Give some examples of everyday vibrating objects. Which exhibit SHMj qdz menv e-..59z.lhqj x5,m(l f8gw, at least appr85-jd hl wg,feq(l zm 5...xqvzjm 9neoximately?

Is the acceleration of a simple harmonic oscillator ever zero? If7)dnyaq +iu 4*uidh3q so, where?

Explain why the motion of l*nbvlx vs)z *nd ;sdi 17a*9ga piston in an automobile engine is approximately simple hvs g*n)x9v1; zl sbd **al7nidarmonic.

Real springs have mass. Will the true pelr28jr2qy9he ,skze 6riod and frequency be larger or smaller than given by the equati,r29hezr 6qlek 28y sjons for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maxig y: 6:h:cltlxacn i44mum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and th-024k 3qrmyzldwfc p-en is released. Describz f02- py3qlmd r-c4kwe the scale reading as a function of time.

If a pendulum clock is accurate at sea fz9 .-vgrp7gq: t6lz ilevel, will it gain or lose time when taken g6zrp:tgf- i.7 zqlv9 to high altitude? Why?

A tire swing hanging from w/,qmf 9sf8qyao: /i.fikx9g a branch reaches nearly to the ground (Fig. 11–48). How coulm9 /sgq iy 9.,oiwf8f aq/fkx:d you estimate the height of the branch using only a stopwatch?

Why can you make wat m: b)ovmx9if(xhj2a5 5sdw;n,xj5tx im. (zz er slosh back and forth in a pan only if you shake the pan at a certain frequhjzzo ,5x ixis9 ;d w5j)m.(mxf5x at2 vmbn:(ency?

Give several everyday exampb *vr*q)6xhjcl*7 -;o2fcjeyska g)tqfxe03 les of resonance.

Is a rattle in a car ever a resonancev*ac-8db g. rhih*6pf phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sg4 w6v lbqai + 8i)6u-d3hwygjource? Why or why not? g4bu+iwlyga3w 8h6 -j) 6idqv

Explain the difference between the )eiknl ay 50n2gp 19cospeed of a transverse wave traveling down a cord and the speedilk5o0c2 ngn9ya)ep 1 of a tiny piece of the cord.

Why do the strings used for the lowest-frequqr;b +sm5 tv x(t:ha3 hztl*.l8mfrz2ency notes on a piano normally have wx *ahrm3t +:q5rmt8htl .s ( fbvz2;zlire wrapped around them?

What kind of waves do you think will travel down lo4,tc ;p;l/f tytg9ya horizontal metal rod if you strike its end (a) vertically from above and (b) hori9t ;to lyf/tgy p4lc;,zontally parallel to its length?

Since the density of air decreases with an increase in temperature+n ijdn), r+xhcean)6 , but the bulk modulus B is nearly independent of cx,rjh+ en 6i+ n)ad)ntemperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons whycs63 eocz b0kz evi4w(0ywdpa,s vb8 ;o9cn5, circular water waves decrease in amplitude as they travel azpiwes0kdy 4s03, c ;9oe6ac(vo bnzvb5w8,cway from the source.

Two linear waves have the say2mo 6u irf +).q1yh:,k opwvf2y) wuwod/2gjme amplitude and speed, and otherwise are identical, ex.dkuj2ghom12:+y)fiu ovoy / 6y,wr)f pww q2cept one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between twmk-zm 8 pgi0 io nxb4tul(3)5rm4)jvpo sections of cord as in Fig. 11–33, the frequency does not cr5om4kb 8i pmz x-(mtp 3i)0l ugvn)j4hange (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are t, 1(+j kzmjal7 ixhya5here any places you could touch it with a knife blade without disturbing the a+ li7yk maz(15,xjjhmotion?

When a standing wave exists on a string, the vibrations of incidenqtc ypn*p4 /l9l:hax; t and reflected waves cancel at the nodes. Does this mean that energy *xqnp4h;:a/t y9lpclwas destroyed? Explain.

If we knew that energy was being transmitted from one place to anok7h 9jy y* k bxc(crtdz6,r01ither, how might we determine whether the energ9yt( rj ,yckhx*z0r6cbdi71k y was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, w + pk qexpxi+*gwdo2.5hat is the total distance it travels in one per * op+qipd2. xeg5+wxkiod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from itma8b tm4n n,t/pd;9:ka3l fnh but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constatb/:; m4nlap9mfn h 83,d ktnant k of this elastic cord?    N/m

  The springs of a 1500-k kodhc87hka0 8wk7cw( g car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequenwhcc(kwd o0 k8a77 kh8cy of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) W* g./5, 6osyc)ei ebxf(sl urchat isirsgoe, 5u x/.f6c ycb e*l)(s the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0./tnmu dbt-(dgu/*n2p 60 kg is hung from it.ut/tn 2* (gdb-up dn/m What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2c-c :b k,w9z;jomxqyau 6m1eu6:v6oj at times t = 0,w cvu:xmu m1qo, 6z;cjb-a66:jyke 9 ot = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g3s qqgz bk-y02o.c,p f is caught in a spider’s web. The web vibrates predominately with a frequencyfbz-2kgy cqpq0, 3.os of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibratesdqw 5 qs+n)-;dc*wzts with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. Whacq-d s )wsdq*+zn;w 5tt is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 te7lgfi r,4 b)himes per second with an amplitude of 0.13 m. Determ, br)hlg4 7ifeine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed -z1qnfala .r l(ia48m of a SHO half the maximum valul 4.m q 1i-zla8rfna(ae?$\approx$    A

A mass attached to the end of a spring gfn -z5 vftb,+is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.3wr-lruuzve:*j wc zq 2xg(:. 915 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the ((x: ur 9:. 2 zje*gwcl-zqvwrunew) equilibrium position again?    s

  An object with mass 3.0 kg i9/akfp.ine mm lb0u0;s attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position,9 kmm;/ble0 n ai.fup0 it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the sf k a8dk*-nd7gpring of a toy popgun 0.200 m to “load” a 0.18f g*7dk8 -andk0-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, friokwo /1)u:8 60,ieysjiq hc lyctionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12j s8uy ,/ilwe0:1)oqi hc6o yk m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates accordingsxcfcb2bs l u)2dx::0 to the equation x = 0.45cos6.4t where x is in meters and t i:slxc2 d 0x)u2cbb:s fs in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a S 2qvkc0 u3+z rtn+m0ckHO half KE and half PE? k vmu320+ crknczt q0+±    A

  If one vibration has 7.0 times the energyi8ofgovd1n x/s ,(bk6 5ft)qm of a second, but their frequencies and masses are the same, what is the ratio of theirbdgkts )85 nmfqx o1v/of6(,i amplitudes?   

  A 2.00-kg pumpkin oscillates fr dubt-u6zo5m.om a vertically hanging light spring once every 0.6z uob5 u.-6mdt5 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical spri o z,t*4f )e*hnhaahg-ngs, each with spring stiffness ahef g4*tn) azoh*h,- constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accordin(hn v9sm v:wn6g to the equation x = 0.38sin6.5t where x is in met9nsn vw:6h(mv ers and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and pfat.gj1-3n9 7uyon q b5*hriB. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest onapngp0: hifj;xz:u 07 the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass; :0 hpgz:afip7 u0xnj an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffne9rnav7) x-gy+ ri/qq16rxv 2r/u ysokss constant 305 N/m vibrates with an amplitude of 28.0 cm wh79o2yxxirrgq /6 v1)v- surr+q/ naky en 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness ckh ji5r:tbq8( onstants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizon(u5g/nw vxerpvba99bp05 c/ mtal spring whose spgx /a pew cpbu(nvbm09v5r59/ring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reachinzcrf9:- :tp7d 1ukl7ss u:sa lg his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculatetur7ls :1pc klf 9s7du::s za- the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in4ro; zk- 5o kwy6z7n7l0vhtby exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple)7hemwzy.w syz 3xf9h5 gfb5 : pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 bm .z 5wy:z y7h)gs9wxfh35fes.)    m

  A pendulum has a period of 0.80 s on Earth. W,j0 b7n/2f l1vmcfwlo hat is its period on Mars, where the af,wb2ocv0l/ 1f mjn 7lcceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lo vc)l3 .dzo)tv)bhlj8ng
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pe mxka7 ,h()1 *3 vbflxfdm/vbkndulum bob has a mass of 365 grams, and it is releasedklm7a( f * 1fkdbxm3/ h)x,vvb at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’stm top,q8er *km) 5gs7 pendulum has a length of 0.9930 m. If the clock loses half a minute per8, e5smp 7qt*mgo)rkt day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for (7 wmxlp/p6vi the maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released frn:h, odn7vr) t8spjl4om rest starting dlh n:jps4t8 r v7)n,oat an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave creln .-) bnx8upndm: 0grsts pass the bow of his anchored boat every 3.0 s. He measures the distance betlgx:0)br- n.mdnn8 upween two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a slf5 l gye1k* : wzxq.qviuyki9:0btm)+7j, sp peed of 343 m/s How far apart are the wave crests (compresw,*ib5k:fpgtz0 u l+.k xe q:sv1yjqi7y9 m)lsions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz)uh3nzzi evn- /57nb +n and tb37 -zuenn/ z5nv+hin ravel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudiei/8t34 om aj3mv5pax nal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one isw 4s2gw/ pah-jqjo j3v+km5e2 twice as dense as the other. In which rod will the 2v h+ -wpoas 24wkj/je3q5gjmspeed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg isrcg ;hf1 kb*i 298o9z zhlk5rr stretched between two supports 28 m apart. If the tension in the cord is rk8kz*chorh 2grlf1b9 i9;z5 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the tzqkz9s p0at*yj/ , c8kop of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bujy z80pt cka/zq,s9*k mps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surfad8cd7()jz fnpe,e d5k ce of the sea. He hears the echo of the wave refl 8ned7 zedcd pk,f5j()ected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake kzq;l6bf 5 hq2travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbbh5k62;z qq lfance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximatyk1if *7 6hkxzed by a sinusoidal transverz6f17xi kky *hse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitud bx la wj5:z3 ym5z+rrawke/oma-4k )04mag+p es, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from th-rpgm)+al40ma5+: a5 ayk34zxz/ j rbkewwo me source?(a)    (b)   

  The intensity of an earthquake wave passing through2j : qfxxera:8 the Earth is measured to be xfer x:a 2q:8j$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency :n4y 0okefy ,wtravel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitew 4, ko0yyfn:udes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but one tr7 gg(u ;pns2pdansporg7 p2 snpu;g(dts three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to movj wfkj+e(9gy .e up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decreasj kegjfw.y +9(e to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other.(f- qzk8 z*fbhd-a9 me (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happen9qk h(zz8db - fa-mf*eed to the energy at this moment?

  If a violin string vibrates at eg hf om6 q:(klrne80:x)9y/ bgf q-jb440 Hz as its fundamental frequency, what are the frequencies of the first four hmjxkg e80 -fbqf /:hon6rqb:l(9)g y earmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrate9m:m u:c; de qow f isfmd37/dtdv2d(5s at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of ew:m3fds 2mo;m ddq/:5dfcidt u9(v 7the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name a 5,vfnbb/m2tg t least three other frequencies at which it wil,bf 2vbmgn5t/l resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequeo 0:qnfm ur1aa u6o-g/4 wqz*jncy of standing waves is 475 Hz, how far apart are two adjacent noon/m6qgwzrqja oa uu:f41 0- *des?   m

  If two successive overtones of a vibrab( h8 3ys85t-jwqhcsg ting string are 280 Hz and 350 Hz, what is thtjh8y 5gs-c 38swq h(be frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the bc)j (mbuf;i x-v +n8bzridge to the support post is L = 62cm and the string is under a bmi ; 8(zfx-bc+uvnj) tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, ymvjb4 zw) 9(gatfb1e2ti -r 6but it is measured to vibrate at 205 Hz. By what percent should the te6t(-bm9 eyjgi wzfb a241tv )rnsion in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measur6 ga0+ho( luubed to vibrate at 2u+6o(lb aguh005 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal stm hp qz,5t/ua2ring is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length is,ha5/pq2 z tum $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of 5ww,+ef ,y;fqlghs1qthe string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave pat1,ly5hfgq s,;+ wef qwterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a0x67a-gyue jv tub at just the right frequency, the water alternately rises and falls at each end, u-076ge axvyj remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at kv)9dq z 9n pdn*,wzj60t +inzs.0 km/s strikes a boundary within the Earth between two wzz* pd )jnvi+06n9zsq nt9, dkinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where th1ke97adwa m*k: u s;phe velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests79 kdhemw1: ps;u *kaa make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense.ugx34b ym(9i x+5szegtc1dro . i 3gi air. If the sound wave hits the cold a c 3+ mx.s13(. yze5ougb9drtx iiig4gir interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthqmdgf7, s0sz;i uake wave strikes a boundary between two types of rock at a 38gf ;siz0sm7,d $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diamete y..hlwdb3 u7jr. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of about buwj3.yhdl. 7 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pac+d6 h 04x7kj w c:ayht dg;b;llo/;oujific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in t;wd/l+4y khdut; bo ja67l; :jcxohg 0he harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiff 2zkv,ae o7rzh4-h medua74 s8ness constant of 550 kN/m Find thkuh2v z7-eda7,o seh 44r8m zae maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretke a bljo*47mjj4xaj ,)x47xk ches the net 1.1 m ,a4kjj a474l* )jxem7xo xbkj. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the *,u-jgao /dkpend of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the freque-o*dpg, ukja/ ncy of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a s*6sf(3jb1syv wpf2o speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constan w63 pb*jso1y2vf(ss ft of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the rigrw3k7jb8t. krm. l2gq ht pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over thmbk l q.8wr23gr7 ktj.e top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm fr 2su69iaaz5r*tmic+6 ejg a/ som the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of r9ugs6a2 iztam ces+65i *j /athe sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equati*jbme+wo;bg86.( 0mu fds j oqon x=0.650cos7.40t where x is in meters and t in sog 0.j6f ;b(q b8dem+uowsjm*econds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with fros0*7hfd)ui j equency f. What is its frequency if it accelerates at 0.50g *ho)ijd7s 0 uf(a) upward,    f
(b) downward?    f

  A 220-kg wooden raft f w4yf4 hsy9w+5jcx 6oaloats on a lake. When a 75-kg man stands on the raft, it sinks 4sw 54xy4hy+f j6cwao9.0 cm deeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musit fj6u3jg (g2 x0.spzucal instrument are tuned to play at 392 Hz (G) and 440 Hz (A)( j6tj.3 z0xgufgusp2 .
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fv)) zw lf,9nmsig. 11–33. Determine a formula (a) for the ratio of the speeds vl)),nzm s9f wof the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibratesz 0tbvk-gez -(i2w(wj at a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to eizit-b( 0jk(-w wveg2zther side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple p h eq-1)-a;sxn*qtq,qj8 ncpharmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the q18p n)*n,q ;xeq-- jtpchqsaboard during the oscillation?

A string can have a “free91b8 f f:ey :63nysmqaelhe h6” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonantmeqn h89ybfe elfa:y6 6:1h s3 vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum haszv v2gmpu;ru/2ab2j2 s6qgp : a period of exactly 2.000 s — each one-way swing takes 1.0z2p6v2sj/ p ; g :bu2g2uqravm00 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring c:*v - qrj:jxslm( c7z /5xfqbman oscillate in the vertical direction or can swing as a penduluqmcrj zx/7 *b:v jq(s -l5:mfxm of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tensio as lhxygi6 /h5+bmp mi+:)is:mmd6, sn of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is6pyi+mm 65g )hmd +,s msah:ib/ilxs: generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring wie+b w6vcm7; *bjlhvd ykh89 a(th spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on tophh+ 89 7my b(ecab*jvd;l6vkw of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyc 7hf11)sckv+f jfnc;ard. The steel crane cable is 22 m long and hashfsfc1 1nc +f);kv c7j a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fimhp agy1e6d,63 lfethi+;qw,g. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy t,hp,6mwh3aei+ fgt6l1d q e ;yo a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz