Give some examples of everyday vibrating objects. Which exhibit SHM, at w6csxfx d:nnd (9 ;de)least approximatsddf ; :nnw9)exd6c x(ely?

Is the acceleration of a simple harmonic :sm*yqsu )8 9(um cly.r9htik oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is appn:q 9,sf 5ybekroximately simple harmoni5e q ,f:bny9ksc.

Real springs have mass. +sm kq+j*k9)ym *plywWill the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an ideali+)s+mk9jq m wky lpy**zed massless spring? Explain.

How could you double the maximum speed of1asjbd+xttno48g gz5,p th7snhgyb 7;9-m y6 a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook6w6 61c/onsgwh gum+coolu7 7 of a vertical spring scale, and then is released. Describe sc oo7uwnmo716gcg / h6+u 6lwthe scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time whenoxsk t5ba tx-l33+td 8 tak3b8d-5+at xs3oltx kten to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. ;i qp3hkji9: n11–48). How could you estimate the height of 3qk i:phjn;i9 the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shsq(a+5d6uy*+yf*u-qvtl t vk3 t fw9cake the pan at a certain frequenyq3 wd- 6ttv*l+cu+k5tu vffs(q y*9acy?

Give several everyday examp+y uv:yvg-a w2les of resonance.

Is a rattle in a car ever a resonance phenomeia+mymzo 6d3tqggh3et 1.r 9:non? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sb5taetj;at oy;0k, k(ource? W5k aekb ,ttj;;(at0yohy or why not?

Explain the difference between the speed of a transverse wave traveling downl;tkn; zk:xv, a cord and the speed of a tiny pizx :tl;;nv, kkece of the cord.

Why do the strings used for the lowest-frequency 7di2umhg)j4.a, 0c5( yt+ayjrlb bwiv;: hjnnotes on a piano normally have wire ;5vd.2mwj htua0ic jh4j(ya +7 g:,b lr inby)wrapped around them?

What kind of waves do you think will travexrnqj p 3s1:i(fz8qd 5l down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizonfszd ( 1 qrnj8p35:iqxtally parallel to its length?

Since the density of air decreases with an incre8((o3 u gyxmfzase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect8x3g ufzm(y (o the speed of sound waves in air to vary with temperature?

Give two reasons why circular wat 9h ove,qv6o6ber waves decrease in amplitude as they travel away from the sourc6eh bqvv9,o 6oe.

Two linear waves have thktx (x ew:a2a1e same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which tra(atk12ex:w xansmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in Fow-(:: pnoqmel;sp b 0g5 a3-sw*sybe ig. 11–33, the frequency does not change (although the wavelength and velocity dpsp0b g a5;:bs3q *-elo(-ow yw:emns o change). Explain why.

If a string is vibrating in kid hs98l 6m3e ce+h 27ibsbmfz;)gt5three segments, are there any places you could touch it with a knife blade without disturbing thb+sel2mfg hetbi k zh;ms8i 5) 379cd6e motion?

When a standing wave exists on a string, the vi; qoxp k:fe3hxy.y ev/7 p(5xgbrations of incident and reflected waves cance37e;xk:/vqo5xyghe f( xp.p yl at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one pla 4/:5fs yb80tbkp rezwce to another, how might we determine whether the energy was being carrie0fswe4z5yk:bb 8r/tp d by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m*ua dc,3ky2 ac, what is the total distance it tu cc3,*ka2day ravels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but mx0o3 cl.a zx:is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of 3x.zx:0 lm acothis elastic cord?    N/m

  The springs of a 1500-kg car cwel(bb5vl i5/ ompress 5.0 mm when its 68-kg driver gets into the driver’s seat. If b 5vibll(e5w/the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale s md);2jjl(;ha w rkp5nv;e8ohtretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stifa( v2r8 ; jkw;hpl5e;m)nodhj fness 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 a freqg9. z7, ea7nabso zzc1qd5wmop3/ bz9uency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg 1za,be77wdgqzz/5c onb s9z9.3 mpaohangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 0hk.ji/y)wrw 11–2 at times t = kw)w0ir j.hy/ 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 0nez)dfg g:m,n 2:ey.q .25 g is caught in a spider’s web. The web vibrates predominately with a frequenc 2ede. ,m:gngy:)znq fy 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 c:ppfrnop4t5+ t8k o6with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the v5p:+ptcp f46tk8no roalue of m?    kg

  A 0.60-kg mass at the end ofl ) r-3*tntczg a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determinenc )rl*zt-t3g
(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.;gkk( r +ds+9hqhey w maximum valu+ hq.wgkh s(9e; y+kdre?$\approx$    A

A mass attached to the end of a spring is stret(/7 lw mzhtarlrmpz-kn20; h9 ched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is , nech,zp5s r9stretched an additional 0.130 m and released, howc,sz,9n5reh p 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 stiffnegsah z7lc 7 u*b0(xe(lss constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is movinzh l77* sub(agle(c0x g with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy 0 p8,ir izmax*i88 z; bqtkf:upopgun 0.200 m to “load” a 0.180-kg ball. With what speed will the balui,8;8r*zta p 8q0xiz :fmkbil leave the gun?    m/s

  A mass sitting on a horizontal, frictionless s 5ytwb) mv,ti:urface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest wi yb5:wtm,) vtith 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 th;yvivh5)bx i fo.p ye.a e3zx;j4;a 2pe equation x = 0.45cos6.4t where x is in meters and t is in 5;zov. epvj;.4x3axb)fhya;yp 2e ii seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and half kvzq m/c*n24 lPE?/ lcm *qn42zkv ±    A

  If one vibration has 7.0 times the energy of a second, but their freque939cuos4 c2hf qw1ol fncies and masses are the same, what is the ratio of their amplitudec93hlwsf u4c12o9 qofs?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sldwg+ei8 7 6w*s/uowa 28 bebopring once every 0.6dgsie6w2a w*w7/+ bu8leoo8 b5 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two ikp),exv dj wy kd;2 qz-e;f +/8kcb-rddentical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency o-; dqb cee28j;dzkprx)v kkw, -y /d+ff vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t r;a 2dlqlx0399gp12vmdxb ck where x is in meters and t is i21xq xg;l9329ra kp dm0bcdvln 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, labe3+pm1 *3 2mnwruuewesled 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 a horizocj*+u 9p.djpmntal spring (k = 124 N/m) is struck by a hammer, which gives the m j+cp9 pu.d*jmass 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 N/m vibrates wi7yq ab(o trjq. -raf-/th an amplitude of 28.0 cm when 0.260 kg hangs from it. t .o-fjrarq7 yqa /-(bThe 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 dmd8v(a uq,d0z6gp:n r): vz ato two 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 att6gqjz9p25mons/wc2 e ached to a fixed horizontal spring whose spri 69czq/ 2w5nosjg2pemng stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reachfu,)n 4acm9 nxing 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 t) c4aux,fm9 nnhe 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. Whshqk0rzqtb +es0 rd2gx +44o) at is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per sec *i x crz/8e:abcol)bsr*a(h,ond? (That is, one complete vibration takes exactly 2.0 s.) :, h/bb(i*a z rx)c c8sroale*   m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, whereag5+xp du2 1ag the acceleration of gravity isg ag+ ad52pux1 about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cxzkc y: o,3 .dyx-bw0cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m2 02uv4looxvvm8efpkn 7ha/ 0c7 /d ro, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12.0dr4 22/n 00hvax/vp om77c kvof8uoel $^{\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 ofw d(,kazo5 0oi 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulumw0o5 az,odki( ? shortened by    mm.

Derive a formula for the maximum spgy*,a+xlhc y8 w3 hc 5+eh hvmufd(q59bv7 v,deed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at2o we)jb3j4md a frequency of 2.5 Hz. At it is released from rest starting at an ang4) 2wedbm 3ojjle 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 crestsfvg *m2tl p2t1 pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travel*1v tmf2lt pg2ing?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 3438tc8 a0 a*pxmu m/s How far apart are the wave up a0*matc 88xcrests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 160u:9x ey9bvh1 a0 kHz (kilohertz) and travel withue9vy:xa 1bh9 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 longitudina nyzxzczzao3)4 f(*d 1l 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 tya) u 0k nhbw ky,ng1xb-q4+br)* rco wg6d);as dense as the other,rxqtbc41 ;ky6dbr )a0wg )nbhk+*y nu)w-og . In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m 8zh3put(zthykq s/h3cw b8,5apart. If the tension in t5 t3,b(ycwhhz u8/tz3hq 8ksphe 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 the top of a hill by a steel cable of length 62v4k)zx0 a/nu 3o(6hs4lsi af t0 m and diameter 1.5 cm. As the gondola comes to thekno z /us(4a v0i )fx3t6ha4sl 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 surfad.;puq k :cc+hexb4/ zce of the sea. He hears the echo of the wave reflected from the oceau;.dp:ce/cbx 4 hzk+qn floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and thibl0xre*;;gl nj q-au)u*ajt. v (wl2ds difference helps in locating the earthquake “epicenter” (wh;w(xu0jlg)a2ja t l* .lv;b - qrue*ndere 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 9qlo pz8/8 pfvapproximated 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? [H8vpop lqz 8f/9int: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earthqua.-.*kw mu :lrgtvad-7a+eqqdke P wave -agv-d.dku:w 7rl e*aq t.qm+passing through the Earth and 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 measured to b )tre svy.h*tm) 0gn2ie .r gvnme)) tyi0t *h2s$ 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 t3g6 n73ixiffym i7j tq. 6x(iihe same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the ampliiifx qi63(mx .6f 3jingt 7y7itudes of the two waves?   

  Two waves traveling along a stretched string have the same frequenck.y n*e5u j8fiy1hm(fum+ j9xy, but one transports three ej.uyk h8ffnxmy+1* 9jiu( m 5times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total f1k2k aj 1(/b;9t9qjb.a nxugfm 8bedvertical distance of 6.0 cm, from the89bk ;bbtxaf2 j1ak9(demf / n.qguj1 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 k60j8b 4bpivli:0un x toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What ha v 8j0bp4:lii0knubx6s happened to the energy at this moment?

  If a violin string vibrateu9- a6jwt2y + lnlrdr(s at 440 Hz as its fundamental frequency, what are the frequencies of the first four harmd lw6r-nt9 +2(ylrujaonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At wha+4iz-1uf (n+sc5ex hmd wr q;jt 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 vibrate+ ;qjuriw+cd (sf-ze451h nxms as a standing wave.)    Hz

  A particular string resonates in fourc;ry dv mx7-u*,* a x9wkgd f)t+ap7zp loops at a frequency of 280 Hz. Name at least three other frequencies at which it waw,uypr p9d7t k7xg)d;a*f+z-x* mvcill resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves onq5 drvw.ch 4g3( ststg(9m9uno5bat; a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent9 r5 gcmtnbg(t9(vtq;w dso4u.3sha5 nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, 6y x,vvq x0f0bwhat is the frequency of the fundamental? q fx y00vxb6,v   Hz

  A guitar string is 90 cm long and has a mbg,dw5ibf* zq 4r 4k5zass of 3.6 g. The distance from the bridge to the support post is L =,zbq5drk *g4 z5i 4wfb 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 string is supposed ;fufk*hq sl.5 to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. . 5*qfkf;uslhBy 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 string is supposed to vibraj18 p:iov;ewzte at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shouldwj zo81 i:e;vp the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mecv5 *724daaulza d*qjvhanical 60-Hz vibrator. The string’s maavd va2 *4d5 l*ju7qzass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pulley. 34rb7 baha7 fsm r:u-aIf the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may bemsb4h 3ru7b r7:aa-fa achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth inagkg5l9)) exz1 , kwzu a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm akz95zl,e kxg1 wa))u gt 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 boundaryctt:a* xxl*q/q 0/w wl within the Earth between two kinds of material. If it approaches the boundarqq* xc:w/*lwxat/0 tly 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 underwate g7e 9l1f4kcumr “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the c4 kl ug9mf1e7incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense z 7ievp/in) g0air. If the sound wave hits the cold air interface at an angle of 25eizp n/)0v7gi $^{\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 earthqu3/bjl7( )+ uteegh pc anklg mk6l,o(7ake wave strikes a boundary between two types of rock at a 38 3 p ,+)hunkg(g76bkje olm(ec/7altl $^{\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)dzlj4u0*c e j mqu xsi0 62rg5/f6jmp to the user’s manual, the dish has to b rc/jp*25mu)d0qi6z 604uslxg jfjmee 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 wavelenfbkce)2n.p a 2gth 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much e ).pbnkca2 f2time 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 stiffnez: 2hst-rpzy/ f z2np(ss constant of 550 kN/m Find the maxi:-zzy rp2 (nhz ps2ft/mum 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 of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m/u: p6i.-kr v4pgbf(hyj -t5 es9vnvn below, which stretches the net 1.1 m. Assume that j kshuvyv6b./9 vtrn:-ie 4 (g-fpn 5pthe net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The g ojco 6,z1*hrmass then falls 33 cm before it stops and begins to rise. What is the frequency of the osc1jo6zr cg*oh,illation?    Hz

  A 950-kg car strikes a huge spri.dd r2sz1: jtpvftq65 ng at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spri.tp 6tz2rq:v fd 1s5djng stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the rx.1/a7f iy s;+eov huaight pace of about 1 step per secosi+a f/hev a.x1; ouy7nd, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograw n1i/ascu*.wm:ry8 b ph record have a wavelength of 1.70 mm. What will imbwu s/*1wy:cna r.8be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibra5x4lov ph1)6k ati5ri hmvz37 dm1 yz5tes according to the equation x=0.650cos7.40t where x is in meterdot763z i5 z1 5hvkvrmm)a 1p45 ihlyxs 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 frequencl r-x+x* u1fk/3fid jfy if it accelerates at 0.50g1i3xu* /ffx dk l+-jrf (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, l2v*z86pv tu git sinks 4.0 cm deeper into the water. When ht*vvpu8 z62l ge steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and ,gu.r nd;z vf(qini *o(0mgsl+gfu3 6440 Hz (A)6g if3ru v+*g( m(si dlunqz0fn,o;g ..
(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 a(oq66xwrai0t canzr02 y-y5 -part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency iti 0c6 (-2rrnyzoxa0a5wyq a6s 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 rhw xl;4dv w:(5br5p eygr+3ofrequency of 264 Hz, and the tip of each prong moves 1.8 mm to eithep rb gv(5hrxy+w3ew;: 54 dlorr side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cycu.9zc8l hrnyr;-dibq/eo- 7r les per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the boardbyld-oh8 rez 7qcu . ;r9/-irn during the oscillation?

A string can have a “free” end if that end is attached w muxoz9n.w-mp9 eb, 1to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vim.1 ep,bz9onux w9w-mbrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing taf6 qv(b 8g2j y9ai(hzk5k;pd nkes nb8 izvk9hp(kj2ya q(5;6dgf1.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in tyume5: z2dlq9fz4r1 bl h6nx .he vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [H:9n6. z1h 4mrfyxdlubl 5q ez2int: 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 pulspm*20j8kg pn c gy);mrqr2;tje is generated at one end, and 20.0 ms later a second pulse is gen;mrrmgkpn yp g;0 jc*j2q28)terated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a **:-n8 + vmwfikoepyoceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is th:- om+ pkwof8* yenvi*e 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 at the junky2: 6w/ly:oothg r 5yrqard. The steel crane cable is 22 m low/y6rrtq y:l2o:g h 5ong and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a pmi);4c qygf b,late 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 ana),q;bgyc4fm i logy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz