What is the evidence thatfxy d/x8/ih7w sound travels as a wave?

What is the evidence that sound ix m wu,na,u7/js a form of energy?

Children sometimes play with a homyf) u-g h2cb(bemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29).(2hcyfb)- b gu Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expe x/agr-kj9mv:ct the frequency or wavelevg - x:9j/makrngth to change?

What evidence can you give that the sc-g*pd92/fzpr rv /hu peed of sound in air does not depend significantly on frequency-r rgcd/ / h2vpuzp9f*?

The voice of a person who has inhaled helium spv5baz2rwtp ;o (a 8;mounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of or,czee plj58 )ygan pipes?

Explain how a tube might be used asyn82zn1u9o ea0(l:7b0wbk txqz nw5p a filter to reduce the amplitude of sounds in variou wznnq1 52awolzy980 7x(:neb 0kb tpus frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced c7kla t )gx yodxf 6(4emwq);;qloser together as you move up the fingerboard toward the bridge?oflywe;q(a;4 6x))kg q7x m dt

A noisy truck approaches 0dsx 09p7 32vh7irms aw(;,xurj ph,.ywazee you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explai 7vs hw2(mwar9 ;sip e,xhe3pu.z70 ar0,y xdjn. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wheryh ,hr(oc3. mueas beats can be said to be due to “intech3( ,hy.u ormrference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered720d jwtf lx4d, would the points D and C (wd 0t7dxwjl24 fhere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of prote5 3m7-7xcwsgzv;nna u26l 4mkkc5xtr cting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambiemw; s7kt-vln5 nx 5m3zrkxu 426c7acgnt noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can beldhu6k 6.pe ;p65ekswc 5m 4dw 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? Explap6 plh6 6kw w;ed5cs4 u.5dmkein.
(12-31)
(12-18)

Is there a Doppler shift if thfqvtfe 2iq(*v0+;/ zobuyx7o e source and observer move in the same direction, w2oxq vb /(+zeyo0qv *;t uff7iith the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sou q ylq*j u-r8-j.vuar0nd heard by a personuajvq8r-0. r yjl*-uq at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swinmnig gj ))rwr/9.(za6nz u;nng. A monitor is blowing a whistle i)rn;r.nnzw)u( /z6nmgg9ji a n 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 the echo of her shoutq n(/h/(qbm -b 8g4l4bzomscz reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the len/mq-q(4l obbm8zh /z(c4bng s gth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just be41itblxa3xh s bdl1tdz+80 ,klow the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly11itz4ldx0 ,k3lhb xb8std +a with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengtsy.yx,49tqq )g(m sl phs in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school eo:x1 6s ct+ ;*ivcid*mtsb*kof tuna on a foggy day. Without warning, an ist sd1x*it :m *cb+ *eko6vc;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 w,5:jgw ex tn,t)m n;qthe top of a cliff. The splash it makes when striking the water below is heard wmt n;,,q:x t5jwn e)g3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stritaa6zmkrr*y :55ph s ,ke the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and thr zk t, 6r5ap*yms:5hae 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-sec .apqoo2 1ejn)ond rule” for estimating the distance from a lightning strpj eoq) 1aon.2ike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the:5st3ysebr+i 9-g+kfpiu44w6 p 7ugpoiz9vl 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 intenst kp p/ ve:sm(-smz:3bity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simul:+6cf s3 cmdjutaneously at a certain pld6s3c mu:c fj+ace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with tebjn vd8/v ku1 ;d)7ffour equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. Whv1t)u;d8nb e/kjd 7 fvat 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-9fhb ptja( *egu 1h18znoise ratio of 58 dB, whereas for a CD player 8u9z1h 1fbj at*h (gepit 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 output of sound from a person speaking in normrrq5e;eph7, d/h7y bxal conversation. Use Table 12–2. Assume the sound spreads roughly unifo her;,r /bye7p7dhq 5xrmly 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 strikes an eardrum whose avj24d2vwqp6bb+d u/ h4- e q.y9wmqytrea 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 ampi+ 7tr8gb)sr.tek ;to lifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to e te.brr;i t +sg8otk7)ach 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 2apile48i6o 6 ip2rdf, .8 m in front of a loudspeaker on the stage. 68da2lf4 ,ip6 riioep
(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 typically4:ysn dxaebgw; 4 x3 arw y);oybjt,79 detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectio ;on: ay)4;ww,dsr abyjx7gb4 y3 xe9tn 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a)+f nyer(q*:2ggnyi j 0o1ft8b by what factor will the intensity increase? In nr+0goy q:8te 2(b1*nffgyji crease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudcogzrq+ub wm;bo- *puv1 m)og*z 9+2res, but one has twice the frequency of the other. What is the ratio of tpz1oouqm*9;r+ *- zwo 2)cgmg +ubv rbheir intensities?   

  What would be the sound levelu*usq8a; c-g w (in dB) of a sound wave in air that corresponds to a displacement aa*ugcs wu- ;8qmplitude 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 100-Hz tone t7sf9dx3di (lby5yta7 hat has a 50-dB sound level? (See Fig. 1fxl97stadyd 7ybi 5(3 2–6.)    dB

What are the lowest and highest frequencies tzb 6tcy;hn/q (jny9flcx 45n3hat an ear can detect when the sound level is 30 dB? (Secc 9 ;3qjy( ytlbfz4x/ n6n5nhe Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound m3t l/0z nl7r7dsmk6eq y1u/elevels. What is the ratio of highest to lowesnrt 073lsyq 7z/mm / l61euedkt 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 frequency of 440 Hz. The 5pid z.eaaf*:vev 2z7length of the vibrating portion is 32 cm, and it has a mass oa ezv.2zd pi v5:7af*ef 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 three am 4lwq:li *g9audible overtones if the pipe is : w*q gali49ml
(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 frequenf2jzaqs jq:-8j/ k5cccy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you asz/jck8 js:f5 -jc2aqqsumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanm 9;nwkn ie+t-ning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes r etinm;w k+n9-equired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency o(z+qb ht4dz 6ef 540 Hz as its third harmonic. What will be its fundamental frdz 4q 6+ztbh(eequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long m +s(mmf(gn uar v :* yoh6bd(-gjaw9:and is tuned to play E above middle C (330 Hz)vb :-+(oufm*y ( ammw 6j(ashgrg9:dn.
(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 minhbwfz5 n +o9bmoh0u5j j)9++j:vpqt ddle C (262 Hz) when thehwq n:9fpn09+jb v 5j5 +otzjomubh)+ 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 a:hzj. 3lhu e:4njh1 gmt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of th9av ;stt6;rdah8 t3tg e flute in Example 12–10 should the hole be that must be uncovered to play D above 8 hvta9;6t td;3s artgmiddle 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 r jkfkxm 7d:-4v v(0yixnco. m3esonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an 3cmm:fxn7k (dy4oi k.v0v-xj 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 endop (h78 i)rsygs. It resonates at two successgy)isp 7(o8h rive 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 d lpfxc pi8c/4zjc05wsnoe*c-;l*f 7m gl,o;$^{\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 auk tx -(q0c8j kbz1j/wxdible range for a 2.14-m-long organ pi xj wtb1c /08xkkq-j(zpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxim a)hev0o cxvuz h29b 3xf5jwbl;.m-(bately 2.5 cm long. It is open to the outside and icb.o( vx0w)be;afhzvbljh3 m9 5 xu2- s 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 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 ad6ja yf hr.(zv1just two strings, one of which is sounding 440 Hz. How far ohv6zf.1 jry a(ff in frequency is the other string? ±    Hz

  What is the beat frequency if middle Cs980emku p wp9 (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, while anot fwhkji6(9qb v*cu 8,aher (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 simultaneously, ek* ijq6 hv8fbuwc9(a ,stimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 35j xy :2 rhvl4fowa1-t/0-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What x/ -at2 yofh1r:4lvjwis the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 H4j5l5gchf 6vp hj5; odz. The tension in one string is then decreased by 2.0%. What will be the beat frequoh;vjc d55g65 f4p hljency 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 tmm ;*6scm,dbary to play middle C (262 Hz), but one is at 5.0°Ca,scd;mbm6 m* and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, ,z t6si l*f8mdA, 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 and C? What beat frequenczs* 8fidt 6m,lies 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 apar aty/+c5xs+ndbso t+:a3xvn*sv8 6p ut. A person stands 3.00 m from one speaker and 3.50 m froxn*o5:pt3vaayn/+ub s6 dst8v +cx+ sm 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 b4v c22 8s4,gu swdgwga piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vivugs wds448 g2,bwg2c brating 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 many fbnm0s g)mr 35beats per second will be hea0 bs)m mr3n5fgrd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1 nrvpat4n*m 5)550 Hz when at rest. What frequency do you detect if yoa54npmvn *r )tu 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 ; h7spvwjh4n3detect if a fire engine whose siren emits at 1550 Hz moves at;n jhwvh7p3 s4 a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequencsxg4)bx )ocmpy.3 7bui f7s6fy if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Arpfomyx sfb bs4.367 7ux)c ig)e 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 zk2+)h7fj y vnthe same single frequency horn. When one is at rest and the other is movj fyn vz+)72hking 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 ultrasonwvn7 :rdx fy3gh5*0* koproz+ic 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 received sou0*yr*+ vzf:dxoh rkg7 pno w35nd frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall qpj .bdx1iy1tl -ol;k-qmo/5 at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 k l-;xk-btqoi5 yo1qljpd 1.m /Hz. 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 movm;sxedi1eq psm;m+v,9 ( bls8ing flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train casi q, vem9x1;8(d; +bem mssplr approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-rr+ub)60 e *yk;wt2z3 daojj vflow speeds. Suppose the devicjzjb r3od; y6et+0avkr)*wu2 e 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 sound source?   Hz

  The Doppler effect using ultrasonic wavno)dsjxf;9hl 0u; -yj es 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 em 4 k, r +w;vfoi4u*nacq,dra:qits sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will obs adi;woucqrnf qva,k* ,r:+44ervers 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 lan/cuk)vo) 7/db dcvg6kh:lps, d 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 s*;aigo m8bryo yj():the speed of sound is 310 m/s (a) What is the angle the shock wavj8r(o)y:m*;gois bya e 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 a(w7g. ),btjc b;xu vpdtmosphere of a planet where the speed of sound is on x)v 7;w ct.pbdjb,(ugly 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 strikes the oce+srvrc z;* *lyan. Determine the shock wave angle it produvz* lcs ;yr*r+ces
(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 xykl7c.d wf ilx.+0 x3c5is0k$/theta$ 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 e,4oqs c3pi4r above the ground flying sr ceio3q44,p faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See 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 sendsj-8)as*r gbelay /0ab 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 mi0s8)jl-/geabrab a* ynimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human wmepz22ip ad3)zs / d1audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displaygqq7o6 k8 bttd5v-r 5k called a sewer pipe symphony. It consists of many plasticdq-v ttrq 5768kg 5obk pipes 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 person makes a sound closqv(ddw g13 9tqe to the threshold of human hearing (0 dB). What will bew3dvq9 g(1 tdq the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound le(ie uz sva ou4m.*s(*dvel when an 82-dB sound and an 87-dB sound are heard simultaneously**s ds.avuezom(ui( 4 ?    dB

  The sound level 12.0 m from a loudspea7 hiweka8z4bp7 g(3 kjker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directiopak34ie8zgwk j7(b7 hns?    W

  A stereo amplifier is rated at 150 W output ar fv y kv-)bguu:w;/,.t o3cxzt 1000 Hz. The power output drops by 10 dB at 1 3.k/u-cyzr)t b fvv;:x ,woug5 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear pn o1yno01gnz +rotective 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 onzyg onn0o 1+1f 30 m from a jet airplane engine?    W

  In audio and communications systems, the gai9k nb(rk(*b.xw2sop:rk+0e(f/dn t mwfg b +an, $\beta$ 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 freq/+ luuufu(mz.md t ;;buency 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 pfz yl43d +u1 /p,lvjpcoints with a fundamental frequency of 440 Hz and a mass per unit v 1,pz/f cj du+pyl4l3length 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 p5m0n wdddirr 4uemv008 9lf e4i7,gja vertical 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 je r0pin v08lw mdum,44geri750fd 9dabove 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 s-u 1keukkp81 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 third harmonic -8u1k1es ukkp in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to res +nou)wxk/7 wkonate 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 500–10ttvs/m(e.moc xnieux /. -*/t00-Hz range coming from two sources. The /m(e.txm-ue*to t/s n.vci /x 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 sound?   Hz

  Two trains emit 424-Hz whikhf ywq2zmhdg*7- g0 )stles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train appro 2 d7 wq)*ghzh0mfgk-yaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appr d;y6eec(;mjl cn 0*stoaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fas6jdcc;*n t( ;melyse 0t was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the dk 3ybau7h4e t1ifference 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 straightawayu3 7htekyba14. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency ofo:h2(:w ;b uppd,r lam 11 Hz. The shorter one is 2.40 m long. Hwbdp;ap, r u:l2ohm: (ow long is the other?    m

Two loudspeakers are at opposite z;1v wk)com-k ends of a railroad car as it moves past a stationary observer)zm1kc-;vo kw at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he 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 wqj zvwkj(01mr2de5y:cvs/1uzc+j + chat beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflec em vc1sdcuj 0wcjj:(5qv/2+yrzk1+ zted 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 fl,a9 hohcqa9*c ying toward the bat at speed 5hc*oh9a 9,q ac 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 moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mogugg26 g;c xvf sxc799th. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms lu;g2 9sggc 9f6vxcgx7ong. 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. 1s 2b1l /04iayr0llo kb2–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played alby2 l4irb0ls a /0o1ks 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 sm ou))0tjn8r9ao 0wwitereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodm)ro n9j oti08uww a)0es. 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 “singing rods,” involves a long, slender n v* gp:wxmnb4g7. m8ialuminum rod held in the hand near the rod’s midpoint. The rod is stroked win 84m *xvp m.ngi7gwb:th the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequewisnp9u ( )o(.t wrvpst*3-mvncy of about 1000 rn-3i) (ut*9tm. wvwpp osv(sHz 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 Machn 6z:sj/mj 2sr 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What ismz6rs /2njsj: the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15al) 4w. 7r40qxr5qwa p9vns hk $^{\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