Give some examples of everyday vibrating objects. Which exhibit SHM, at 48mae+t telmkl fou *x8q,1v,i3(l m dleast approximat4mmo1l aq,8evxt ( *,dlufm ie+tl k83ely?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wher 3c u;bj+jpju 98zgem1e?

Explain why the motion of a piston in an automobile engine is approximatcnh di-o;3wg3*fvky*x 2 fs6fely simple harm3 fgwh6c *dyxn* vis23fk-f;oonic.

Real springs have mass. Will the true pere9 z*/ nn+ rv6zfsm*xp/jeq n7iod and frequency be larger or smaller than given by thp 9/ n*xn n6jfrszzeev+7qm/*e equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the,kj4;9hxdn fhg* -aos maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale+d ladi5njs;:, and then is released. Describe the scale red+j5n:l ;iads ading as a function of time.

If a pendulum clock is accuim 7c-ua7 0nvlrate at sea level, will it gain or lose time when taken to high altitul7avmu 0n i-c7de? Why?

A tire swing hanging from a branch reaches near xs(:w j(qv 7odpqmz;ug0z 8a.ly to the ground (Fig. 11–48). How could you estimate sjx( ;oqmvd(7 :uq8apz z.g0wthe height of the branch using only a stopwatch?

Why can you make water slosh ba2hd*ho( rp w5:d;k lykck and forth in a pan only if you shake the pan at a certain freq*pdk5yw2 l;dk(o h:rh uency?

Give several everyday examples of resq( y-wgyn:v;f+bzq3 q onance.

Is a rattle in a car everfvl7 w/byz:6nu)jmgr5c:d-e pq/ vr 9 a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of i laafsk,psc145 j.uy*ts source? Why or why noj5a 1kauf ,ps* c.y4lst?

Explain the difference between the speed of a m8 fi ctv rph;a,8n -,c0oas0ftransverse wave traveling down a cord and the speed of a tiny piece of cs 0am fhpi;,r0t8cfnvao - 8,the cord.

Why do the strings used for the lowr;co/durwya1 6qus *j/n7p z 9est-frequency notes on a piano normally have wire wrapped around th17ac 6dq/r rnpyw;s9 uj/ zo*uem?

What kind of waves do you think will thj i +my7s98ezravel down a horizontal metal rod if you strike its end (a) vertically from +y89 zjm hse7iabove and (b) horizontally parallel to its length?

Since the density of air decreases xe ku:uv )yont57 hc9*with an increase in temperature, but the bulk modulus B is nearly independe:*c 79y )t kuoxve5uhnnt of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves)s9+rbgpf75 p (eor ch decrease in amplitude as they travel away from tcreg5 9r ( fh+oppbs)7he source.

Two linear waves have the same amplitude and speed, and otx ge l. hx8f;it9pat6()gxrv7herwise are identical, except one has half th6 itxvt(p 8r.lxgehg 9afx)7;e wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses tdqsg32av6 1 mg:b-l t5suv0ka he boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocit6lgmb 3aa5 s1suvt2g- 0d:kvqy do change). Explain why.

If a string is vibrae5i0yky (kvc/ /r6 zupting in three segments, are there any places you could touch it with a knky /z0r(ky6vu e/5 cipife blade without disturbing the motion?

When a standing wave exists onl 682gsi7fujxr)la9h u xu38b a string, the vibrations of incident and reflectedu)3ib2u9f 7g6j hlslxr 88axu waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how migiult 0)ulhb-4htu)i0b-lt4h ul we determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoepimz1mj3q w2 *s SHM with amplitude 0.18 m, what is the total distance it travels in on wzpi jm2q31*me period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fro7kzj :qi p.pobgy(4u 4m it but is 85 cm long when a weight of 1jz:kp(7.oq4gu 4pib y80 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg crgdij/ s(0 5niar compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the jg/i(nis0d5r frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretcwybc-(p0. euuhes 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spri.u-cbuweyp (0ng 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 +:hpms 7tph 1u;p klq+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.p ;ph uk tmslph7+1+q:38 kg hangs from it?    Hz

Construct a Table indicating the position x ofyje /q5,4 mfsz the mass in Fig. 11–2 at times t = 0,tz4js5,e/ mf qy = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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’s web. yn2d) cb6cfw8hpw.k7 The web vibrates predomin.w)d6ycpk 28nbc7wh fately 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 vcd l9 *zr3)vfo+s7duy.h nc* kibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency ivsykr dl n*czc+oufh 7.d)*93s 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times p s0c,8lxuuk6s er second with an amplitude ofu6kss l0 ,cxu8 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;rxb*z; ;7/n*j jei7igv x gt3zpf 3u,zf7oex the maximum valv*ijjfz,3g e /7g*3; 7 pt;b;on7uxefxzz ixrue?$\approx$    A

A mass attached to the end of a springpxt9 y8 r ny)dx1b;inv(h) 8kpp:ei:l 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 stretch an8)yymgt;6b (-1cboe807 / h4 bejrqbwwbk res a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take tje 4b0ykqm8w-(th1 w7or )an8gb6y /r bec;bbo reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring e(,kbvkk 8fyw 1+l pwvj9b odc2/mg( ,with spring stiffness constant k = 280 N/m and is executing s wc/gkkl(m1ef9b,kpwyb o 8d(v, j2+vimple 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 compress the spring of a to-oouz5f +g 5adt s717nb tf+wxdg3:x ey popgun 0.200 m to “load” a 0.180-kg ball. With what speed will tws 73ab xnod ft5x -fdt51oeugg7z++:he ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attach4/q77 txae e2s*ofuwied 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 thfta w uq 2o/iee7x*47se 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 * b),-givuavc to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Deterc )- bguv*i,vamine
(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 *jq.pi1qn ;hs :av 2flis the energy of a SHO half KE and half PEqp2jn* ;s.qilv fha:1 ? ±    A

  If one vibration has 7.0 times the energy of a second,wvw5 rnl629mo dbrz:; but their frequencies and masses are the same, what is the ratio of their am2rmw w ob;z9:n5r 6dvlplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring onz .v wvd6e f19u,;nagbce every 0.65v. u6g adv9nz1wfbe;, 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 d :)xj rwnw92jkcmb+f ju 2:;gdcj;+tsupported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What w:29r :mwd2+kj j) xudc +;;bjtnjgfcwill be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in mdcu1aral (6e))sf/ z keters and t kfc )d (zar/el 1su)a6is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeledxe/0f/ 5q+juvezd: eqn*7zrx 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 of*w3h pd w,i/vw; m+f o 3ngj25kidg3yp a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determiw mi,3iw *f3o g j/kvpyw3pd5gn+;hd2ne
(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 Nzomu6yc,3kwgze/ 2y ::mhyl 3/m vibrates with an amplitude ofym:g 3my6w 23:hulzk/zeyco, 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffdf7n/te2j(h r l,bjv5x(hc 4i0aji7 tness 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 0.0 svwcvn)j0v 0 s+(a:dapqv t)600-kg block attached to a fixed horizontal spring w0 jvp cdvsn)(a w 0vsq)vt0:a+hose spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with masgn28,wjg4w :z.ecj w9nd9ccs,l*a )p s:dkgus 65.0 kg jumps 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 finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched lenc cp) wcwgj,,aj9s9udn ke.:g n:d2wz4s8l *ggth 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 its u 3j79box n gt 8bois/wj56f9x
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one h.s x.ygcptif+)bb.qi 5w( z*swing per second? (That is, one complete vibration takes exactly 2.0 sis )yzpq ft*.+ bih.cw.gb(5x.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where z sy :li+5qy)pthe acceleration of gravity +q :yip)zys5l is about 0.37 that on Earth?    s

  What is the period of a si-8igr klg ob27q1-jxample 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 penduh-ued 5d +8g7pnh x3b cb x+6ii6ouq8olum bob has a mass of 365 grams, and it is relea5c6xdu8h7u3 d+ ogobxqiip b8 -ehn6+ sed 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 p/n;h4fo; tq qfz/7 n5wnx p;mthe clock loses half a minute per day; xnpqomphw /z7f ft5 qnn/4;;, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for mlvci ao+j5 y;0 vso.+the maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequencc3:ri16vhp ho y of 2.5 Hz. At it is released from rest starting at an angleh hi1:r63voc p 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 passd ;qg;:q jc,hgj b8mp8 the bow of his anchored boat every 3.0 s.;pj; gcqhm8bdgq8:j, He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels wit8 hewad(vt. r-ftyy9 2nb; es8h a speed of 343 m/s How far apart are the wave crests (compressi ;d fwb8tay29 sv.htey r(e-8nons)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz mqwj3jl )-0ka) and 0kjlwm 3q)j-atravel 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 longitudinat vd8 zj2t-j t8j0-oo iqu5j6bl 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 7jn yj11/mlc+q6ss-z3e -fkbau9v a fas the other. In which rod will the speed of longitudinal waves be greater, an3s kvj+l fy /1q7sam9cefjnb6 u--1za d by what factor?   

  A cord of mass 0.65 kg is stretched between 6cpjagphkh14*pq*9 k two supports 28 m apart. If the tension in the cord is 150 N, how long will itp*p6*9pkh4jhg k cq 1a take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of lehgmok 3h w./tu9:qfv x.vra xc3- 69qcngth 620 m and diameter 1.5 cm. As the gondola comes to the end of it 6wumax-x.vh/.to 3qc r hq93gkfc9v :s 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 o( g m,aed1a5wpf his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?,gam1pw (dea 5    m

  P and S waves from an earthquake travel at different speeds, and this ;4e7 sc(fsrynpi ib -.difference helps in locating the earthquake “epicen(;ryinfse c s4. ibp-7ter” (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 wavb 7*+eikx e1 nszcax,;e can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typicecia;n,eb*xk s 17z +xal of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an ear)pr. (8wuumb6qa enmi(0pe qe2v8p3nthquake P wave passing through the Earth and detected at tmpuwq3mbep u8n6i(p (. 28 nav rq0)eewo points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measurw3ct +286: kytqeuxw red to be +:ucwe qxw2t3t 8y kr6$ 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 throsq (. (neicxw 6n/mv.bugh the same portion of the Earth, but one is carrying twice the energ/c vmsxw6eb (nnq.(.iy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have thz+g0r:eo4g7ugnj w 8pd yuc/ 8e same frequency, but one transports three times the power ed owu c0/87p4gzgjgn+ 8r:u yof the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move +h .4jmt4mdagfl p1 z.up and down a total vertical distance of 6.0 cm, from the lowest to the highest.zalt4jpmf+d. 4mh1 g 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) Skkir( ao6- dc*hri*x 3g5iihz/etch 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 oth(h * 53dr*/i-r xiioachz6g kier, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its f kzjkdens2 9q;u7dk-7undamental frequency, what are the frequenci esdjk u27zkk-n9q;d7es 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 whatztpq+5 om.nv.0f.k 3:hfsom c 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 stf5m0 k .zqo.sf nt.vh+: cmpo3anding wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Namew8;eh r o; cqt2hx0m5a at least tc 2q0;atwmheorxh58; hree 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 freqpjvoo, - 9sws2uency of standing waves is 475 Hz, how far apart ar - 2opsv,swoj9e two adjacent nodes?   m

  If two successive ov8ne ks; m18e6crbm*kjzsn 8e) jz5x)v7of;c u ertones of a vibrating string are 280 Hz and 350 Hz, what is the frequenzjeo6 j88 ) nre81 nsx uecc *bv)5fskk7m;mz;cy of the fundamental?    Hz

  A guitar string is 90r g g2ak0+;n*0f inzdl cm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and 0 gnif grakn +;*l20dzthe string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar s;q8)t q iq-sug/e1k a1oqn,bftring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hb qf a/qesgnti-8o ) u1q1qk,;z. By what percent should 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 stri09yv(ep * s*5 i7ejc;rmc+wuzgk;h7p2ror tz ng is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in thezywucgs t i5+;jpv*9 zkr7epomr2e 7r0;c*h( string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached tolnmkjd0uck)d,0 r**:q8q rvm a small-amplitude mechanical 60-Hz vibratorrldcj)qdmv, *k*: kn u qrm800. The string’s mass 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 theqw.;vu p mn7/o string may be adjusted by moving the pulley. If the hanging mass m is fixed at .mnw;uo p7vq/ 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:5 dov+g8jta 8w+zyv s tub at just the right frequency, the water alternate+a: zgy8 8vw5+sj tvodly 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. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary withim-ajwe 0rn7.68 fkrwen the Earth between two kinds of material. If itf6rjw8 knm7weaer - 0. 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 ka0s k1rtc rl6 qh2vy*,s :ki3“shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave cratk vissk:,612cy 03 qr*lhrkests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold,b01cahmu.x tlo pf88 zpb4t4, dense air. If the sound wave hits the cold air interface at an angle of 21bh8x4 t0b a fu,pc.tmolp8 4z5$^{\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 boundary be+.j9iui v63rwt fa dh4tween two types of rock at a 339a4 i. hd+rt uvifw6j8 $^{\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 m5 x7:0vcuc jcx in diameter. According to the user’s manual, the dish c xjxc:c07v5u has to 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 travels across thee-za c2yhb:eyv)3xl 6 Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during3lebeh yyz:v) 6xa-2c tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 bd.xu,st(c uqc,, bb::sjo w+ kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides w,b(xdw.s+tcqb usj,,o c:u b:ith 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 fro3k;xsxk094e hn yz lx6m( z2cxm a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves lzx 0xm k xn4eyls2hxzk3;96c( ike a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of qp1/).-jlsy1xqyep m a freely hanging spring. The mass then falls 33 cm before it stopse1 -j1s). yq plmq/yxp and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compressv9f k35 v;pxotff3i3ming the spring 5.0 m. (a) What is the spring stiffness co5 tk3vf xfv if3opm;93nstant 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 coffep 3eglgpsrwq rmr/69:,j, f5ye (diameter 8 cm) at 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 speedglg,,/: sprq9 6wpe5rf3 rmy j of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8ajd0t92 c,do8x 0rqwiak qf; 5kx7.xb cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency ofaqdx5;.kt0bc9 fq,a 2x8ox rwij 7k0d the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=,exhce.tl)v5ak rn h2a :1 ;msc:kv1b0.650cos7.40t where x is in meters and t in seconds. Determine 5x ken)m2s:11caavkvt:b . el ,h;crh
(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 witmlc/q.k-503 hpakzes h frequency f. What is its frequency if it accelerates at e0k-.a3 lk scmhqzp5/0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the btz)eb * + 7z0n qsqqa:(tybdkp b5+r;raft, it sinks 4.0 cm deeper into the water. When he steps ofsbak7brztq; npe+ y b5*()z+0dq bt: qf, 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 mus4 2z3nhm px ;1uamzao+*oi:mkical instrument are tuned to play at 392 Hz (G) and 440 Hz (A). h1pi zmo4 amoaz* ;km3u:xn+2
(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 tr( m95j+g a ha2jvx0fbhe stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the ahr9aj(g2 b50 +vf jxmwave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 26l80poh) ofjq rv10eb+4 Hz, and the tip of each prong moves 1.8 mm to eitherbqj8o)p r+1 e00 hvfol 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 oscill fu- w1gd lu7jtbut9;2ates with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board ca t2-bud79gw; u j1uftln 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: b ocg4je6ja21eb1 o vblib8gff29k0egg3x2 to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string witcvg4fabbgoi1b0xe gel j1gk j8 o f23:29e 6b2h one end fixed and the other free.

  A “seconds” pendulum has a peri/xc /,w5kljb6lp0bj bod of exactly 2.000 s — each one-way swing takes 1.000 s,p6bbkl 5wj xj/0bl/ c.
(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 vertnex.z,ee c h/3ical direction or can swing as a pendulum of small amplitude, but noe.czx , he/en3t both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tens3 dc:j p*ow(r6 6nkeysion of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at t6p(k3 ejcrsody6:*nw he opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceilingmri ml :/.y*1c.ebh cz by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillatc.b */1mz:mheil r.ycions 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 at the junkyard. The steel crane cable is 22ira( d0q)n a)b m long and has a diameter d0bna))( iqar 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 an1;wv m-iw gzisb/t. /tx.y,v 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 w;-vz.t, y. ixws/1 / bmvngitthe 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