Give some examples of everd lmie0g+u-*g+xny *j yday vibrating objects. Which exhibit SHM, at least apn +iyx *m *d+l0geu-jgproximately?

Is the acceleration of a simple harmonic oscillator ever zi kpjzy)z04w1bhs1k bd)21 ziero? If so, where?

Explain why the motion of a pistonk,;:nv/ iu tv: 9e zsxiznag*, in an automobile engine is approximately simple g*z,nv; e9/k :au,s iv:x ntizharmonic.

Real springs have mass. Will the trub 5( yu-k:uiowe period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized mau:iuobw y(5 -kssless spring? Explain.

How could you double the maximum speed of a simple harmonitdvi/8 bf6ijd;5gmb6 c oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring s1lcri9re c5+ccale, and then is released. Describe the scr5 c9rei+l1c cale reading as a function of time.

If a pendulum clock is accurate at sea lev5 / bkwahch9a *y1pboxwgp -*/el, will it gain or lose time when taken to high altitude?9ygkha-phb/b 51w*/ xpoa cw* Why?

A tire swing hanging from a br (r-;pk/ b5yq*cc ryjdanch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a strd/b*q ;y-yckcjp 5 (ropwatch?

Why can you make water slosh back and forth in a pan only if you shake the pan abz.l5 *e02)fash xeert a certais*ae 02ez 5lex .)hfbrn frequency?

Give several everyday examples o6xr8 cwa;argcjaa-c,f: 5:zb f resonance.

Is a rattle in a carzfud1+4 8mwd u ever a resonance phenomenon? Explain.

Is the frequency of a simple o sn5v f/*:z op)hx0* txqtf,tperiodic wave equal to the frequency of its source? v/fs,ooxt*tphq05nx z* ft: ) Why or why not?

Explain the difference between the speed of a tux8co ;ym 8 fog.i/+mlransverse wave traveling down a cord and the speed of a tiny piece of the cord./8 fu.ool;yc gxm8im+

Why do the strings used for the lowestm g*m.0dl7hd qu5c1fa 4xu 9my-frequency notes on a piano normally have wire wrappc1u9 * gqydaxfd47m 05.lhmum ed around them?

What kind of waves do you think will travel down a horizontal metal : (;mn.t zmodcrod if you strikd;zt( cnm.:om e its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decrea21wm6f kc, q-* huwrjxses with an increase in temperature, but the bulk modulus B isk-rw, 6 j1xcm w*2ufhq 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.h o0ayja:h n4y travel away f 4ao h.n:a0hjyrom the source.

Two linear waves have the same amplitude and speed, and bx;v (ow90ojb 20,mj- nwv rbiotherwise are identical, except one has half the wavelength of the other. Which t; 9bv2m0(jo in,xw -0 bojvbwrransmits more energy? By what factor?

When a sinusoidal waveu+*ld v ss1y7r ag d+lw29cb4m crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength a m lu4cg+ywsv7l+ ar9*s1b d2dnd velocity do change). Explain why.

If a string is vibrating in three segments, are th49p0 t,a hv)k+armoqj57s blyere any places you could touch it with a knife blade without distub0 r)7sh+t op5q9v 4ykaj l,marbing the motion?

When a standing wave exists on a string, the vibrations of incido 8 fea20xrw,x 7m.bvxent and reflected waves cancel a,x e xwxb2.7aovf0 mr8t the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one plac+xwov14 ypw o)e to another, how might we determine whether the energy was y o1oxwpwv+4) being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the vdi./. -a ddpp9 etci4;ep; ugtotal distance it travels in one pcp;dgi d.;taiue4pd v. /e- 9period?    m

  An elastic cord is 65 cm long when a web7 kot ixzs7+cu) kmcj0c, c;5ight of 75 N hangs from it but is 85 cm long when a ws+7,mcc 5uxi7 zb ojtkc);c0keight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver g2r x38(9 fdx5q zqlkfeets into the driver’s seat. If the car goes over a bump, what will 5d 3r8 x2q(xzf9fklqebe the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kc.da,bq me,/ kg fish hangs from it. (a) What is tqacbedmk .,,/he spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with v8kq(ww-q2 a ma 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 from it?wq-a mkvqw2(8    Hz

Construct a Table indicating t6+n s ghad*;hkunnq8tb3ox0/ he position x of the mass in Fig. 11–2 at times t = 0,tagqhn 08/t;6hnb so dk3x+ *un = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 yqnz21(fbx9c yws unl++ 3;xl :fove0a spider’s web. The web vibrates predominl 2 s(9 uec;yf+xwnyq :1+nvbz30 fxolately with 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 iwux9)wf wu5yx0 o-o3 frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the 5w) yw3 iufw9ou 0o-xxvalue of m?    kg

  A 0.60-kg mass at thiq0v ; 9:)qjlwlx gbw2 9azs*ue end of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Deqw g2 q 9j0vswl izu)x*;b:9latermine
(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 equilibrium5uiamfgn *7vju; 85cbueq.t 5 is the speed of a SHO half the maximum valuevu.j5fb5m ncai u75;*qe 8utg?$\approx$    A

A mass attached to the end of a spring is stretched a di:w hstx9r9k6(qb qfh -w djazi21do27stance $x_0$ 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 spring is std,xz3p. lg.zz retched an additional 0.130 m and rg3d..lzz px z,eleased, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness const5i /pim jrb.hs5yck,0ant k = 280 N/m and is executing simple harmoniiyips5 /kjhm c0r,b .5c 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 5ey+a d3.rjnzi62ctfa j .*zt N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With w*+ 6rt zy3efaci .5 .zn2ajdtjhat speed will the ball leave the gun?    m/s

  A mass sitting on a r2)5tjqxddma ;rk +/o horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is requia roqkdj25xt/)+rd ;mred to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where xadk k:ablr+s; w;+t* k is in meters and t is in secondska;s bkar ;kd*+t+wl: . 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;t xepd ky 2wbvb9(g5- a SHO half KE and half PE? ±yb(v-; g9bpxdwtek5 2    A

  If one vibration has 7.0 times the energy of a st72gdmk o--md au 3,to h *pr3rqxhrg+o08sh/ econd, but their frequencies and masses are the same, what is the ratio of their o h/h 0-u at*q3grmd r,dosox7+2-tgk 3mp8hr amplitudes?   

  A 2.00-kg pumpkin oscillates 4y 5p9w7 u2moih zylf5from a vertically hanging light spring once every 0.65 s2 i5l9hf5zyw ympo 74u.
(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 i oc)v3pzgjc9a,m emiv /o-+s. .ubuv:dentical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequpim.e-bz9 ) vjvmoo.c3+:vc/ gausu,ency of vibration?

  A 300-g mass vibrates hwkyeeyn+kj1lc 3 2,mp68o* taccording to the equation x = 0.38sin6.5t where x is in meters and t +kno8pel t*6yy m2 j13khce,wis in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examplqqvj)kc. gzmvwm 8rzda) 631;es 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 t vxuj 9b6zwaeb.25)hrhe end of a horizontal spring (k = 124 N/m) is struck by a hammer, whichub2j9w5z.bax ve) 6hr gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305;sufkvr;u97h +7k nwq N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (77uk nuhv q9k ;s;frw+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 sp3et z.j hf pj3+4cnyv*ring 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 ( za.12vdzqo v rjd; wba(:8ljhorizontal spring whose sprvzr:.8 (a ;b d1d2zjlvjwaqo (ing 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. Afbf u(so(+u (d(lz3zto ter reaching his lowest point, he oscillates up and down, hitting a low point eigb utdu((zls z3fo( +(oht more times in 38.0 s. He finally 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 . odd/u br jf 0cwx.sm+sskw8 /o,n42g60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly onew7tn3f 5m - q :uh,vnszu ipuwf9qav4p* n2.8h swing per second? (T vs8v, -h4wpzaqt ui ff3m9 hu2 n:7nnq5uwp*.hat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What ivk(g:x t7pp gdx hqx/-x)d5e+b(vk(us its period on Mars, where the acceleration of gravity is abo-+dvxk(eqg7 ( :d x5xt) v ppbxk/u(ghut 0.37 that on Earth?    s

  What is the period o4yd ,hzcstq3v 6j cs6/di9gs-f a 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 0.760 m, the pendulum bob hadn *ktk x r4p70-t b(e)efoj-hs a mass of 365 grams, and it is releh *f-ebkt t (0)o7kexjn-4pdrased 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 a length of 0.9930 m. If the clockpp sj gyyd .)+h1d98os loses half a minute per day, how should you adjust the length of the pendulum? shor y)9g s+o.dp hp1jyd8stened by    mm.

Derive a formula for thedcp(vd1km)ua+k,ik o fmpu j8 lv nsr 8*23g1/ maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is releasedh q;9-lr7g ply from rest starting at an anglerqlh7 l;y9p-g of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchomb+i)1o fer,ored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wav i,or1+f e)mboes traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 kyu7n .kz2fv0m/s How far apart are the wave crests (compressiovf2z .y07kkun ns)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiloherue fk.7j)pe7*0px o: w ylr.ejtz) ap f :xeylwe.7 pjkj7o0u)r*e .nd travel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of lon-)djfq rni2c ot ys7j:5w d54ngitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulua0f g6dg2v9rjw+tt x2 mk+ dt,s, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be 9vw2,tgtxgd f+ar6 +2jdtmk 0greater, and by what factor?   

  A cord of mass 0.65 kg is stretch gf-kgq9 )w i;8g1 unz0of0vnted between two supports 28 m apart. If the tensionwu- t0)n q ;19nggzvo80ffkig in the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to thex1j/(oci 8am-d v*f1 5ezjirg top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As theo jei 8fv i-1majc*zdg 5/(1xr 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.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. He q) ns 90xdxv 4,9rtzewhears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is thz,wt0q4xn ) vr dxse99e ocean at this point?    m

  P and S waves from an earthquake5 ,u2pgd6owl9km 1r py travel at different speeds, and this difference helps in loca ow5 rmlug1pdp962,ky ting the earthquake “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 approximatedbg+*tpm)jh, / z w :kbjjtbd83 by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitjkmj) 8gb bdttbh/ *:3+j pzw,ude 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 amplit0 oua9)z 6gvrludes, of an earthquake P wave passing t9u0o)lr a vgz6hrough the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave fu2l oe(fg6h9 passing through the Earth is measured to be u 69gh2olf(f e$ 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 wc v(6oxsq 1nliru,f ic2mlaxc77+7,travel through the same portion of the Eav7qu i 6,f2oi+7cl1a x7src mc,nlxw(rth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling al47 .e-wygwon/3krr hu+dp( d,pe3sbtong a stretched string have the same frequency, but one transports three times the power of the other. What is the nh ygp3wp r/ s.-,(etddb r+ wek7ou34ratio of the amplitudes of the two waves?   

  A bug on the surface of a po obzy* 5a09qlyx2j.zvnd is observed to move up and down a total vertical distance of 6.0 cm9x2ybz.5*zo0lv a yqj, 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 moving toward each other. (a) Sketc(jk-zgo6 1oaccllism 1u6b,2 h 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 m-klbsiuo,1lgjc16co6 ( a2z 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 fundamental frequency, whatai6rfb(f2- mm are the frequencies of the first four har2-armf mf 6(ibmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibra9zj rztd9t6 )guj,wfxr0 4xpamk x /.7pbn/v; tes at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the tuxkg;7p,m tnr b)px.v9jra0/z z/9d6 4 xfwjend? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a fdi3*6e , znzrhrequency of 280 Hz. Name at least t h,ei zrz36*ndhree 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 of stan(it, ont1a/pq *cb +uvding waves is 475 Hz, how far apaiu+q,co t (vpatb/* n1rt are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what is1pzqtq +90ksb0 bx2n0 ba cif; the frequecxqb9+0i 20bf qta1;0 skb pznncy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the md6xd/ e vxv.;;)fst wbridge to the su) xvsm;/ .v6df;edtxwpport post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar strinyz4bn)y8zlt+v7;sfng 9g 5o ng is supposed to vibrate at 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 frequency?So the thre n;nf4ys7+ol8 nzyg vz5gt9) be frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is cogjn3 uh-j72supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. Byjjhcou2n - 3g7 what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attprsf5 y)c/vy-d.joii zl +; *tached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length is cv ifjsi;y5t-z/)l yo+rp.d*$3.9 \times10^{ -4}$ 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 by moving the pulpa:vd98qz lj4hx4o2 qhr)vo, ley. If the hanging mass mq2 h44 o)pjv:,xqd o8r hal9zv 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 tub at just the right frequency,qo ((mbx t-uwuy9 mw86 the water alternately rises 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. wmw8(qx u6t- om9ybu(What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary (uqg e+ijcw-0k av *0fwithin the Earth between two kinds of material. If it approaches the boundaryi-*qeg (caf 0kwu+ vj0 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 velocfl6pw/ fm b,(b t49alga a/.*nw prlb,ity changes from 2.8 m/s to 2.1 m/s If the incide,/flapw blwg9ab6mft *al/ b4 p,n(r.nt wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travel (pd rrq gpzgx+qk6ce.;ft2 yu1hs328ing in warm air when it hits a layer of cold, dense air. If the sound wazy; gk2qx fe. g8r uh1q(dcp2 r6s+tp3ve 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 bohi56h;h :pa kdundary between two types of rock at a pi k:h dah5h6;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 in diameter. According to the user’s maj:o3 58) n8f kv5updwrqggj+q5gm)qwnual, the dish has to)qk5d3ug+8w5g jrpf5 w q o8jmg:qn v) be pointed in the direction of the satellite, but 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 250 km and velocity 750 km/h tr,cbwd,9o8ec 6w0pdi qavels across the Pacific Ocean. As it approaches Hw e0 d6bo8,p ,9cwqdicawaii, 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 to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffbg .zuri .20t v1w gv3jhdjr5)ness constant of 550 kN/m Find the maximum compression of the bumper if higrbt3uj 201vzvg. r.j )5wdthe 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 frop2z 449o f k)iw/ekggkm a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simpfk 9)owek pi4 /42gkgzle 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 t5wn*7xkve uhu52/ r+nu7fgr the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to v7unhtux*r gefnw+ 2kur/55 7rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spriwsz u xj y7 3wkil3fvup;(38s4ng at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffnes78lu z4uj;wws x3vk(yi f33sps 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) au1tr 3 x,axg, w4;1xzeodwvi;t just the right pace 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 the speed of waves in the coffee. xiex; a1wr; ,wtv4dz o1, ugx3   cm/s

  The ripples in a certain gdl, p+ j 35mr,6oftpu0bpla7jroove 10.8 cm from the center of a 33-rpm phonograph recor570lppbut,ajj6rm p, +3do lfd have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrate9xdodf+9:cv42gpm n x: w ky;jf2zwr4s according to the equation x=0.650cos7.40t where x is in mezgp2v+94y df 4wx 2do :xw; jm:krcf9nters 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 :m)bl svo t2j)sv7eb +with frequency f. What is its frequency if it accelerates at 0.50g (a) upwlvej) )t+7 :mb vob2ssard,    f
(b) downward?    f

  A 220-kg wooden raft flo:c gaea9yr4 v6ats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, 6 vger cyaa:94the 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 g v6mi:k2xf rxcm.i2+440 Hz (A). i fm62 r.xv:x k+gi2cm
(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 downv 4jcc- gj e7f(sgq*;h the stretched two-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 wavelengthje hcjc gq7-s;*v f4(gs 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 frequency of 264 Hz, andrj2p)p;sk 7q1 gno0jl the tip of each prong moves 1.8 mm to n0) gopp2j;jksql1 r7either 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 si4/(ju*z hao/yxt( rgvmple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can hrj(4gu/vto*/a y xz( 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 “free” end if that end is attached to a ring that can slideudzec0;h+f 5lskp aenz.-/t+ without friction on a vertical pole (Fig. 11–57znd +klfhtu5zes.;0 aep+ /c- ). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each o ;si*n)xggp srg,ak- :ne-way swing takes 1s)n*, ;asiggrp-g :kx.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 oscill(r v +/+;/ bkrpbhwotuate 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 horizobvw+u/brp h+;kr/( otntal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A vt 8;m2u 0 tkljg4*n1pbm)ui6v dqqp0pulse 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*tkd ; b6ium08gt2lm1 )nvqqu4pp j 0v meet?    m

A block of mass M is suspended from a ceiling by a spring with sprinka:4a)tv/-e94i;acqu y vgbog stiffness constant k./v:gt4vi )-eoa 9uk 4;q aybac 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? (Assume $m \ll M$)

  A crane has hoisted a w+ m2qcn5pm5s 1200-kg car at the junkyard. The steel crane cable is 22 m long and s5+ nmm q2w5cphas a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a ;;dy09yedfrd plate as shown in Fig. 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 freey 0d;f;dry d9quency 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