. Since lower freque xez p07d;wvz+gb d5,jncy sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the a 681+i ;r li;wie*iet+oryd fpresence 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 thrwe*8iid ;etoy fi++ia;l16r is room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long/pvmhln z6db a/:+ ob+;h:bbs, 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/ /hpd;z+bsno:l+6bv:mb abh 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 hear;vx4acp/ s5pp ing for the human ear at a frequency of abxp/; sap4v 5pcout 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 grou1ep7dc;ao o x,nd hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’ oe,do ;7a1xpcs altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 s7 n/ sujmtp-)$^{\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