Give some examples of everyday vibrating objects. b04kca) dtz7z Which exhibit SHM, at least approximateab7cz ztd0k4) ly?

Is the acceleration of a simm;rbp iw zmyk:q(u- 2m6w 0/efple harmonic oscillator ever zero? If so, where?

Explain why the motion of a p z4t5kqcf*n5 viston in an automobile engine is approximately simple hk* zctn q55vf4armonic.

Real springs have mass. Will the true period and frequency be larger or smaller avh4ipida/q d, 7ln8( than given by the equations for a mass oscillating on the end of an idealized massless sprq48daindl7/ pia , h(ving? Explain.

How could you double the maximum speed of a simple d )y u+ elw+h.15law. osy iy0n6tnxs9harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a verti;-ywxie1e-pp ysh ;zw;9v- qa cal spring scale, and then is released. Describe the scale reading as a vw--z;-hpapyse e1;w9qx iy; function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time q1fq +-;mxw,/i iktr gtbz22fwhen taken to high al,+gfq/x1tmq 22 iktwr zf;bi -titude? Why?

A tire swing hanging from a branch reaches nearly to the ground (F-k1hz.zfu6g 9z c9sbyig. 11–48). Hofghysbz9zz1u.- 6kc9 w could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only6glqnx;j9l; e if you shake the pan at a certaql;9nxel j ;6gin frequency?

Give several everyday examplej qdbzdeor 9lwul,zb o./0nm 2)hz/8( s of resonance.

Is a rattle in a car ever a resonance phe;/ g6r g)uskow y0:;wk/zsnk inomenon? Explain.

Is the frequency of a simple periodic wave equal to the fr xvmjo 39qrhqe41 47asequency of its source? Why oa1jh7xm4 oq4s9 3ervqr why not?

Explain the difference between the speed of a transverse wave traveling down 2wz fk cuz(vs4v5mq 52a cord and theuvw2mq5s5fz 4vk 2(z c speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piap62cdo ,ym(d/ugw jd;qy)gc 0no normally have wire wrapped aroun6)(u jpodcd q;yw,2cdyg m/ g0d them?

What kind of waves do you think will 1yspb2h37y+;1ns+ yovh gm* kp+ vdhztravel down a horizontal metal rod if you strike its end (a) vertically mb s+ v1z+hydg*h12n +;p vhkypo3y7sfrom above and (b) horizontally parallel to its length?

Since the density of air decreases with an h 0f5mrii.+. j*ixmq uincrease in temperature, but the bulk modumxi0i.5qfmj u .ri+ *hlus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as the glo h+tc;c*.(c)t) x8fbq yc;:eligey travel away from the lhq)oleb tc*(i ;c 8fg: xce;c.g+yt )source.

Two linear waves have the same a9p(dvkv ,phl*cg: o1 dmplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmit o( vd*ppk:,hv 1cg9dls more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord a; hz.fn9wzvbz ag6r48s in Fig. 11–33, the frequency does not change (4zvb9nhz6.ar8 fg;wz although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could toyv+2*j;;u :ej6ahhp:ohs qv p uch it with a ka;j s:heuhv6h v p 2j*;oq+:pynife blade without disturbing the motion?

When a standing wave exists on a string, the vibratiq) j4z i5-aymgons of incident and reflected waves cancel m4g q y5)-zijaat the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to an41 :grv bru8xkother, how might we determine whether the energy was beirk184rxvg b :ung carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18ctj62a exywg5cd1 h m)095nw-sjrax6 m, what is the total distance it travels ingc- sj6)w9ey w6 2n510d hxa5t jarcmx one period?    m

  An elastic cord is 65 cm lonvcczwdf 71* ; fiigz(,xfhy/;g when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this zz g1iw, c/yhi;vf(cf*dfx7 ;elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets 4g ekg(sve4 tb;h+6ckinto the driver’s seat. If thv 464ete (csh+gkgb k;e car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-x6g kb9y ina(xixzbb456,qr/b,d +b e0i z d7nkg fish hangs from it. (a) What is th,n9iaq b 6r6 zbdxxg (k5b7ezn +x0,y/bbdi4i e 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 vibryj: qah jsn--uc273kqxp 7; nu:qqgwhfa9z44ates with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if onlayn94ckfq xujh w-u:34zhq sg7q - pj;n7a2 :qy 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x0u;j )w:dysww7 t,/in rieem1 of the mass in Fig. 11–2 at times t = 0,t = m )7sdiw:ijew/;0 r1tw,nuye $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 j9gqk,i ib lp 2z7vj830.25 g is caught in a spider’s web. The web vibrates predominately with a frequency qzk jvb2 lji3p7g ,8i9of 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 vibrates with a frequency of 0.88 Hz. When an-l1hycv )++fs fh)ksv additional 680-g mass is added to m, the frequency is 0.60 Hz. What is th vl ck+f+fhsyv)1) -she value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an ampll50cg,b;- q*gnj 6zyesig3wj itude of 0.13 m. Determiney6ggjzlicg30b;wj* -sq 5n, e
(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 os9itci gt;* lwlz16)l f a SHO half the maximum value? *s6c)l zil;1wg9tilt $\approx$    A

A mass attached to the enfjn;*n 9awa 0id of a spring 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 0.315 me d kk )j--;n+jp;lnuw. If the spring is stretched an additional 0.130 m and released, how long does it take to reacpdln )-n+e- j;k ;wkjuh the (new) equilibrium position again?    s

  An object with mass 3.0 kg i g4nunt oo 4/gj,8fh-ds 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 equil/ognfnh4u,d4 8t g-joibrium position, 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 spring of a toy popgun 0.200 m 4uxdymu)z ;3yto “load” a 0.180-kg b zydmx43y)u;uall. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless s5s kh r2l4ne/+doyut .urface 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 0.12 m. If the mass is released from rest with the spring un lor42set/d5. yh+k 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 accor., fcurydd uy0x;+ .scding to the equation x = 0.45cos6.4t where x is in m .cydufxd.0s c yr;u,+eters and t is 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 SHO half K)5rjg w8 f:qchntd1r2 E and half PE? c8 51fwr) rqt:g n2jdh±    A

  If one vibration has 7.0 times the energy of a second, but their frequencienq cgv6 mh;nwy*zy tmzti8 5,:h 4/2ops and masses are the same, what is the ratio of the6thmvnni;y,4 copz*t: qw ymh 8/g2z5ir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lighsxm, 2t)4s gpbv u(z9it spring once every 0.65 s. 2v(gi,t) 94 m pxsubsz
(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 ;k1qbohe62 )szl th*j springs, each with spring stiffness constant k (Fig. 11–49). What will be t sjoqlzh6 *k2) e;hb1the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where dt0xcpo h7nd7q : .2tmx is in meters and t is in seconds. Determine tc ho70d2tqpn7dm.x :
(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 exam15i,bg9mz-kzd2 apdu ples of SHM, labeled A and B. 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 restlvm*yyjwp-4df,*8w m(mwmh.f eu. l8 on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial -.*m( mw. 8jl mu4mv,ewpff*lw dyy8hspeed 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 stiffness constant 305 N/m u qtnukcivz3-mcb ar(/ ),s4.vibrates with an amplitude of 28.0 cm when 0.260 kg han3zkt u( -4.rua )sviqmnb/,cc gs 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 constants (djbnphg7 /*+v i gdk6$k_1$ 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 horizontal 3 ;n7boli l;s0jvhbx u 5*wft hm(zd+o9s t/5rspring whoset jzrb7 +(hms5xd3l*i/ 9t nfboh v5;wlos; u0 spring 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 mjzln079a fd yia.zos79pn6 qkb .:*treaching 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. Calculate the spring stiffness 67mfozayzs n: j0dip.tl 79.n* bkaq9constant 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 in exactly 60 s. What isb:/a)uhlahx70n t ( o,nqrsb6 its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simp:)x;0h6ot,vd4gf 3 wodsp *;dk qjmbfle pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takekvh b mw*t)podq3;jdo:6sgf x4 d0 ;f,s exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mgy,frr)ld7 3c1th) o33tu y ilyk+ 8t9 zi.oggars, where the hr.39ld olt3c oggity, 7yt1)+)yzrufgi 3k 8acceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a lfq7 8nu3i-)e)g( ctyn:jpjzx 91fyc simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0b v*i3x 1+j-:o nowfun.760 m, the pendulum bob has a mass of 365 grams, and it is fv1n 3+*inojwoub :-xreleased 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’s c wk+vq2lgz7ao kt3wpe1 6k.5pendulum has a length of 0.9930 m. If the clock loses half a minute per day, howkw 3zg6pok+t 7la 2w.kq51e vc should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for th gei74b8zhk )de 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. Atn); v)1aow/worynv e+ hp9u9f it is released from rest starting at an angle ofoa9rvu;on ))wpvw neh9y+1f/ 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 crests pass c xi re6iu9ye.;va/q0the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are t0eqx9 /ycr ;uev6.iaihe waves traveling?    m/s

  A sound wave in air has a frequency of 262 wx sry )eokl7j4cu-5l1j/se1 Hz and travels with a speed of 343 m/s How far apart are the wave crests (wue1l )co14sej-sx7/j5lyr k compressions)?    m

  (a) AM radio signals have frequencies -bgiwved; 9s;t :38tbuuyl s 4between 550 kHz and 1600 kHz (kilohertz) and travel with a 8s34g tdy biu:estu-v9;lb;wspeed 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 longitudinal wamf,tc /pa5wa1ves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as densenvaz 5hc+ v*,zg stb a3+8 yh-+ik2zyj as the other. In which rod will the speed of longitudinal waves be grea 25y3hbg iza t-ykn*sa+ +8zvj+vz,hcter, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the ten a6kplc(b(n5psion in the cord is 150 N, how long will it take a pulse to travel from(6 bna(plk5pc one support to the other?    s

  A ski gondola is connected to the t h+*o2v 7jiagbop 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 bumps into the terminal and sends a wave pulse along the ca v*bo2h+ij7 gable. 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. of8awac(p)mh(mi* vqxe r5tp1/u7a his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s laterfi 1rw(qhea5aopcu )8m a *p/v(xmt7.. How deep is the ocean at this point?    m

  P and S waves from an earthquake trtuz jn-ihjhs) z)5/6gavel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbang6/ jhs j-t5hziu)n)z ce 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 approximated bd+l. ;mcjd,y ly a sinusoidal transverse 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 tll jdd.,+ m;yche acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplfh (y) ,chstr7 z,;aipn3i5ekitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the sou,n ir5 yhe7s (t)pz;f3i,kcah rce?(a)    (b)   

  The intensity of an earthquake wave pale 9 kr8le::u4vwdhx7ssing through the Earth is measured to be wlvl:ehr9ed4 78 u kx:$ 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 frex5/ d2:ut.mlfxcen b33pf7nh quency travel through the same portion of the Earth, but one is carrying twice the energy. What iscnh:b/ulnd m353 e.tf x7 fxp2 the ratio of the amplitudes of the two waves?   

  Two waves traveling along a strp 73i1 w5ocd-xhcbuhh* v+4bhetched string have the same frequency, but one transports+41- c wicbp3hbuh *hh5vd 7ox 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 mov 7a, s+0n(yzwd;ac: wx eatid*e up and down a total vertical distance of 6.0 cm, from the lowest to thwyai*a zc70dxd+aw e:n,;ts (e highest point, as a wave passes. If the ripples decrease 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. (a) Sketch thy/ d4, xny( 4pcps,gjje 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 /p(s4 4cgpy, jd,nyxj string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequen7(j;ob.yan tufanj0wn+ :f)u cy, what are the frequencies of thj;b7 n.:nj 0ya(tw f oufnu)a+e first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when g;p(qc t29; yd cyqin(2ownl4unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.); ( (y2ci4tl2pd ngnwq9;yocq    Hz

  A particular string resonatewljxe3 ;))ql)( aqunfs in four loops at a frequency of 280 Hz. Name at least three other frequencies a;)ulaw(q) 3xjel q n)ft which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on zoctk(j ffx,l)o9ao0 /qqo )*a string is 92m/s If the frequency of standing waves is 475 Hz,9f x0o ( q l)fc/oakotzjqo*,) how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 chn/v6othmw +b/a -)pHz, what is the /) +mv6o-hb wachtn/pfrequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance frotp5mb eb(t38g m the bridge to the support post is L = 62cm and the string is under a tension of 520 N.pt 5bgemb(8 t3 What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, bu2ki4pc-;d u ) 5fvjokdt it is measured to vibrate at 205 Hz. By what percent should the tension in the strino cd;kvuif24-p )5d kjg 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* gfgbct1 9)cx 7n)zha 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequenxn1 h)cz9b7ta)* gcg fcy? decreased by    %

  One end of a horizontal string c3t9ccgc;r*gw e1 p,f is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mas wr c3fg;ctgc*p91ec,s per unit length is $3.9 \times10^{ -4}$ 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 the string may be adjusted b wn.h,.hkpyq* y moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wavenwp* .qk. hh,y patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency k3y51eg4a y;,zx8g- ,os vg nsbj/lxfazxo+ /, the water alternately rises g foz g/xy/ ;g+y41n-zabvo3kjss5 ,,a xlxe8 and falls at each end, 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 traveli1yf0 g60w, zntiybp l5ng at k.0 km/s strikes a boundary within the Earth betweb0yl5y0nzp 6fwt i 1,gen two kinds 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 the velocity change6wapvi0z b0xpyj; 8c xc3yy5 8s from 2.8 m/s to 2.1 m/s If the incident wave crests make a ; 368xpj ywx00icyy58 aczbpv34$^{\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 ajc2:wv7qbhknbt;f-; il8or/ da+z9wir. If the sound wave hits the cold air interface at an angvldtq;wbo 7a 8j:- r; +2hcbkn9z/fwile 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 earthquake wave stccy 2+jwitvd6),zq4 zrikes a boundary between two types of rock at a,z+i)cdqwcv62z4j y t 38 $^{\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+9phoh 00m9gu kav4uymw+ngy n4( vk. in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of +mk4p9k0y(hn nvyggmu9vua o w.04+h about 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 kti-a044+d u qc ctdw;km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the 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 wtkd;4qa0c4u- +c idtto the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a sp lvqs c+2pr,fiwi0;9 mring stiffness constant of 550 kN/m Find the maximum comlw9s,;i2r0 vc+piqfmpression 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, whiv u b,c)vc(d74 rr;,;pkht sfoch stretches the net 1.1 m. Assume that the net behaves like4(7dfch,u; rok; )r vtsbvp c, 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 end of a freely hanging spring. The mass then6*s ;a 6omco06cez2ailcbi *w falls 33 cm before it stops and begins to rise. What is the fr0m w sa66a;belcc 2*i6 zcoi*oequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compressiacva q2e/ +m6eng the spring 5.0 m. (a) What is the spring stiffnesee+avc/ a26 mqs constant 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 (diameterz 0bg0tro by/+ 8 cm) at just the right pace of aboy bg rb0t0/zo+ut 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm l4aacrvx0 1eb o0u:ll z4v2q- phonograph record have a wavelength of 1.70 mm. What will be t: v-14oa4uxq2clll 0ar0bvezhe frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accork, qnr;q2a o9:f-g0+hscnzft ding to the equation x=0.650cos7.40t where x is in meters and t in seconds. Det+n :2a tcs -o qqgn9;krh0zf,fermine
(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 frequency f. Whlu)e8vv71n zeat is its frequency if it accelerates at 0 ee7nvzvl8u) 1.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it r o(::i5nskoiryak8cv1t16usinks 4.0 cm deeper into the water. When he steps off, the raft vibi 5i:(or6 s:1 nky8ukrtcva1 orates 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 musica o1)vz*ty y0efkq6u5me+qii -l instrument are tuned to play at 392 Hz (G) and 440 Hz (A-1eif0em6ivq *y+kzy qtuo5) ).
(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 trc9 8sn2lr1evijs4sw+gv-u 9 wo-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in t 4r81sgnl ure9isv+j wc2v9s -he 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 vibrates at a frequency of 264 3): xxo2hx1x vwyhte; Hz, and the tip of each prong moves 1.8 mm to either s xtwxhy:v 1 xho);x32eide 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 harmonic motion of fre/v2tnc (eu;) pgsdf1iquency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can (2c de;)snuvtgp/1 ifvibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that ca2wbd8y pn7 sbgcl*06 bn slide without friction on a verticalwl* ycn0bd8 b6p 7sb2g pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has box ;5n5mr5pj6ahuv*t +w:jl a period of exactly 2.000 s — each one-way swing takes 1.000 s j 5 lju*vr5xa5h:6;+nwtobpm.
(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 can oscfta0.isu 5+goillate in the vertical direction or can swing as a pendulum 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 uoi agfs+5.0tswings, 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 uq4ptl 388i:sj g xx*qe;fp5t bnder a tension of 255 N. A pulse is generated at one end, and 20.0 ms later aq3 xe 8:lsjt;*bt qpif8xp g45 second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceilinq5/b 3;khvzkpg by a spring with 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 pen5h3qpz k/bv; kny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-1 o 7x2 1ktpvb vosexef-un8(,kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze s12kse8p e 1v v-o,7(xxfnotubtarts 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 Fig. 11–58 (which also giv1rxpz1-m gbqlsjk.sz- q 2,q/es 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 to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello p-skqg-q2 rs.qbx,m zz 1 /1ljis 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz