What is the evidence that sounk8e+ /x8skau/0j n j( 7rmmldzd travels as a wave?

What is the evidence that sound is a fo66yc up7ym+jq (huu m)rm of energy?

Children sometimes play with a-wh (da rr+ 5/u -mhpnf8dpgo; 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–;u adnmrd 5pf--+w gh/p roh(829). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or )*1 yndn0 ;ad wve 9n4biqj.jrwavelength to .rnjwby 9i)d nqa1d*4 j0e;nv change?

What evidence can you give that the speejf95 q4ex paq4d of sound in air does not depend signifi5qa 9xpfq4e j4cantly on frequency?

The voice of a person who has inhaled helium sounds very hivppjj34 2b/ylgh-pitched. Why?

How will the air temperature in a room affect d+ -j:jd wbzd7the pitch of organ pipes?

Explain how a tube might be used as a fpwkf1 z- g1on(ht/e ;xilter to reduce the amplitude of sounds in various frequency ranges. (An example is a car enz1 -1 p/t g;k(wfohxmuffler.)

Why are the frets on a guitar (Fig.7*j 3njhb6 uzc;pz7 yuo w6rw3 12–30) spaced closer together as you move up the fingerboard toward the bridge; 3bc3pw w6*j7rnz zhyu 7juo6?

A noisy truck approaches you from behind a building. Initially you hear it buqdp54 /51x.hkat jfsb t cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency dq fb s45tkx5j1h p./anoise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “int-: feh5,pglf(7u as h hv3z.kmerference in space,” whereas beats can be said to be due to “interference in time.” Explain.kpzmg 5evlfuhh,:s7 . -3h( af

In Fig. 12–16, if the fr1x d2qshtcs0 3equency of the speakers were lowered, would the points D and C (where destructive and constructive interference o3 12dsth 0qscxccur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who 8,i1l( 0giugnqmdhr- q* q-6vok3h zd work in areas with very hi*d3,hd8m0l - kg6q qizgrno1vh(iqu -gh 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 h)nk.c;ytkaoojr )wpb+9* : l Fig. 12–31. 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, (a) or (b), are the two component frequencies farther apart? Explain:+ )kht.al*yo orb ;c) wpjk9n.
(12-31)
(12-18)

Is there a Doppler shift if the source and obseru 1* 9x02q iucbduyvz/ver move in the same direction, with the same 2yixu0/dcv*uqb9 u1zvelocity? Explain.

If a wind is blowing, wilbzblip r y+142l this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelengtb4lzr2i1py+ b h or velocity changed?

Figure 12–32 shows various positions of a child in motion.7k6b v9gwu1im8dlt p8er ed ( on a swing. A monitor is blowing a whistle in 69md 8gerwulbpk81 v(t. edi7front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the e)xh 0njk3vq)g/6dn(; easc.u fqq1 sv;0bizwcho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting;;xqqswb (jcv h3 0quadisvg)nf6n).01 zke/. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belox 8poo4d3,ckzc1d;8:ds afkk w the waterline. He hears the echo of t:k,1pafz4ds8 o 8d;3 kdc okxche 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air d9uajunj q * 1y,5 *6wsyfcre:8q3odjat 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 obo )rom h si/r1k;psw8(ttcwk 2310 xschool 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 b;(os wkotw18rc)r / 3t 1mxko2ishp 0before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when s x:,(6wl6armtb)ft p ctriking th 6:6m, txabp( )wrftcle water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to th1r +,q 0/ aavyek6iygbe ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air andv/b6ke1 qyaarg ,0i+y 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-second rxk bfofwe ) g ;l-.,.m7gtbqb:ule” for estimating the df l7b;,.qgf-emxb g)tb:k. owistance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a s5fo3m71h 8l3lr c cqwbw:asr(ound 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 a sound whose in;(8+ qlqai rpjgak, j*tensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of vi x yuk*r+kc*s+tj(3e0z2tl95 dB when fired simultaneously at a certain place, what will be the sound ll stk ( *z+2e0+kjvx3cr yi*tuevel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane withui-kbj ;v. k*b four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What soundvjukk; b.- *ib 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 sai fiz85a5lz5 k2gz nf+cd to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eac klgzfcnaz2+ f58zi55 h device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fr; ,owo ruz6tuww,8u,jl3 1xmhom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly luw8uouhj 6t ,,w1xw3rom; , zover 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 strikes an eardrum whose area fd;5f qn-:9tv8b(ari+ kdqgx 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 ic8tz-p:h)iii.v ;tn /wpgtg 1 : cdaz,s rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect aih an -1,8p )iz:t/p t;wc.tvggcizd:t 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 fronj4p 6f1 c1vek44f zlrr,/xn fst of a cr4/xjv 44n z r1p1 sfe,6kfflloudspeaker 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 :6o(q+s(c dunfu)nni oq /2/)s pom budB. What is ti62bn(oq:)d/su pu /on csof un(mq+)he ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a s0k,ozjh yh:h /a(d omyn4,y)kound wave is tripled, (a) by what factor will the intensity increas,o hjdh)oyh/,z 0kn myky4(a:e? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampl35cni7w at(; t70uy szf c/iznitudes, but one has twice the frequency of the other. What is the ratio of theytiuf(cza/ncn 3 z0iwst7 ;7 5ir intensities?   

  What would be the sound level (in dB) of a devql,p6h(dz z m6/k*l9ws q6sq, ,jtsound wave in air that corresponds to a displaceme,dptqsqjlz,e 6sqh ,(d m 9*z6kwl/6vnt 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 nw 9u.;qzrsfcu6 aq.8 100-Hz tone that has a 50-dB sound level? (auz q cq8.u9 .s;nwfr6See Fig. 12–6.)    dB

What are the lowest a-dkn1r:vg;:gpp nca ;,uhbi:nd highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig.g c:p ,brnvhpa:: ki-;ngu;d 1 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is5x+d3np mj6i)vkusvst wbw(-2ft 5w8 the ratiw(52)vb 8wnu+ki3xwspt56j ft- mv sd o 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 fun56eol. oart )xdamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.a)t x.oo6 r5le35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What6pao:2m+1pgvxy1 aznz;/lzv f f8* d j are the fundamental and first three audible overtones if tz 6jpfm vln+12; g/yzovx*z :p adf1a8he 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 t57edaf rr hm 03ubc6j/.y8s jlop of an empty soda bottle that is 18 cm deeey5d 0jca76ulmr3h8f / jr.bs p, 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-tu kua6 -ctki73ybe pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range ctiu 3y a-k76kof the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency o syw6:1(yqtalw0zf4 of 540 Hz as its third harmonic. What will be its fundamental frequency a owwf41(:qt6y yzs0l if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar strinw7b k+o5c lf(ng is 0.73 m long and is tuned to play E above middle C nbl+f co75 kw((330 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 middle C (262p u) jov.ckv:l82h7zs+0uo yv Hz) when thsvh :c0 lvjo 8 ov.z)pu7y2k+ue 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 at 20 6uqj:k -ni/cmaw*o s7 $^{\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 holeogl+t 1fsargg:f z87yl( 1 f2h be that mus a : l(2sl71tgz+8ogfr1hfgy ft 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 pip(bpg9 b2fp,sbu di9xz;z;t g(e can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open oru ,z9pix;gz;gbbd9(fb2(stp a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at 3rw7 4cch5zoq two successive harmonics of frequencies 275 Hz ano 3cwc4rzq5 7hd 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 opyk-wsd c* c-nq wm3823m+yr $^{\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 lcj ni) gte)2yj1m12d.14-m-long organ pipe a1)jdlimej2 c 1n 2y)gtt 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 thfr;6 hbt7x /fce outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of thb f/;67crxf 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 tryo.ntunmvsg7p 2 66-re ing to adjust two strings, one of which is sounding 440 Hz. How far off in frequency numr t67p v2geso-n6.is the other string? ±    Hz

  What is the beat frequency if middle *i4na nv ww:d7 e3.t:;srgprzC (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, 5mu u/ v9j kcp+6+eahdo; wgr/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 apum;aeurc9d/khvjogw6+5/ + re played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sound0vve p*tnjto7wy u. (0ed with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your r*0 v(v 07wuojptn.y eteasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one 1 ra 8n0gtr* f97*cywfjx5lh bstring is then decreased by 2.0%. What will be the beat frequ**a 5l ytf cghjx891nf0wbr7rency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each i-()n(t 4vjf(x69w r)vhqnhqg et r(xtry to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0 (jtqi9v n wtvfe)g((q6hn4)r (h -rxx$^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hzl1 m:tmll1 p 6*ypt b5xts8w8u; when A and B are soys lx16t8t5tl 8wbl1pm :mu*punded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C 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 one sp iva)jn*d9 ,wjeaker and 3.50 m from,) n9jvj w*aid the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a p q2b3kb/r*/lpz i* pdxiano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132r/xpbp*z d/q3b kil 2* 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 wavev:,ub lww5ud7km8y1z c8e*lu( h3vi llengths 2.64 m and 2.76 m in air. How many beats per second wz7d,l81uuw ue8vciy(k : *vh lmw35lbill 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 when at rekt8li+biknde ;uw3wv,u y61 *st. What frequency do y 1i+nuwv38;, idkuwt6ke*ylbou detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fi (jy9i( 0wcssaa3b87fc6vmzb pk 4ty* re engine whose siren emits at 1550 Hz moves at a speed osyvsa3j(cfwzib p*m 6k(4 8yb7 9c0t af 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequenx w a8nz05k,23mnnjzi ;d lh(ncjur5*cy if a 2000-Hz source is moving toward you at 15 m/s versus you movikr na(n i5w 2 3c;0j*z 5nhm8dn,lujzxng toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the saf ;(/6wjj p-on/192xzf)elbeic a h ilme single 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. What is thfei) ajx2 lz9b hlpfi/1(j-/o wec n6;e 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 renc*6/6l5f scet )w vk8y fo.bm8 eqj4pturned from an object moving directly away from it at 25 m/ejc4f*votbny s8 f 6e)5 wcm8q.6/lpks What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s 8 fzqy,5 e:izwel6 i+sAs it flies, the bat emits an ultrasonic68,zisfw z5le+iq: ey sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a nml8c4ll2r)n;bur 0igvm 4- omoving flat train car at a frequency of 75 Hz, and a second identical tuba p n4ncmvmrb4)u- rog2l0 ill8; layed 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 meterrc:yy2stf +o* rwf9n/ uses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the soundf c9ytw*rnoy: f+2r/ s source?   Hz

  The Doppler effect using ultrasonic w q/j6 i799vb.dv - atu-qaqogsaves 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 frequealz58fuyz ,x r s6.x0wncy 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who a,6rx0z5 ysu.axlz w 8fre 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 spe mrvfz:( ct; tk2ni5d8ed 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 9;pzyvo*7p6pnt eu chi b)z*:where the speed of sound is 310 m/s (a) What is the angle the shock wavz7;p :t* 9iu*6eoycphn zb v)pe 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 the speed of soun5zwmyzui;c1( d is ocu yw5zi1zm;( nly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s stlqza0kc ;u/3jz di:l5dvs1 )-mb:wx orikes the ocean. Determine the shock wave angle it produces lq/md3zbluj:5c1zs )i dxov ;0-w: ak
(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 p-dx kaw* gvq0*lqy03 $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhe+o j6we(.k:*ah lj jrmad and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear t:lok(j* wam6 re.jhj +he sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar deviceqz93eb0 zbw* k 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 pub9b3kqwe0 z*z lses (in fresh water)?    s

  Approximately how many octaves are there in the human audible raz:tpz oe5 t;s+f8/iptnge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displz4z a6fr6dkr)1rl1wkd: ;s gqay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, whicdkrfs1)6z;rz d1a4q wg6:lkr h are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close jen(bl9. tjk )ljb4w 3to the threshold of human he4n3 9tjbelw(k l).bjjaring (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soubiv +maep)/b +nd are heard simultaneeb mav+bp+)i /ously?    dB

  The sound level 12.0 m from a loudspea 9i,f0;d; c ksr0 rmop ml)0f+fq;onofker, placed in the open, is 105 dB. What is the acoustic power output (W) of the rmoo;0f 9fd l0k,); nc i mpo0fq+;sfrspeaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops3t /ke2zmr kc. by 10 dB at 15 kHz. What is the power output in watts at 15 kHz?3mzt2kcek .r/    dB

  Workers around jet aircraft typically weaha21z gc *u94 +t4nvkxypat:xr 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 airplant n2:1xv*44cg xuaz9khp+ yate engine?    W

  In audio and communications systems, the ho:( gcw.*hcwgain, $\beta$ 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 frequ 3 dluwdwua *x1*: 9alz5-wpcrency 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 c5q)krl4 2n,4 kditknkm long between fixed points with a fundamental frequency onn)tki d 4kkk r54l2q,f 440 Hz 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 filli pgcv;.ibxp7 pq1p4*n0xo 2iy zgr94jgh3p9ed 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 isipgv p4pyn 92 hip1x9oir;zq0jbc7* 3 ggpx4. 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 .o. ym qwk pr)ixt6:1gmass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the thi1p6ow. grx.:t mkqy)ird harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to res9cnxpub3a 07 :eg-s pbf /jjy.onate 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 soura a ynzg31o9;m 5qpah)ces. 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 0.3m y15oq)hnaa9ga3 pz; 4 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 conduut: ( * 8ot)hs83 zovrow4qieector on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the spees(u 8z ovh:38 et o4e*qwt)oird of the moving train?   m/s

  The frequency of a ste ba2 wfo4 9a6mx66 (haw0u)6qyoftv clam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fas(f ot2favhc 6b6qw ol69 6um0)4wax yat was the train moving (assume constant velocity)?    m/s

  At a race track, you canl tdxdcn.80x+ estimate the speed of cars just by listening to the difference in pitch of the engine noise bxl0d. d+n xc8tetween 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 bepdmja ikc,7ot 7az415at frequency of 11 Hz. The shorter one is 2.40 m long. How at71,amio4 jzdc 57k plong is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves p4uc6xgl/ hnl fs9c/h +ast 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 of4/nc hxc9 lh/lg6+suf 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 ;;8f u )cand m;h*yjvx1,n 2vgwvhaj* the aorta is normally about 0.32 m/s what beat frequenm28*,xg1w *anh; an )cvj;yj; dvfvuhcy would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a 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 oq -gnwq5;g:)yqnk b/ 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 t g5byn- /g owqnkq):q;he bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as uyyl4d., eqe*it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms l.y4*yde qle u,ong. 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 atso.d0w(v(4esnfpo6le 68 4b bpg)yAlpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. bo)vnae.wst4fe68g(0( bpdlpo y 64s 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 presence of) 7tevxot0dq0;k;c5 nbcda -q standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room ;o)-v kbtd7qcxqat dec 0;5n05.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves :tb odbk hbmc- 5,n34ha long, slender aluminum rod held in the -4bh, n35bdkc mbth o: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. 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 hearingqteyg,sn 1 21p for the human ear at a frequency of abop q e1g,2ynst1ut 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 gro+oy4, uekmy9bo jgqo1ihkxj *y n 6(9+und hears the sonic boom 1.5 min after the plane passes directly overhead +q6jxjy(uyb1n goo+o49mk y9e,kih *. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ,1bw8 uw cjmj*is 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