Give some examples of everyday n r1:;jb/ijm * dt(1m /pn4cber)u nqfvibrating objects. Which exhibit SHM, at least appr(; fjjpu i n 1rqenc */)mtn:b1d/mb4roximately?

Is the acceleration of a simple harmonic oscillator eve3;9(o /hlifdfmxt(gc r zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately sime,5 otu:brqi. p,qri:et bo.5 ule harmonic.

Real springs have mass. Will the true period and fre8onmgv/213 z0 5kbt/+v defp d:ruihzquency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless s8ht z3dvor vi /bu:m2/ndk p5e1gzf+0pring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO)?pg8psz v9gbv5r5h ;oj * t2qy)

A 5.0-kg trout is attached tp.2wtwtjpd73 iir 6,yu6yu t*;jisz8 o the hook of a vertical spring scale, and then is released. Describe t36p p*tw sjz ytjuu,id6t;2i yi8wr. 7he scale reading as a function of time.

If a pendulum clock is ac2beqv:,h) gl x-5r nc8lratn5curate at sea level, will it gain or lose time when taken to high altitude? c8avnr,2 l5) enx5 lhrgt:qb-Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–hwxy,,/cx g w:0 v0kox17:aebtqo wd448). How could you estimate4goa,o/hw tk 10 c y:be,w :xxwq0x7dv the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you oage4lm8 e(k 5shake the pan at a cek84e m5a gol(ertain frequency?

Give several everyday examp0c(cdy c mco gz6a062nles of resonance.

Is a rattle in a car ever a resonance phenomenon? Explai q9 *n +h2y6b wm6lt 4prv.oi+b+daztyn.

Is the frequency of a simple periodic wave equal to hs-ihg-p lyv e:d1 0o9the frequency of its source? Why or why i:v0hl1o ypde-hs- g9 not?

Explain the difference between the speed ofivccccp1z:;apl *a;v)f f)n 8- /yck f a transverse wave traveling down a cord and the viyz/clccck; :; 1*a- )v8ppfnf c fa)speed of a tiny piece of the cord.

Why do the strings used f.xq/*whg ub- (1r pxsswgc8*5l3wzksor the lowest-frequency notes on a piano normally have wire wrapped around thekh*35ws(-s r* 8 c/ .bzxgxl1uqwwgpsm?

What kind of waves do9q,y u jq :/znbbl*z3g you think will travel down a horizontal metal rod if you strike its end * u z3qbb, zglq/y9n:j(a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, ocipvrf :gz2 m.( 6ak/but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air tm .v p:i(/6aroz 2gfcko vary with temperature?

Give two reasons why circular water waves decreasyr xp5drka/y s8s,/8 darrl (7e in amplitude as they travel away from t rxyk5,rs( py 8/dr 7/aa8rldshe source.

Two linear waves have the same amplitude a ck7 eyj4qzl,c b783qand speed, and otherwise are identical, except one has half the wavelength ofcjqyz l7a8c47 k b3eq, the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of coj.dxd8l3+0v idx 3r rprd as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change8rvr+ x3p0lddi dx3.j). Explain why.

If a string is vibrating in three sei. /;buo3:l(sxjcfjz,l s s- zgments, are there any places you could touch it with a knife blz,ilu/ jx;o j3f:.b ss (zcs-lade without disturbing the motion?

When a standing wave exists on a string, the vibrationdh 7vw/ *hul sob,u6o8s of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Exp h/l soh,7dwuu6*v8 bolain.

If we knew that energy was being transmito u9h th89:txtavm *;vted from one place to another, how might we determine whether the energy was being carried by particles (material bodiesot*t8mvu:9 9ha ;xhv t) or by waves?

  If a particle undergoes SHM with ammi4-flkmapk9)s r1- i plitude 0.18 m, what is the total distance it tl 9f4pmai-isr-)kk 1 mravels in one period?    m

  An elastic cord is 65 cm long when ku2148widoz*: 0q nha)vnetsa weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this 4w ) v tinknoq*s dea8z:hu012elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drivem i31kp9 620nt cxtij hyje1;xr gets into the driver’s seat.y9 j ;mkn1xp0h2i 1tte63ixj c If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it+:) g7xb rm *e+lc jvw8su;ouu. (a) What is the spring stiffness const*ur+w+xo;) 8 :c uug7sj meblvant $\approx$    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 frequency of 3.0 Hz when aeg rf06uiwha 24del: )w ur7:ru*r*la mass of 0.60 kg is hung from it. What is its frequency if onlewdwgr4 f:rru :h7al*ri02u) aul *e6 y 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. pyb29+5uudrz f j l+o:11–2 at times t = 0,rl5 9:b +2pu+ oudfyjzt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vkcwef /g; +zk3g2um: a spider’s web. The web vibrates predominatg guce2f;kwz m/v:3+kely 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 frequency of 0.88 Hz. Whe(u ;pxq uap4)tad y12x:v tyb*n an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is thp vty xy:12 a *4uu)dxba(q;pte value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per s )2*o.vnbdyjw econd with an amplitujon* 2w .)yvbdde of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO halxez*p-e b1d d5 .yzh)pf the maximum valez-1*pyz5e)hp.b d xdue?$\approx$    A

A mass attached to the en-; v .lzj0pjko+tp xp7d of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring isfar4ww t*n0u1nr68 l d stretched an addil*8 1n 64tf dw0nurawrtional 0.130 m and released, 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 wivv4w.8vxw k8 x9th/u9cra 2kfs6r*wdth spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of.ca*wk86x 8urfw hv9 sw/vrk42xdt 9v 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 80b9 brtei186whk dtjy:h61 (f q.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg b16 j :kbey8hqrf it9b1w6 h(tdall. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is a*c:iz *dkr4plttached to one end of a kidr*z plc4*: spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the 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 accordihdpa 3bx/3 *obng to the equation x = 0.45cos6.4t where x is in mebdo bh3*a3p x/ters and t is in 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 frtun -f w k-lsya.c9p yv(el-9-om equilibrium is the energy of a SHO half KE and half PE? v leyt-- 99kp(y-.c -saluwfn ±    A

  If one vibration has 7.0 times the energy of a secog z*k6s)ieqxaw6 . :xtnd, but their frequencies and masgti.:zqawxe6skx)6 * ses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a ver1zdg)hqs+jg gg1 .x+d3lm7vyhn d2x7 tically hanging light spring once every 0 hjgq+s7g g2n3gx.d)l7y1dh +1vxzdm.65 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 tw/ 8m rmlgr jhk2)at y,bglad9*6)u)axo identical parallel vertical springs, each with spring stiffness constamlhkg9abxga )l dur*8 6)r a2t)m,/yj nt k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to5fkxtky2oh*m7 v zw49 the equation x = 0.38sin6.5t where x is in meters a 94hk vzwf mxk*oty725nd t is 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, labeled A and B. Foax7eera. e1 )pr 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 adr .8eyntnk 9-qvj3jvn*ty 9+pmm** a horizontal spring (k = 124 N/m) is struck8*9d*yt3 n v ynmtm* j+pr. -9najevqk by a hammer, which 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 305hz7)n my;9hq htw8 tq; N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocim n; wh;q7t8q)9hhzytty 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 sq+i4i dw93g dnprings, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horik*fcf5 j7g*,g k*lwn,3ioq mbzontal spring whose spr57,*q* 3wkfo,fjmgnci*gl bking 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 reachil,ue5g q0 h+wlng 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 awglueq ,+5h0 lnd 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 vibratiofc yqr6 js*,b(ns in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly o3x m mh45ztx - q.vvppj0s*d3zne swing per second? (That is, one complete vibration takes exa0* 3zdspm5vvt4j3zxpqm -h .xctly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its pehus-r0 t 2u.qbriod on Mars, where the acceleration of gravity is2qut.us h0-b r about 0.37 that on Earth?    s

  What is the period of a simple penr)/w zj; m43oez rs 7qlc8bt8ldulum 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 penduluj, h6ol dd/ u+w */ung-weyj)pm bob has a mass of 365 grams, and it is releasedwjuj e*lw pyn6u)g- /,do+/dh 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 clo bde s)9 b95wjhob28vvck loses half a minute per day, how should you adjust the length of the pendulum? shortehbwsvedj9v5)29b ob8ned by    mm.

Derive a formula for the maximum speer0xq7ki); yc wd $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillateoa2( n* cn4qrhs at a frequency of 2.5 Hz. At it is released from rest startinrca2(h q*on4ng at an angle 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 zz.fbbd n )/5cw m qq),o7pp2ccrests 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 travelic wb)q57 zz./mocq2 pnpfb)d, ng?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343lbe*dq kzl3m92-h*9l zf,5k kb r6jmj m/s How far apart are the wave crqjklzlj 9,9 z fm 2m*56*d-kbhle3rbkests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz a ;b520hamvm00qnnrkqwcr6 dkq f 183q nd 1600 kHz (kilohertz) and travel with a speed of qr1;q m0w35nq0kcm0vb af6qnh k d82r$ 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 longitudi8 ixw) 9awwns:j9r9ke4jsy1 l nal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same ev;zsg(/ eq*pkgk4x*p2 zz q; nlastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudvgnpxe*z;s2/ ;qkzq4k p( *gzinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg zc k)kipka4 h )hk(n.2is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one suppok ha)4kz(k2nkh). icp rt to the other?    s

  A ski gondola is connected to the top of a lm 8m4s*tds3 5e 5krp bi:q8gnhill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.s83i5 n*8epbt mk drql54msg:
(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 shva;j sn4hp4 y-2 .y,we3 qrji5sspax/ip 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 pointr 5/4qyh3p;yan iaxej,ws p4j .2 v-ss?    m

  P and S waves from an earthquake travel at different spee x3:,:g bjw5uysvkia oc(+w7x ds, and this difference helps in locating the earthquake “epicenter” (where the distur3g:iayu(bw v xk,5ojw +7:scxbance 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 approximate09 abdhel,. ocste29 od by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include 2tae0b9. soo chd el9,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, acmdro )l/: x0mnd (b) the amplitudes, of an earthquake P wave passing through the Earth and det xdm0/lmr )o:cected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wa(;ia 01 rh+qlwudyst:ve passing through the Earth is measured to be h+w0a(tyis1 d :l;qru$ 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 l fch. nr2r./hfrequency travel through the same portion of the Earth, but one is carrying twice the e lh.nhrr2.f/ cnergy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequed2,my 2 ,:qysz3pxzfw ncy, but one transports three times the power of the other. What is the ratio of the amplitudes of the two wam :2 qzdp3wyfys2z ,x,ves?   

  A bug on the surface of a pond is observed to move up a0*edl9 dqzpz tu4.or :nd down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm lz:pqr4 otz de*0.du9, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig.rj-j 89k0aun m 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directjjk- m80r9nauly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamentali;vb1n k:j 2cc frequency, what are the frequenc1inc jv;k2b :cies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 2(j:j vox0n/gt zg1z4w94 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down vwj xg z4n:j tzo(0/g1from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Namep s4vq6o,al:s7 gp5vb at least three other frequencies at whichq:s a4b6,p spov5vlg7 it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a stringzc1wd 9 jhqp61 is 92m/s If the frequency of standing waves is 475 Hz, hcpq9j 11hdz 6wow far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz angzf j iiv4 j(cj1n+-8gd 350 Hz, what is the frequency of the fundamental? (1n8jc i fi gv4+g-jjz   Hz

  A guitar string is 90 cm long and has a mass of 3.l2g9t mu56m ,lyn7rfib qz3 7s6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. Wm lz6qgu5 3 ymrb,s2t7in79l fhat are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is zsyhpj, c*+p.r4s;m rmeasured to vibrate at 205 Hz* zcr jm;ys4sph+, .rp. 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 string is supposed/bt: pmpo6 hp )lc7kf8 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 frequencpm /)f8 lcpko:h tp76by? decreased by    %

  One end of a horizontal string7,/0bzsuj ek 2 efy,uq is attached to a small-amplitude mechanical 60-Hz vibrato qe7/yf20bu, kejs,uzr. 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 the string may be adjusted by moving the pulley.//.uoa;s9+wq c b oiu3ynmbh- If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 mb;hsucmn-yq 3 i.//wbou+ 9o a?   

  When you slosh the watt0bszt/a : ki:er back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a stan/ iaz: 0kbst:tding 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 trajnjcw-+ o+l5x hy(t/aveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approac/xjyc5 wl h+(tn+-oajhes 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 “shelf” where enm 06y6nnxe) the velocity changes from 2.8 m/s to 2.1 m/s If6emn0 nny )e6x the incident 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 g iwawnq) mr8;dxf4*(air. If the sound wav8fmdrw;4ga)n wq *ix(e 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 boundary between two types of rock a5xm37nr dvz:in ;z7h rt a 387 vri d3h7mz;nz5rxn: $^{\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 manual, the6n w2uzijp*b b 2icl(gz.-um + dish has to be pointed in the direction of the satellite, but an error of abo.u-zg (2pi6 unczibb+ wj2l*mut 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelengbg+ay z;b /e/ze7jd2yth 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 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 2/eyz7a;zbge/y j+bdshore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a o ea3ov ;jju1 of1r/a+spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximaa1+j oevaf/ r1oo;j3 utely 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 , .qb-ape, uqem below, which stretches the net 1.1 m. Assume that the net behaves like , .-b qa,peqeua 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 w b v(,iz8wq;kdm2m(n end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscilv kwqnz2m 8d ;,ib((wmlation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 mq 0 vsl/9ek,sw/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is q lsekw,s v09/the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup ofa7/l*f buk/j7329pxb iln fr u coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and j 7fbr2lk/p9 u*lfbia/ 7unx3 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 f:):x 5u8o3/ei gpzhyy ep1roerom the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What wil rez31::p5)yipog yo 8ee/xuhl be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=px)pz(ap iwlz5h7s 830.650cos7.40t where x is in meter8(p5p 7lxwp 3)ahziszs and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if it acc)d 4 v p0b+lcrfc9sefr9frp;/ eler9 e+sfr/lrb)49prcfdpfv c ; 0ates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 2jc1ce+m f/fq75-kg man stands on the raft, it sinks 4.0ec c+f1m2q fj/ cm deeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrumenzf: ca ie iiv5w7 (n6ym+urn9(t are tuned to play at 392 Hz (G) and 440 Hz (A)(:f+6wyn9 vure7zi cmi na (i5.
(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 the0kge,ft +n-veh;. novi4cp +5l2ugqh stretched two-part cord of Fig. 11–33. Determine a form,4lv0g-o+5p k2e+eqhn.v nt if g;uc hula (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 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, and the tiip45wb6ismeph 62v/ kp of each prong moves 1.8 4im 5pibvp62w 6skeh /mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscilshqm vzz0ryf:9 5r k9:lates with simple harmonic motion of frequency 1.5 cycles per second. What is the q50h9 y9v::zsfrkrzmmaximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ribi +2+ ,mreazbng that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed +mr zb+2e aib,and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-wal8y dow5kevm ,;g5sp5y swing takes 1.0005kpw myvg;s 5,5dl8oe s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the verih o wdno*3 :h-v*g:mytical 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 horizont3vhn* m-i:y od*wg: hoal 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 z v,li31,g rvq-dkijk0vkb5 ,mass 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the oppositei v ,b-jq5g0 rdk3,1vi k,lvzk end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spriokdlk/ r68dmpfj 3 h6/ng with spring stiffness constant k. A penny of mass m is placed on tkfl6j/ k /h3d6o r8mpdop 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 1200-kg car at the jun7ku whq:w+t 2vkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at th +: khwvq2u7twe end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig.nix83w*4spiwa * ob h8 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 v8ah48 wi*pobs3 xwi*nibrating 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