What is the evidence thajjap u q01oyh i53j3p u0(dmu/t sound travels as a wave?

What is the evidence that sound is a form of energjwifi;a v b8,i2is,gc5.d) ogy?

Children sometimes play +jclt d k(+yhm-x /f2c qx3koxa02t:z with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into t:cj x0 3y2xzaxdqlm th2kk+-f +oc( /one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into m65t )g5b1 vpt0orwg4 n wd w5dd+lq0dwater, do you expect the frequency or wavelength to change)wt ld0 w 5514w5q06 nddtrmo+ dgpvbg?

What evidence can you give that the speed of sound in air does noftks8n; 8sgrvm r566zh(*gi g t depend significantly on frequenc (n mikr6sv;8gg5z fgt6h8r *sy?

The voice of a perso zzkrc2/*o2si a 44ulqn who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affec,usg 4tee3.6lo +khcc +gs;al t the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude gbe0/ m1h2-howf: st pof sounds in variousg /m-hew: sft2h01opb frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tonj). (c1mxx cpgether as you move up the fingerboard tom (xpjxnc)1 c.ward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but cu;kmd356y pdgannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of thegy;5 md3du6k p high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to b:r :kgske rn8x3l;e:c e due to “interference in space,” whereas beats can be c srn8:xkeg: l re3k:;said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were 6v+,m)/.efcyhi k3 pwcs/flqw8 erx/ lowered, would the points D and C (where destructive and constructive interferek,sf/ lcwp 6m. crfv/3whi yq+e8)/xence occur) move farther apart or closer together?

Traditional methods of protecting the 8lwfshj* v/w s39d5ppc t42mjr 4+kwuomqd;)hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce tc r sql5wm+8f3uo9 stwh d24 pmpkj 4*d)jw;v/he sound levels reaching the ears?

Consider the two waves shown in F5 )c+ nintm0grig. 12–31. Each wave can be thought of as a superposition of two sound waves witirgcnm+0n5 ) th slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same did tzk75/js d9 czg746ih.ah swrection, with the same velocity? Explaii.hjs4gdcsawdzt 5zk 67/9h7n.

If a wind is blowing, will this alter the frequency of the sound heard cw1gteb5 (9a( chta:) lxw.zq by a person at rest w 9ga.c(ebw tlza chxqw:5t) (1ith respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swin 6/e)dls oi5k9kb7kth g. A monitor is blowing6hdt57 b/)ks9kikl eo a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for ,8 8kt (qcnqflz; r-li3ob0qg the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. cfiq8lq(8kq3b 0-lg ,r zon;t $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterli)z 9wyqfm/iy vjh05 v/ne. 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)j 95hiz myv0/vq/ ywf 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 a *o12 n9l ib.kfda+xa icl6*oat 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 above0)i1uonov6-op x mi 5v9zwz,r a school of tuna on a foggy day. Without warning, an engine backfire occursr9z 6oiz0, )1o5-vinxumop wv 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 makes when md3dvim5pud k/ko7eu*j7e6z a6; dn7striking the wa u7d6pejik5 ddn6 o;mke/maz7* vd7 3uter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees5 8s+syyf1 0boq*:1ft3c yp6 yzt gqok 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 t gyq6t1 8zff k*q5yo3c0 + sy:b1yptsohe impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of di5f6 kkijzdtb(mg() 1 n. q6opestance by the “5-second rule” for estimating the distance from ap1i)k5z. ge 6 jmd6(q nb(tfko lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1 jx06wmxbrz hc1b)28 s20 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 intensivlq -tq9a1n)u,,5t e+wmtv ogty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levelnazom 1m ri h-oj9qb.,b9n4p / of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add in,q1pozaijb9onmn . rh4b-m9/tensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wqi 5 psk2u,gzr1b3wl6r/y *z qith 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 shut down alp skbyqr6 13g r2*zqu izl5w/,l but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sig0dp .m d2j:eeznal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the sij.z d:p mde0e2gnal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pso k b:.pp-0fmerson speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly o p m0okfsp:-b.ver 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 arggk y ck6uw6/74,ndse ea 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 gp+no gi s3)+lis rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudsg+ipsn ol 3g)+peaker 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 obk7 dfrzq/z1p xh9+4 m in front of a loudspeakep7/dhkfr 9+ qz14oxzbr 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 leve; tlcy ;)ota7hl of 2.0 dB. What is t;hyoca;7ltt) 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 sound wave is tripled, (a) by what fatwbu82zhg sn wtp -(e8iv7*8 actor will the intensity increase? ib8 (gn e8 thp2w7zstaw*vu8-Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the fhpvz x /:wk4olz : -y:y/8kevwrequency of the other. What is the :-l yk zy /:4h8:vwwkz /xpveoratio of their intensities?   

  What would be the sound levelmmm*8,set) zk h:0l.g3m scg j (in dB) of a sound wave in air that corresponds to a displa * 8jegmhkss)mg.:zt m3clm,0cement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level tezgb26axj6n.+s t;fr c+; c fjo seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12– 2zb 6 rc;6anjt;+ s.f+fjcxge6.)    dB

What are the lowest and highest frequencies that an ear can detect who-t+ mt 2 0uysqfq1gx ald,8*oen the sound m8+y xgf20,stoqou 1*t-a ldqlevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is thyw/ e)- oxq.*uvt z.on fx8he2e ratio x. 2*o)z eqevuh-nt. 8fo/xy wof 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 freqsm3or5j l/ 4izuency of 440 Hz. The length of the vibrating portzjs/lm3 i4o r5ion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first th8xa s8uz :5bvcpl ;g*hree audible overto p8 usa8lxz5 :vcg*b;hnes 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 blom:ifw3 9kt)2lyui yz* l6ono26sw s i0wing across the top of an empty soda bw*:2 mlziy stk2il) 0i6sonf69w3 uy oottle 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 lgpqn rr0gf9z 30n5h ,pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the rang hr0 r,5zgpnl0qn3f9ge of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Whh/ la/i d, mhw-wh:vyk *-anb3at will be its fundamenn *h lwdm:vkhawb-h,-/i/y3 atal frequency 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 to play E above middle t:dzdii:8 :a mC (330 Hz). i:d:aidt:z m 8
(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 olo+4-*oa ig wirgan pipe that emits middle C (262 Hz) when the temperature lao w-*4+i giois 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 uf8(zaam9s +,erob:j $^{\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 holef z.9le8cbu b+ be that must be uncov. ez+blf8 cu9bered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, bu hx4 inakc*3*+wflgz, au6u-et not at any other frequencies in betwuu3ai f4**lhwzg-,e an6 x kc+een. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. 4 . meb8m)ga( :gnztb ym5tc0gIt resonates at two successiv )tg gbb0me 8gz:4c (nytmm.a5e harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 58r3r s fc+ayc$^{\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 ttcv: t x/s9hj hk*u:9 q:mt5. b5d-i(ozlv uqjhe audible range for a 2.14-m-long organ hv:jot .:l uhsb /*59iu(9tm:vcqtqk- 5dj zxpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is app;ih*wz nx/o ctjw; ;2lroximately 2.5 cm long. It is open to the outside and is closed at the other endch;nlx ;/owwz* jt;i 2 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 striww44f,-.db scn yak(ungs, one of which is sounding 440 Hz 4,-4f kys(aw budwc.n. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (2o(rib*kwhv 4v-0u6rb4zn*uy8s p2yd62 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 oked/yjoq2g+.s+rla a:p2i b c j1:v023.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when play01jyqar2:.b av/dipeo+g+ j 2ck:s l oed separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9 i3 dg-c:ug+kl2;nm y zbeats/s when sounded with a 355-Hz tuning fork. What is the vibrational freque3znd2g- +m:;cg ylikuncy of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294kyv:m2k;iy 3 y u-xdt, 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 tog2u ky x;-ymt:3iv,ydkether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to wrt* u3f4sij -k -gb0zplay middle C (262 Hz), but one is at 5.0°C4k gw z0i brt-3jfu-*s and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fo8 0z gwui58gdfrks, A, B, and C. 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 and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A i08z85fgg u wdand 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 3.00dyqyz67iu,)*wibs2g m from one speaker and 3.50 m fq z)i7u * sigywb2,dy6rom 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 suppo8y( .vk r1p ,zq:ohx 8qo(unxnsed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 sv(y, r (qq pn8kx8zo:hxo .nu1 when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many3 a t7*0guu-ygalka)a beats per se a7agag3 - lt0*uky)uacond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire e-epezh,t b/rl l)3ba; ga1s-jv.j9ln:2c vr yngine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a:b, cl vhjyrepe -2gt r1a/3.lzanv-;lb9sj ) speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detehjw58lee 2 es,ct if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/ssh 5l,we82j ee
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20m8i ,m+ qmciyo9 hz+ezo1 l6c000-Hz source is moving toward you at 15 m/s versus you moving towc oz+o6 c+9 iyz,e18lqmmhim0 ard 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 same single fr76bxgdq, 6jh9*dn t80tzs shrequency 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 the frt hj sg67d6bd s0rqtz98*h,xnequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends outg;rfa1e 3ktlvjo mn( 3 e(-)xq ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the recfmq3;3 1 enk( levoxgjrt()a-eived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ud-5i(b0 yg3h pwigi6zltrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hea3h(wi6gpd i5y -g bzi0r in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler b6:ww giw g06;i,sqy5 g +4cvavb(jex experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the ;5:4+6x0gew6acjwv iv( i wg ,bbqgysrailway 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 wv8(rbx9zko/ 2sp l- zzjkq/ fi/2ufpp b4p )c,aves 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 iflpbizvk4r2 p8jk xu/cop9,z-)/ qf(b/sp 2z f blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usijx8pg nx)(6 owng ultrasonic 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 sou0/9i vn pkj;nwnd of frequency 570 Hz. When the wind velocity is 12 m/s frojn;/90k nwpiv m the north, what frequency 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 sxc,5b2)u mk zipeed 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 l91i lmawq;gs i6m12f speed of sound is 310 m/s (a) What is the angle t2llai f1 q wsi9gm16m;he shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphr fcth .* qlb0qf5k*;5,qbr grere of a planet where the speed of sound is only abqh.bgff5bk*tr5 lrqq0,r;c * out 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 travelinsy1.tpjtw c9 q70r mv4e:2gi vg 8500 m/s strikes the ocean. Determine the shock wave angle it prodyte v gr7tjs10. 42c v:m9ipqwuces
(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 1l,ii ,lj eungu/ s29c$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and seq gbt3w :96xfv-3mks ye a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the 39gv-:bm3s6tyq wx fk sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sou5w9lk;v f cdo+uuy)lc7/dl p1nd pulses downward from the bottom of the boat, and tdu5 pkcc; l olu97)vd/wf+y l1hen detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octavwocg dl/tjck4 yi6).2es are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sew(x rfz ,xxznms9nf+q vg45)p*er pipe symphony. It consists of many plastic pipes of various lg (qzx4pfvx)rn ms xzn*9f+ 5,engths, 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 fr (x78dh uipl;kom a person makes a sound close to the threshold of human hearing7;x ulkhp(d i8 (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-ck c oc8w-+q ytcz9d);n0hg,fdB sound are heard ,qchw+kc nzytdc;o) cg f0- 98simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What ihi lg msf7e, ;t4j bm+)r6net,s the acoustic power output 7 mgs,m bltih6t4e;r e +n,f)j(W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dropsfs 7yv.+oda l:qcpj 7+ by 10 dB at 15 kHz. What is the power output in watts at 15 kHsqy7c7aj+.p d: vo l+fz?    dB

  Workers around jet aircraft typicalvx(de.c )ht)ll bx*j3 ly wear protective devices over their ears. Assume that the sound level of a jet airpla)l*v). t clbe(jdx3x hne 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?    W

  In audio and communications syst 6hi2buo:alm7siy s4hp3f(u2 ems, 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 viobw tgh a7if5:jwq. 57ecod 75ulin 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 scy.l h46odt cd7t4z3is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length of 7hcsdd43 o6l4.t zy tc$6.1 \times10^{-4 }$ 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 verticu zi i15hv/d:qp ou..+ghviaphci-8 .al open tube filled 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 distance from the tube opening to the water level is 0.12/- p.c.zdv :ph au+vi 8iihqogu i5h1.5 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar strin 58k4ob8 l/a2+vibmbd8 sklym g of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundam8m oky2vs+l5/4bi mkdb8 l ab8ental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one bz w5ww w mt7nr(;7.cufull 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 sources. Tm.ehv 2( /b-zsgnte4fhe sound is loudest at points equidistant from the two sources. To determine exactly what the fre .s(f he/ -ezn4vtbm2gquency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the qkvt9q9 )f:m(n+ejs mpl - qo2stationary train hears a 3.0-Hz beat frequency when the other train approaches. What ik (+s q n929ovq)qmp eljt:mf-s the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you ish owpdekf:a:)6 kgi a 04;pz*y 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)oy d0kizp;:a 6k paf*w)h e:g4?    m/s

  At a race track, you gxkai ,:a /jqfo4u5+d1tmz3mcan estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fm+gd3o1 x5 j:4u aq,zifm/takast is it going?    m/s

  Two open organ pipes, sounding together, produce a my/b anr(:afl ;r .tcn3bt/n9beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the on9af.bclm/ta r ;r:3yntn (/b ther?    m

Two loudspeakers are at opposs+e :uq4q zpyzd y/9k2o, uy:aite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer sy:qu zp ue:y9,a k2qo+d/4yzwhen (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 flow in the aorta is normally about 0.32 m/s what s u-:+ tk1j*eew8pxtf32 qj erbeat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red bw3 suqetexe*-j+82r1f pjt k: lood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moty 5/* zxegyw o+:j9.8hpjdw zeh at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat d5e8.e+gyj/wyx ow:*jhz 9z p 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 moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. s ryl4hd;2*ukThe pulses are approximately 70.0 ms apart, and each is about 3.0 ms l *lkh;rus2 d4yong. 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 senr73nko-ssi i b/9vtw(a:p2n/ka4zjz oj) (ja d signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a mus9za7as kztsj2kw joa3(bi4(:prn /)- jvn/oiical 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 stands qhysc5 tk8;y.7g sf8ing waves, which can cause qgt ;7fhks8ys8cs. y5 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.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “s83 x1;aiufytqinging rods,” involves a long, slender aluminum rod held in the hand near th8yu qti1a3xf;e 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 thres-ac7az1 ./hkj kb3ix*.fk rifhold of hearing for the human ear at a frequency of about 1000 Hz ik./ jb7hiakf*i3r f1.az- x cks $I_0$ = $1 \times10^{12 } W / m^2$ 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 grb;j(i) ,,m0ud 1cyptglvse( q ound hears the sonic boom 1.5 min after the pli1jgmlv )(qdp,y,se( bu t; 0cane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat kr+z,t*on oa1 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