Give some examples of r st 0s60nhc3d cqm:8;i:wpb feveryday vibrating objects. Which exhibit SHM, at least approxima :c0fb;rtp3hs: q8mdwcni 6 s0tely?

Is the acceleration of.9/ls c. .hp0hp gd iav1os2bp a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximatuwsb h9*9mqarmv)u8, ely simple hab9ua mr s8hv*uqw,)m9rmonic.

Real springs have mass. Will the true period and frequenc1ucz7a.;f g ta7vmyi)y be larger or smaller t g7 cymf.17iv;)uza tahan given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximu)c6 usdyt3jj5*u; uj0d* 0 3lzuvbpqbm speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertwf6 zzee-z( /lical spring scale, and then is released. Describ-l6zew(z ef /ze the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when tgx/qu2 o i6y y4,wi)/e jvphm3aken to high altitude? Wju4 p/, yv3/y qi)m26xeiwghohy?

A tire swing hangingaq ik k/dn:(kdql wt550)l8sb from a branch reaches nearly to the ground (Fig. 11–48). How could yokl :bsnl)0 5kiqadq5 tk8/ (dwu estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if youvxt 1q8 fzec 7wa+hd/(nb- s,l shake the pan at a certain freque1v7bs, x(w8f +zctlnq/-a hedncy?

Give several everyday examples of resonk+lcdab8 . (efance.

Is a rattle in a car ever a resonance ph3cqdua2 ,x r,6m2duojenomenon? Explain.

Is the frequency of a simple periodic wave equal to:g v a5-p8ll(q zkuym*kx8d)x the frequency of its source? Why(kp8: dm)* vlxkl8qgz5ya- ux or why not?

Explain the difference between the speed 9zl;u otb8u3 w36 qlh3 qusk:kof a transverse wave traveling down a cord aqs6k9 h 3:8blu;ozkq ul3ut w3nd the speed of a tiny piece of the cord.

Why do the strings used for the lowj3rcrn0s.ojjy 5 hgw+)(b *b mw6)yd pest-frequency notes on a piano normally have wir *ynbj m)3rdwoc r.hg6spb0 )(+jj5 wye wrapped around them?

What kind of waves do you think will travel down a horizont p -ga6sd twv;g zuf;1w1rk06pal metal rod if you strike its end (a) vertically from above and (b)pf6 r6wp-g1kua td1 ;gvzw; 0s horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, a8x(w0nt g 0jobut the bulk modulus B is nearl (ta0n 80xjogwy independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular47mho (n0tkc1c r 03bxye7jmj water waves decrease in amplitude as they travel away frxrn0hjmjmytok77c3410e ( bcom the source.

Two linear waves have the same amplitude and speed, and otherwise 8*lw(n 6sqzr( 2fqbhkare identical, except one has half the wavelength of the other. szb6 k(n wr (2*l8fqqhWhich transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between tcrkvx(615w 1 kwo10(lkyq zd two sections of cord as in Fig. 11–33, the frequency does not change 1kwt0y1(r dzxl w c(q1k6 5kvo(although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could touchvt/i+.(gho i4d (wzjf it withwo 4 ifjd/+i h.((zgtv a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflect k3 3bf21rkepied waves cancel at the nodes.2brfkke331 i p Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one pl mu7g1eea f(i)ace to another, how might we determine whether the energy w(i f7ag e1)emuas being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the tota7p fpl6zr)ts5l distance it travels in one period? ps z)7l 6rpt5f   m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it bur ood ,op6.6jwt is 85 cm long when a weight of 180 N hangs from it. What oojwp, 6d6or.is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm wh c/v x4)ldabu7v*h9jn en its 68-kg driver gets into the driver’s seat. If the car golcvujh)7 *4 axd9bn/v es over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a g.,kl6ce mh,h 2.7-kg fish hangs from it. (a) What is the spring stiffness cone,g.m, hhlck 6stant $\approx$    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 pl1 hu t p+..e4d.+w2smkdlbo with 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 ku.om.+ led shp 4 lbptw2+.1dkg hangs from it?    Hz

Construct a Table indicating the position x of the mass l +zmflqjhjg 4 6p.urp1b 5o42: yu9kr4r0rvlin Fig. 11–2 at times t = 0,ky2luj 1b: 40r94zg5u4vhp+ .lf lmo r6pq rrjt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 cau 3 2 +htzw)7.g)cn cxrf6oorsoght in a spider’s web. The web vibrates predominately with a frequency of 4.0 Hz.xht)zsrgofc . )nc o +6or32w7
(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. hgz9wx+7(m w v bebm/1When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value /bzmhvw xm7ge 1w+9b( of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 timzdar5 ); t q.0xqkpvq go;,vh8es per second with an amplitudqzv,; q5vpg 0)aqd t8hr;ko.xe of 0.13 m. 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 is the speed of a SHO half the max a2 ltzsc-,x1nimum val 1 l,2-tcaznxsue?$\approx$    A

A mass attached to the end of a sp(r/ 3ewtk. mr;+cmru kring 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 m.kijua:zxo88rn ;a, (.+ mpnb(py)byf If the spring is stretched an additional 0.130 m and released, how long does it take to reach the)oy um+npy p,b;.iaz x8(nkj(8fa:br (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spri7bpqit e2ei8uqi7 * c jw/)ip,ng with spring stiffness constant k = 280 N/m and is executing simple harmonic mq8i / bpi2j,iuq eew t*pci7)7otion. 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 compress the spri4g:9a6m l+yfmtc g2 e8t9x elcng of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed wg2f e+6cxmmg 8yt:te 9acl4 9lill the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached yu 9uqykq, m-fw/v(0yto 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 ,/ y-qymf9uvquw y0 (kthe 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 according to the equation x = 0.45cos6.4t whrs-bqjv il8iz)18:f jere x is in meters and t is in seconds. Detbj lsijr v :8i-q18)zfermine
(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 ymo (k(ap(z * las8fa6of a SHO half KE and half PE? oka s(ylz8( map*(6fa±    A

  If one vibration has 7.0 times the energy of a second, but their frequencies an+ogshd0tn- g 7d masses are the same, what is the ratio of theirtgng+0o7ds- h amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lbih2 i irg 56c4wrjp.0buq6o4ight spring once every 0.65 s.rc6qw4p.6ji 5uhib0 o2g4i rb
(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 parall2jv: wqvc6u chai-2/bohb) r2el vertical springs, each with spring stiffness constant k (Fig. 11–49). What will b hq- o:ihucv2c 2br)2j6wa/vbe the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t wh klcwxgpq 5 )isvrf*5 ;w q;1xlyj(:0were x is in meters and t is in scpwqv(lly0xk);rwg ;qw * :s 1ij x5f5econds. 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, c b eznhxgs, :x4c+atdxwo 5v+;:t3p -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 7mne gktx: wpzy)- 0;qon the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Deteykx) :mgtpqn;-zw 0e7rmine
(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 stif nic4lc*bkjw5 c /e34ofness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through cb nej 3okwc5c/4*li4 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 qx)vfunf0 obc v i2zcj2 u+2z95ha4,htwo springs, with 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-kg block attached to a fixed ho28,jfl(y* zo esc6cbvrizontal spring whose springclyj zv,fsb(6 o8c *2e 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 jum io1tm z;x)+hxr eci-5ps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally1hiexz)5c+r - mtxio; comes to rest 25.0 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. W t,iqekh :cem;;5 n. /x.mdocjhat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendul1nwxm)s3nqap8i:dkdpt e8 /-um be if it is to make exactly one swing per second? (That is, one complete vibration ppq x3-1d 8 :nm/)kawnsdtie8takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth.6b*plb:upqriox pv10oat - 1o5io2z* What is its period on Mars, where the acceleration of gravity i *r5pbza oiuiblv x1po 2qo-1t0p:6 *os about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long i.leu pf1-k oloo1n7q :a/zo5
(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 pendulum bob ha*+73xrzauu +rr+ cbdk 0gy/ mfs a mass of 365 grams, and it is releaseddzy7+ /ux*0 gm+fr3+curkarb 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 pend-9 rx/fj1b wnk- +p)tz.u,ocxzq by2dulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the l9txwy xbzr1z-jb.2+kq dc/,nu)o - fp ength of the pendulum? shortened by    mm.

Derive a formula for tgn/7 qsopau, 5c ogozl//-h)lhe 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 a01x /,idrhhb-bs*.voofbb- r frequency of 2.5 Hz. At it is released from rest starting at an angle of 15h.xv s-dob0r1/h*, bbrbof- i $^{\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 anchored bo)ii;:hy+dpot : ftsdw w27g4lk.oxs3at every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travelinf og42i y.wdwsl3di);7 +pot:h xks:tg?    m/s

  A sound wave in air has a frequency pw7i r1hu-b4;ay/blkw ov (e gge;;( fof 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (cg4; b;lwrow (aykb g e7h/;p-fe(i uv1ompressions)?    m

  (a) AM radio signals have frequenciesp qiq ip,(ud*3 between 550 kHz and 1600 kHz (kilohertz) and travel with a ui3 (idpqp*,qspeed 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 kcn;- 2 1um:r w;yt7dqlj1ja glongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elkq5nww.4l wj6jv2 lyxs .k..lastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and 6ql 2j. nywlw4..k5vx. ljwks by what factor?   

  A cord of mass 0.65 kg is stretched betwee7k.61i h ts-v0 tm+byv y 0rvcc08xjrfn two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pr+ jxvb 0mf0ct s0yv.6ic781v-tr khy ulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a h+cr+kt lx3 0naill 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.c aklnr+t3+ 0x 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 hi83 xufb-tja e(cvr)9t s ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor (89e)xur3c -tvfbt jadirectly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at diffje4t ,zvki- 9ik l 27jl43euahts+y(derent speeds, and this difference helps in locating the earthquake “epicenter”e23y (4zhjv,k+jlsieit 4-7l9dt uak (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 w k,5qx v2a)b* )socx;ahowx2z ave can be approximated by 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 the aoav)xk2q2 )s; wx*xbza 5,hc occeleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an ztkcpms6ul 1t+mo1p8 n- p*v0 earthquake P wave passing through the Earth andmvlppo1*n cs1mp8k u +zt 0-t6 detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is meas :tqo 04mh3m 7:bgreieured to be 7moe3egth4 mib :0: rq$ 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 travel through the sameagv,zc+0e0o x9zw j0sn bp +6k portion of the Earth, n p0 cvbzw,o0xe +0sa9z6j+gk but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frgan/:okq(x 19s cw 0ojequency, but one transports three times the power of the other. What is the ratio of the amplitudessgn k1xo(0oa9:j/qw c of the two waves?   

  A bug on the surface ofeb 1rk,(9su hu a pond is observed to move up and down a total vertical distask(u1b,9 urehnce 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 F7kaekcavb 8xgvym 4(6v1w 1tixkf6;5 ig. 11–52 are moving toward each other. (a) Sketch the shape of the string at thwtk xg5 7;6(xa akie1fb8vm1k 6yc v4ve 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 at this moment?

  If a violin string vibrates at 440 Hz as its fundame+u8+i)ngrjcr 6 xmqg3ntal frequency, what are the frequencies of the r3g+uq8n+rmcji 6g x)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 what fren:pk5lgp;q :9p1kz :p oukv+uquency will it vibr;:kkpo up95:nqp lg u+:1p vzkate 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.)    Hz

  A particular string resonates in four loops at a freque7l(f ip6zlxu *ncy of 280 Hz. Name at least thre xfllp6iz*7u(e 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 string is 92m/s If the frequency bcim,m;18v up5 gl 2ozof standing waves is 475 Hz, how far apart are two adjacent nodesm;zic52l81 uovg p,m b?   m

  If two successive oveawo 9um+ 3l3ncrtones of a vibrating string are 280 Hz and 350 Hz, what is the frequency nuoc la3w9 3+mof the fundamental?    Hz

  A guitar string is 90 cm l lnbv( p ...qmand0b8cde:h w1ong and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the funddn.18:mvp aqd(0.ecn . h blbwamental and first two overtones?    Hz

  A particular guitar string is su/xc uc br;4zuk,wz0r6 pposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should0;wuxzr,rk zc6u4b/ c the tension 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 qrb o*/+.wez 3hvyi/dat 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 fow/+hy/ e .irq*vdb z3requency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude m8:wbqq14 f xuf sf *ta7,ruo;uechanical 60-Hz vibrator. The string’s mao*rfub s8 7wf x:qft;,qu a4u1ss 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 x hxh35ax+a r oz0o:k2string may be adjusted by moving the pulley. If the hanging masx 5a+xzx02ah3:rk ho os m is fixed at 0.080 kg, how many 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 tubnxdwt .z2 ic1032sq;5uz suqd at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at. c2ndxusz;ud 103 st z5qqiw2 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 lhwf;0y(*d i0lmme u8 within the Earth between two kinds of material.ymdfelli m8*u 0;(h 0w 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 “q a jpt4l-p21ashelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave cres 2t4lapa-j1qpts 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 o f 7zh(xmhr:,layer of cold, dense air. If thex7( hmrz:f,ho sound wave hits the cold air 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 earthquake wave strikes a bobx3ip0 k**.dhmfhrp 0r z:s)i undary between two types of rock at a 3ihmx*pr pbf id. 3z*k)0h:r0s8 $^{\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 diameter. According to the user’s mae3fhr y k6z -.)rh/p3)kxltoc nual, the dish has to be pointed in the direction of the satellite, but an erro x).otrfrkc- p3khlye3 6z/) hr 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 250 km and velocity 750 km/h travels across the 7bpju z 5dgqx(m;9mb7Pacific 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 tsunami x;75 z9mmj(bgpuqdb 7s, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a sprogb.*bpt d6.q ing stiffness constant 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 conservation og6 t*.obdbp .qf energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m bel( j3 8. :perpwnutz(o72atfil ow, which stretches the net 1.1 m. Assume that the net behaves like a simple sprinjual(2p7rw.83iz(noe:t p t fg, 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 slw*/h j2rpn m+3eic6thpq:b)pring. The mass then falls 33 cm before it stops and begins to rise. What is the fr6rl+ m c*:/3nwj 2ehpp) ibthqequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compfqo,e nfo+w02duvf2b3 a9yj ;ressing the spring 5.0 m. (a) What is the spring s;doq 02wae+b uj fnf 9y32v,oftiffness 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 just the right pacpeccn* ;z rfki4 wpi;n8+ :e3ce of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate ircp; kec:nw+4 *8zfn3 cepi; 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 pvc 4; bkkd0a)ohonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?ko0;vcb kda )4    Hz

  A 2.00-kg mass vibrates according tobcw c:7jlbbh6zd w03ne,oz) ; the equation x=0.650cos7.40t where x is in mzbn0 e cz3hdjlbow,c;) :b7w6 eters and t in seconds. 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 is its frequency il6lhs)w+hg 0 qf it accelerates6 qs 0hl+lw)hg at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft *b7:u*x9n 0goyqjhr 9 zb(yar, it sinks 4.0 cm deeper into the watogb 0rq r:*b9yza*xn h97u(jy er. 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 musical instrument ajl.efvq t (uma e9+0fe0p;3 ssre tuned to play at 392 Hz (G) and 440 Hz (A).fpfls+u 9e0.a sq; 0t3emjev (
(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 Fiu5e9nzxx9h g*g. 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 thgnuh59e9*zx x e 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 vibrates at a f))y0 su0/(ron wjyvjpxu wq-*requency of 264 Hz, and the tip of each prong moves 1.8 mm to either siyj n-pj)o uq)ux r/v0w( *0wsyde 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 cycles pe;go9 f* t drm97n:hwiur second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fi *d:;f9irmgton7wu 9h g. 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 can slidesnr0- -ro31+fqgbdlvk r 4h/h without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with3b1k-f /r-vhnslh4odr0qg+r one end fixed and the other free.

  A “seconds” pendulum haa5( pkhg pbyr )bm4e6oo1b8y (s a period of exactly 2.000 s — each one-way swing takes 1.00mg ( ba1y )r6oobk(pb584ehpy0 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 spr ba1jbvp ;k,0iing can oscillate 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 horizo j1ib0;abp, kvntal 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 mastsnh/ 2;pq8 b2qx8n)ua,kqc ts 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and n;tht)c/p,88x 2u2qna bkqqs 20.0 ms later a 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 ceiling by a spring with xg vi4iexl)k80tfvh2 my b )05spring stiffness constant k. A penny of mass m is placed on top of the ble0b 4xigh )ixvkvy8t 20f l5)mock. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car a gcjwfid 7f.kg97x5w2t the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car boungdx wic.gw7792ffj5k cing 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 c5vqw7 :w 9u9sh kk0(h7 xqoyeFig. 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 to a mass vibrating on a spring, estimate the fr wvq7qk0xushyc:(7h 59e9kwo equency 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