Give some examples of everyday vibrating objects. Which exhibit SHM, at least l 6iqd;oorbp8k og(;.approximately? d;;ropg(.o6kq8 il ob

Is the acceleration of a simple harmoni4o r 1vx6l7g nhpa/xswi q7v.6c oscillator ever zero? If so, where?

Explain why the motion of a pist5 b8fqm .-jntcon in an automobile engine is approximately simple harm.jtm qbc 85nf-onic.

Real springs have mass. Will the true peri/l. z/qx:,mnu/*fztpsi 4caiod and frequency be larger or smaller than gaq/lcxu z/ mi*s .f/i4n,:p ztiven by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simpl+6f5(itq k2 -zww+0qqf xyc d nvh;b5de harmonic oscillator (SHO)?

A 5.0-kg trout is attac(/zk pf9zc+ f3aegk*c hed to the hook of a vertical spring scale, and then is released. Describe the scale reading as a functi /zp(fzgk ek*a+cfc93on of time.

If a pendulum clock is accuratek 3-ggegg6m.g at sea level, will it gain or lose time when taken to high altitude? Why?.kgg3 g 6m-geg

A tire swing hanging from a branch reaches ns k/jkd:hj b)39enmg6early to the ground (Fig. 11–48). How could you estimate the height of the brgmk)k 9d63eb nj/ s:hjanch using only a stopwatch?

Why can you make water slosh back and forth ikf/y x0s6l;/x mttl p:n a pan only if you shake the pan at a certain frequ0y6x/plm:fs kt;l/x tency?

Give several everyday examples of r.ggjsdr)b;r eio+ 90 vesonance.

Is a rattle in a car ever a resorbz/ wpd+4p; 0 d)ccwc)d;ip/il vpd *nance phenomenon? Explain.

Is the frequency of a simple periodic wavwu2 (2mnxai)n+ ; yyyxe equal to the frequency of its source? Why or why yy );wiu+ yn2xn x2ma(not?

Explain the difference between the s7hzv 15 zb(0 1qicrunvpeed of a transverse wave traveling down a cord andq0r (biz1hv1c z5nuv 7 the speed of a tiny piece of the cord.

Why do the strings used for the lho),*pmi-a ywp ( 0qa0v(qhzh i;2unyowest-frequency notes on a piano normally have wire wrapped aroui,nzh0)0ova m 2puq-y*aw(h hq;i(y pnd them?

What kind of waves do you t0/fjz*nsl sat x99x..qck yk1hink will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paralqa s0 z9*.tksx9 cf.nly1j/ xklel to its length?

Since the density of air decreases with an increase in temperature, bjbt*4 h6gzah *ut the bulk modulus jtbg*h*a 4 hz6B 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 wat::h4)84 x vpu) gwyt1 eeimwuser waves decrease in amplitude as they travel ahie4yp xuvwwe8sg) 4u:1 :t)mway from the source.

Two linear waves have the same amplitude and speed, ande8j,ghe s+(c+y.v 4 av n0 o+nsfja0xq otherwise are identical, except one has half the wavelength of the other. Which transmits more +anj+xyg e eo 4( asvsf+8h0nvc 0j.,qenergy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of u9pn3;h wi9cncord as in Fig. 11–33, the frequency dou9 9phin3 nw;ces not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in thq*x)5 ud,;ycb8icr j kree segments, are there any places you could touch it with a xcj u 8d5,;r)yi*qkcbknife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incid22fi*f )zx xy lb 7ja4e3r,z 23lmnbfuent and reflected waves cancel at the nodes. Does this mean tha42x7nzxl z,b)j f3 i2erf lfb23y*mau t energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to a,ubhmj1+ tx t4nother, how might we determine whether the energ1+, 4hbjumx tty was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitu,vo 2q neq1 /cm-r;v3 d ygi6d sl329pbsib0dzde 0.18 m, what is the total distance it-3g/1dn63pver s q0d oi2,dvqlzsm9y ic2b; b travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it b-n* zr bmlrd2mt4fv ;4ut is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord fzd b2 lt4m;m4-r*vrn?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver getsydlh0u2 0 zt8t into the driver’s seat. If the car goes over a bump, whatdyz8u0t2thl0 will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when x nor*1jm* .yda 2.7-kg fish hangs from it. (a) What is t.dxor1* m* jnyhe 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 wit; 0r6s 6idicrpvpt.;k9pt v p.h a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs i; ri6p pt.v9 td.r 60s;pcpvkfrom it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times t h p6d8/eqvv cphm9+g5ase;0j= 0,t p/de 65chhvv0+9mg; e8a pjsq= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 g is caught in a spider’bubr) utjdbsckuwfen 8lu604p,3: ,z*/ v v1ps web. The web vibrates predominately w lukb*6vn,3/f)vsu pcpeb rjz wb1ud 4u,80t:ith a frequency 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 vibrates with a frequency of 0.88 H;hj7f )0ts 1mwiv3ghwz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value; fh1jv m gi3ww0tsh)7 of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times pek2m1f.c y,xz y3qifpab7 .tt;r second with an amplitude of 0.13 m 2q3paxcfm zy;, fy b1tti.7.k. Determine
(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 ir fve,4xann j u44rs5 t)v-k/js the speed of a SHO half the maximum valuv44)en/ur,fjv s n 4r kx5ajt-e?$\approx$    A

A mass attached to the end of a spring is stretv vy:n/efoxsfx*(j. 4 ched 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 m. If the sps( a*ewyl:s u)ring is stretched an additional 0.130 m and released, how us :* aleyws()long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg rh +b2t;jb4 lcis attached to a spring with spring stiffness constant k = 280 N/m and is executing simpl; h2c+ bbj4trle harmonic motion. When the object is 0.020 m from its equilibrium 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 codvx f 4c/u;yy)mpress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what fd /uxcv)y4; yspeed will the ball leave the gun?    m/s

  A mass sitting on a l nxd22ls 9 irvdl1oh-8.2c srhorizontal, frictionless 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 0.12 m. If the mass is released from rest with the spring compressed, the sdlilolrx98 nv2 -sh21r2d.cmass 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 according to the equatio jn 9,by.odzql732arsn x = 0.45cos6.4t where x is in meters and t is in seconds. Determ d,qz9a3l s yo2.njrb7ine
(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 ,a5suj wt x8q81)c vlh68toidthe energy of a SHO half KE and half PE?tq5)xd ol1u8th a w8 ,8iv6jcs ±    A

  If one vibration has 7.0 times the enero*xo;e 6w5iupgy of a second, but their frequencies and masses are the same, what is the ratio of their amplitu i;xe*o o56upwdes?   

  A 2.00-kg pumpkin oscillates from a vertically hangvyv7 w+h, bai)yd d7k9ing light spring once every 0.65 vdy, h7+yw7av9 di)kb 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 0zwr4wbx,be- om: 6ii by two identical parallel vertical springs, each with spring stiffness co6 bz,irb:e04iwmowx- nstant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x =a 5.+d,qjwu widw .f6c 0.38sin6.5t where x is in meters and t is in seconds. Dei5d j.6w,.quwwa+f dc termine
(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 ex.bvcm3w94g.vhof ssc ,wb 46hb+r u+p amples 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 rest on the end oi;g na96.riq*b 9.+ngt bdubwf a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an ii.g*.6 gai uqdt9r nbwn;+9b bnitial 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 stiffness cjk s-ac(8 -v7a5w rjpq1iiz7e( mro 4wonstant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) q s-8w7o1jeaa4vii5 pcrw k jz(r(m-7 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, wittvfca;j47y vn (+t 7uzh spring stiffness constants $k_1$ 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-kgequp3o3pi 4) umx2d:r,rn4 c d block attached to a fixed horizontal spring whose spring stiffness constant ,:i4 rexq pd3p 4onruc)d32umis $ 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 ,ttdg*b d -1ji 1d6bxrx de9s2bridge. After reaching 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 xis-d2ex91t d 1d* bjgb6rtd, m below the level of the bridge. Calculate 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 in exactly 60 s. What is i s +i+g/xlc6djw)rq f n4*uu9ets
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to9y 1 5pfo,or.u; fphga make exactly one swing per second? (That is, one complete vibratir.o1 hgap;5oy, fp9ufon takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where tyapwpvnfj0(v7 63y8w bj;g /o c-6v*d(nc hbdhe acceleration of gravitfdy; *wvogdphn 6b7yvn/ cj(w0j8 -p 3b(cav6y is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cx :-zax/zv /d/bo/awer5n m* mm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple e.srya-:8,ng idn3s bpendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it iss:i 8y 3ebnag.,- nrds released 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 pendulum has g k,h h/gg29jpa length of 0.9930 m. If the clock loses half a minute per day, h p kg/9hh2g,gjow should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed j(z+k rh9q* uluc4z1r$v_{max}$ 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 rempu- 4mc:vpo+ ng4zw, leased from rest starting at an angle of 15cvwzup:m- ngm4 , 4o+p $^{\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 the bow of his anchor8i9q 8 y*5 7oubsz xn0mjq5ubled boat every 3.0 s. He measures the distance betbx0i98qoq7numlbu5y jz* s5 8ween two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 2jr )vr :;o6rdv62 Hz and travels with a speed of 343 m/sv o;: rr)jv6rd How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) ,xbd cpu*s9r4 and travel *4r,usbcx 9dpwith 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 lon,k. 9rs66k t/hbh )xzbg7lfk qgitudinal waves 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 dense av ,vk((p 2fsz(isnu*g s the other. In which rod will the speed of longitudinal waves bes vg( ,(kz*pv(nu2 isf greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppok4r,3fe: nkrd rts 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one supporrf:k,en3 d 4krt to the other?    s

  A ski gondola is connected to tinhny x/s t3wk3-r 4p/(q h wi-e)/ajghe top 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 cable. It is observed that it took 16 s for the pulse to return.4pwkn 3jwas)/(y -- /nigieqr xhh3t /
(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 sidbc1po)ta8 3,ranpw3pm (u qn*e of his ship just below the surface of the sea. He hears the echo of the wave re,w8pb 31cnropaap(uqn)t 3 m *flected 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 earthquake8rnxp:c +3ru m travel at different speeds, and this difference helps in locating the ear px8urn +:3cmrthquake “epicenter” (where the disturbance 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 by a sinusoidal trans+vbe e- sl9z7averse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequebva -l+ s7ze9encies), 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 amplitudes, of6*6ex,y r:qqvn8gp. 7pksh x i an earthquake P wave passing through the Earth and detected at two points 10 km and 20 k* epqvi ps x66rnqkgy:7,.h8xm from the source?(a)    (b)   

  The intensity of an earthquake wat oyit btkhf86z;f9:fj(wwtfa- ;u1+ve passing through the Earth is measured to be ft:at -zof(ut9hy;tbw +wf1k 6jf ; 8i$ 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 the26 iq0)e4 z,kss3r zhtihyh7 l same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What iss )24 yekl3sh rti0 ,7h6zhziq the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string havex*sv2sm *wbf.y(n+v)/,u xtjw tg0 v z the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two wasusz,(w 0w./n vvvjt m xtx) b*2f+y*gves?   

  A bug on the surface of a pond is observed to move up and dowdjys7ihr/ 0cl qhk, 1.n a total vertical distancer,. 0 qihck/ld 1ysh7j of 6.0 cm, from the lowest to the 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;o8l25x4ji9e tarhkc5 dzcvmla; 29 9k d:eun moving toward each other. (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 happened to the energy 22dvu9x9a; 5e4:rzl n km5 d8oc ac jelk;th9iat this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are tmam8iccx.5 6)d+w :msnyj -inhe fw6m58cmjnn ic-sy.mai+ x :d)requencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At wh(wxq8dwf pp0/qx:rl3 at 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 warx: q fp8qd(x/wlw0p3ve.)    Hz

  A particular string resonates in four loops at .;i z(9qyhn5 q(xxoto a frequency of 280 Hz. Name at lex(yqo qn;5txoz( 9. hiast three other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a stw(c0o mzud6 a9ring is 92m/s If the frequency of standing waves is 475 Hz, how farzac0 o6m(ud 9w apart are two adjacent nodes?   m

  If two successive overtones ponu4y : d;1 nal (;ycg.ryxv;of a vibrating string are 280 Hz and 350 Hz, what is the frequey (;gl d;x.oyrn a14p:v; ycunncy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the b7 nxsszfyx o 8ei4oo/xm2,),n ridge to the support post is L = 62cm and the string is under a tension of 520 N. What /ofxion47 e)xoyzn s2 s8,x,m are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 H .pafon7x k.9bz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the stripban7x fk.9.ong 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- a7znek b nq3m(ffw:5, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by ( fbqn kz:7n-wa53fe m   %

  One end of a horizontal string is attached to a small-amp-a l 4wjra0.cpxzd74b afb 7r2litude mechanical 60-Hz vibrator. The string’s mass per unit lenaa74 zl ap0bj.74bcx- wfrdr2gth 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 t tin. 3+zd 5(i bxd2k-hpqpf8the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how mak t( + ptiq32b8xf5n dp.izd-hny different standing wave 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 rig0 acwh6/j4nts ht frequency, the water alternately rises and falls at each end, remaining relativencths6/aj0w 4 ly 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 k.0 km/s strikes a boundary 4zr5tzapxw r.ztk6 2:within the Earth between two kinds of material. If it approaches tx24zrw5:a 6.zpt zrkthe 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 ve z 4 dhjip74vu8agy9* fbb,oi+locity changes from 2.8 m/s to 2.1 m/s If the incident wafb9uy+jhz4ii *a4 v87b do,gpve crests 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 hidy 2lo,mnvdl-; ;c9v its a layer of cold, dense air. If the sound wave hits the cold air interface at2vc;lymn id o;dl-9,v 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 earthquake wave stom7 p/j 9fdcuo)-/ufyrikes a boundary between two types of rock at a 389-yuod )/um fp7/coj f $^{\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 ;ra(5xte.8 (4avhz it2mmpzyabout 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, b.2ye( (;rhz 5tpz8imt4xamavut an error of 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 25bj5 v:5re swc nkh;fh,4q bc/60 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, pe5h;rv,wbf :ke/46s 5cnhcq jb ople 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 stiffness constanu wc +ync)-sf2u z8iji o,oe7-t of 550 kN/m Find the 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 conserva c7ii,oefu2)-s-wj8zn oyu+ ction of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m beqfzoq,b1y y7f 0fr;:plow, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, z07ypy q,1 obrfqf f:;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 theo ik .,d92fwj/ nthus5s05yab end of a freely hanging spring. The mass then falls 33 cm beforbfh2j na0s9 y dwo,5u5 /tisk.e it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a spe khfi,-wv07dw*b d m4bed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What74i,bbdww0 v *fmh -dk is the spring stiffness 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 (diameter 8 cm) at jus2cq ;:btkj tf6t the right pace of about 1 step per second, the coffee sloshes more and more utkq6b: t2fjc ;ntil 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 cebdi+t92)ps u9p,k 7n8vv,n gadfl uc6nter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What willf699,+) vp8vtpgi,7c2ab nundk s ul d be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to (dd;a,ob xn:k4 fytg+the equation x=0.650cos7.40t where x is in meters and t in secon ,f(;b nx:4yd+ dkatogds. 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 frequency f. What qom7zck.lu 5 3vik)x5 is its frequency if it acceleraz7.l co55 )kvq3um xiktes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a la;yy4ulsu m2z1leoc/8so, (vk ke. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When hec8ml1os uk v;yz(/,luy seo24 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 musical instrument are tuned to play at 392 Hz (G) and 44u7;- lnvetr:3kk +ho,oo;vtfi- vp0v 0 Hz (fn3o-l- vv;r;o0,e:hk7 t ovtpv+u i kA).
(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 Fig. 1jntu* o1yze e)woa310 1–33. 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 the two sen0o 3yj1) atouw*e1zections. (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 l5 0bv)q5+p g opzbmq8of 264 Hz, and the tip of each prong moves 1.8 0lzp b5q bg8+qm5opv )mm to either 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 harmonic motion of frequency 1.5 cyclol rnpire 9 a6p5ha8q5z 613ul61xynfes per sec531r nyp8xrq feial19h6u6zopa6 nl5ond. 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 board during the oscillation?

A string can have a r) 7qfw+n0* e rqqrsj8“free” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths r+*q )wsqrq08j 7nref of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly ; b(oko9+g y( ya+q7n5 qbtnbs2.000 s — each one-way swing takes 1y7oos ( n+qbqt5g+bbyk(9; an.000 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 can oscillate in the vertical direction or can swi* jyvhik)z kn,3m.fc +ng as a pen zj) y+vn f*,kimkh3.cdulum 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 wiming,jl/y,: zk1t 7u i4,ce 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet? ,,jkl,w: n7iizc1tem/4i ygu   m

A block of mass M is suspended from a ceiling by a spring with spring stip4or2xtk p2.8 r-f lbjffness 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 top of the block? (Assum rlfrto jx228 bp4-kp.e $m \ll M$)

  A crane has hoisted a 1200-kg car at thehu17; scv8ve awiflo66gu0 /f junkyard. The steel crane cable is 22 m long and has 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: Rawlif 8f 7;/ 6us0v6hvc1eugoefer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–5+:z)3s2hknohzz4uf5m oq6a78bzsc r/ e yc/x8 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello54boczayzu/q+7zxsf s 8zhk/36n:c2m r heo) 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 is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz