Give some examples of p mm;k3+/xhxk everyday vibrating objects. Which exhibit SHM, at least apprh; +mp/3 xkkmxoximately?

Is the acceleration of a simple h9v9s3r wqb*p qarmonic oscillator ever zero? If so, where?

Explain why the motion of a pisssez x+) bd+h*oul8, ,bf+sv fton in an automobile engine is approximately simple ofe)zbluss b* + s+,+8vdh,xfharmonic.

Real springs have mass. Will the true period and frequency be lavc dj owf/,(c5rger or smaller than given by the equations for a mass oscillating on the end of an c5o(cw,fj/d v idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO(fmcu*:,wyzskf;;5 a :1p6ma p a hvhe)?

A 5.0-kg trout is attached to gw(i ;0jm vt,athe hook of a vertical spring scale, and then is released. Describe the scale reading jw;,i0a v(tgm as a function of time.

If a pendulum clock is accurate at sea level, will it gain or cxb2c14ws ls 9x9ts vby p sy,4.0iwk 6dil.x)lose time when taken to high altitude? Why?itpdy xc4s l 2b6iy, .lksc1b4xw9)wsx9s0 v.

A tire swing hanging fr:8ilfu*c :9w /obssll om a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using onlfw*l:is9 :ucol8sl / by a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake tp v:boe9,r ismes )5g9he pan at a certain f,s)e5risp:bvgm o 9e 9requency?

Give several everyday examples o g: ;mkdtlzm50 9i,lamf resonance.

Is a rattle in a car ever a resonance phenomenon? Explx.2v w- rt-sin 1ty os52ab7amain.

Is the frequency of a simple periodic wave equal to the frequency of its so bo5m +e9sp slejk2w;*urce? Why o2+esb 9 ;p kwl*s5jomer why not?

Explain the difference between the speed of a transverse wave traveling down a ce,g+q1 ne (1m jt7pxyaord and the speed of a tiny piece of ta(x+ej11e7q tp mny ,ghe cord.

Why do the strings use +8cg7uxrj ri0d for the lowest-frequency notes on a piano normally have wire wrapped aroiu 8cjg0r7+r xund them?

What kind of waves do you think will travel down a horizontal metal rod if yo2j r fuij-/eq0+g41s+9s lnn rzkle5ru strike its end (a) vesj- n4r j0+5z qrnrg il/u+e1f2lse9krtically from above and (b) horizontally parallel to its length?

Since the density of air decreases a*n e5,+p nltywith an increase in temperature, but the bulk modulus B is near,p +t5ey*n anlly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel m8mrt 5 jlc:1eaway from5l1:recj 8mmt the source.

Two linear waves have the same amplitude and speed, and otherwise are iden u ey7w (t2gh1*k9iii gf::kkktical, except one g*f2ku w1: 7kghe(tk:ikiyi9has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crokqo(d g1rm3p( sses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and vegp(k q mr1o(3dlocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could to(s evv8dec s)*vv rd,3uch it with a knife blade without disturbing the motir8(d*vves ,v)c3vd eson?

When a standing wave exists on a string, the vibrations l (/,qp ukgd,q7zh qf0of incident and reflected waves cancel at the nodes. Does this mean that energz,,qdhq0f(uk/lpq g7y was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how migh9qw7sgo,xmhkjz4 1u i.uiw4 5 t we determine whether the energy was bein5iq1 kw,x9i zuhu w4mgj47.os g carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitudf0: 77g ass+fni2ee;osgm. cue 0.18 m, what is the total distance it traas n.igs+:0cfe f uo77mg; 2sevels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs a54m;m ar(yihfrom it but is 85 cm long when ay;(ri 45mamah weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver get.i66rxnm9z c 53 onmzx h6ema7s into the driver’s seat. If the car goes over a bump, what will bxrm9z.aom6ih6mn xnz5e 6 73 ce the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish jmhxn:zo,* +mk,*;zbake g /ihangs from it. (a) What is the spr o b,*kmhixz/nj,a*gze+ :k m;ing stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a fre 4nyx04d*hmvi quency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 x4 v4d0h*nmiy kg hangs from it?    Hz

Construct a Table indicating the position i7l;ka etr/n-5ssei* x of the mass in Fig. 11–2 at times t = 0,t = ; eiilret-n a/5*k s7s$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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,m mtmo5g4h 3n is caught in a spider’s web. The web vibrates predominately with a fremnmo4 53, ghtmquency 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 vibrv h/d0 h.oo2eyates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.e hoodh0./vy2 60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per secob aige .j*d6g na2j29jnd with an amplitude of 92 *nabaej6gjj. g2di0.13 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 2 m8/ 7 cj*zqyjte1 +ued)bdmyfrom equilibrium is the speed of a SHO half the maximum value?)1dcu7 yz ejm+tybjme*q/ d28$\approx$    A

A mass attached to the end of a spr-y x etec0(te;ing 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 sprg+yu)mh.a cv o+n8ha1ing is stretched an additional 0.130 m and released, how lo agha+8c n+o. um)1yvhng does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attachewnoz 9l6xir71df icnl7k82,z d to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilib18 c , zd677n9nir klwil2xfozrium 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 comprq1 sm1dr d-dzx7x5 wvrr564k ress the spring of a toy popgun 0.200 m to “load 1dwsvrmrd -6zr qdr5k57x4x1 ” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is atbh4z v-q s0*pttached 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 with the spring com *vsp0b4t-qhzpressed, 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 t rrex7+.m i0rlo the equation x = 0.45cos6.4t where x is in meters.rirxl0me r7+ 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 from equilibrium is the energy of a SHO i1o2 5l4n4j1u0sgucigj dwrkf4m+ b/ half KE and half PE? ± jdwmfj4nu5ogu +4r0k4g /b2ic1il 1s    A

  If one vibration has 7.0 times the energy of a second, but their frequenb:vzw2p )y jof7of6d. cies and masses are the same, what is the ratio of o:wvp)j 7.o2d6 yfzfbtheir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once 5 : luyf:pcxz8every 0.65 s. yuc: x:pz8fl 5
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, eac a --dlvkwx-b4h with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrationx k- v-d4lbw-a?

  A 300-g mass vibrates accordibj* j dyu *tkqd9v7 /2uvd/cp0ng to the equation x = 0.38sin6.5t where x is in meters and t t*/p* 2y7jk/ v b j0uvudq9ddcis 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, n208xlqo( wtsev1gy7x7m,w blabeled 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 horizontal spring (k = 12w at 4pwm9amfu9(m8p54 N/m) is struck by a hammer, which gives the mass an initial speed of 2mwmp4 u (99taapmf58 w.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 stiffnes*(8b 5ib*kuzefufqh1b;m jc4 s constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point kcu*z5j(*q u4 mbbf;f 81hbie(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 stiffness c 4owkzir gvn0: x-md:s7vfznl:t 8,( p*.dvydonstants $k_1$ 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 fnre,pn*a * 8 g3jtacj;ixed horizontal spring whose spring stiffness constant j,nta8 e*a cr*;pgjn3 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.kjl o9+s8n4kt After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He fin9 l4o8ntj+ kksally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactlyr.2sso4ark9d.y q-3h 9piby y 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it 84od*lvwcr i(is to make exactly one swing per second? (That is, one complete vibra(odl vic w48*rtion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where f/,vu+89l6rsuwe dqz0i.twm the acceleration of gravity is about 0.376m, rs fl tivzwd809.qu/we+u that on Earth?    s

  What is the period of a simple pendulum 80 cm long 1i c7lgt3ul p,
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 up lz(jgj4b 6mx3z(3gm, the pendulum bob has a mass of 365 grams, and it is released pg3ju( b46xmzlj z3(g 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 avyowd8e7 q.u -ht7lh/ ,j a0gy;qh7ql length of 0.9930 m. If the clock loses half a minute per day, how shoulq7.q; /7qlhgl8t ed hy,a0j7 ouwyh-vd you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxiwezb5v0 ;xf33stzksebrpc 85t m/4js h2 v3w7mum 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 oscill/y:wtq+v7j (3 e ar;ixb)hdmmates at a frequency of 2.5 Hz. At it is released from rest starting at an angle of 1rwtbjy /mex+a; i)3m7: dq(vh5 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow dm0ck0enl4c o dxq1qk 69/,ud of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wuo0c6k, d0 dm1/qx9 e4dnkclq aves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with .g-x-1 o kasndcfa-/la speed of 343 m/s How far apart are thelcgf a--d/axn-k1s .o wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohert r:r /0/e6jr9mxvm( /aamnwrvz) andxmn r/ arwam m/ e9:(r0jvr6/v travel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal wafifu 6do ecoo 2g5 6;gvy:q288krwbw1fwx3d ;ves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but ov6b 62 ublwqhvlgo-9( ne is twice as dense as the other. In which rod will the speed of longitudinal wab6uwb hvl2g-v(6qlo 9 ves be greater, and by what factor?   

  A cord of mass 0.65 fz23 pvn0ab 9zbz 5-xf 2tp:mskg is stretched between two supports 28 m apart. If the tension in the cord is 150 N,sf-zz bva0: z35f2nmppx t b29 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+7 eowdc-c31mbxroo 0 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. om7+ 0r1 d-wcbo3ex oc
(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 be,dozvf 2 hp6x:3mo jo.low the surface of the sea. He hears the echo of the wave reflected from the ocean floor directlo.3 v :pdmo2x 6zhjfo,y 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 this:vmk/gahadnhp:jhm q588 -q; difference helps in locating the earthquake “epicenter” (where the daqmp8mk; 5:8/vj hhqhand- : gisturbance 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 surf6n ikyatw:q4j+ mf:vce +8a q1ace wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hvyak8:t6 aj n+fiq mw41 :+eqcint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplit/hf hxvrspd,:mey;cjs 3/ 40tudes, of an earthquake P wave passing through the Earth and detected at fth s;r/3,4xspdm: j h/ecvy0two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measur/sl:pujtz pf:jvb),i * dq( cz9thp;w16eoz:ed to be fp;o:j 6hdp:tt s9/vz 1 b(euzcq)ilzp:j*,w$ 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 thro5+f9 b5hw +6hmw)wlvb (vvg asugh the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of th5+h+ v6hwvgfw(sbaw9 ) vlb5 me two waves?   

  Two waves traveling along a stretched string hav61/t1c a 5mlj,y fsahfnw ,.pae the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two waves?1wfah,s . pm actjfna, /6y5l1   

  A bug on the surface of a pond/xnsr 4,n14uta )xqgn is observed to move up and 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 cxsu 1r n4xg/nq t4n,)am, by what factor does the bug’s maximum KE change?   

The two pulses shownp7cf i5.fo53fc ,yuc n in Fig. 11–52 are moving toward each other. (a) Sketch the shape oc37f5cc,.nypf fu io 5f 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 has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequenc5ebvle 9; a+rxy, what are the frequencies b5xa; relv9+e 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. A lgu9o-nor)i 8 1oi(zbt what 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 zoou9ro( nb)18-ilig a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name ap9c64( ucvsi prq9-hz9 cudn 2ceh6q)t least6 6zqh s2hc-vuu4ncprq99)i ( e9cpcd three other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing wave nbf;0o(7k vck+tnuux:-3 g zps is 475 Hz, how far apart are two(pk:+3ux70n vkug-f;c oztn b adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whatyfnmg)v((6p- xl2khq is tlqpx-n) gf(6y(km h v2he frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. io1b: fjxzc1d+/eh 3m0 xfq4aThe distance from the bridge to the support post is L = 62cm and the string is under a tension fmz1x4qhjo:eia1fx db3 +c/0of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar st.*gpyp*laa1q *l5as8ktgpf3ring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the sp*l5ql*kpf *y1ataa.p 38 ggthree frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measure gmjwg2t76bu( 45 0bxeqgz hh,d to vibrate at 205 Hz. By what percent should the tension6hb gughb(mgj 5t2,x0ze7q4 w in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechaniuep51)9jhacre +k yi.cal 60-Hz vibrator. The string’s mass per unit lengthj9ce5 +hk iu.y1)repa 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 lengtj xbvc1vn- l ,gd.4 n8vgeiq.8h of the string may be adjusted by moving the pulley. Ifjnlv.,.gg4x divc 1b- ve8 nq8 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 m?   

  When you slosh the water back and forth in a tub at just the right frequen2wu jtq3 mku68my7op4 cy, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub imy4 q3p7m8jtu2w uk6os 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 boundar;japaj)o: ro4e+e; c r9p x5fpy within the Earth between two kinds of material. If it approaches the boundarj 9roocpa5a;e;4)pje x:rf +py 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 9g p82.u(6iszaxo :gg;aipg c“shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If tsioa ppg : 6iacg(gzu 2;gx.89he 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 warm4(z woz38e 6l cp5gfqt air when it hits a layer of cold, dense air. If the sound wflz p58 zg4eqtc6w3o (ave 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 stgl6n;ib/o)i6h f 7yzirikes a boundary between two types of rock at aiy lbioz/ hn6igf;67) 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m d5airroa-4q mji0 :d /in diameter. According to the user’s manual, the dish has to be pointij:i am4a 5dq/-or rd0ed 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 the Pacifi 02 7uo28ee mjj2wp5iteopxf /f5hl;ic 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 tl 2 ;u0ft2xfi5o7jjeop/ eew5 8p i2mho 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+eof e.4p; o5 a9dbexynn1 e;k,vc hefv87a,d stiffness constant of 550 kN/m Find the maximum compression of the bumper if theb a+ex9f7,v de, ehon. ;e5ecp o1 n4dka;fyv8 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 winwk iq yo ,4-;iqjjo77ldow to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simplej ,y7j oq-kqiiw 7;o4l 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 spr c+koaqo(a2wub7 j2i6ing. The mass then falls 33 cm before it stops and begincqk aj 6i 7waou(b2+o2s to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed oc3aez(r zq1s6r kg ,1hf 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the sg3(zsr k116zqc re,ah pring 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 ( 4 td*qim, lu24q(dhshwbxb5/ 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 speed of waves in the coffeeh/ sqbtu,4whmdxq d*52i4 (b l.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograph rc) xswief+zs .7id 55record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted? isdwe5z)i.5csxf +7r    Hz

  A 2.00-kg mass vibrates accordin3jl1,qac 0 yzmz3g y0ig to the equation x=0.650cos7.40t where x is in meters and t in seconds. Determinag1 i3 cmzjz00qyly, 3e
(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 ity+c* sx /,qdw-hvq5sb accelerates at 0.50 wq ,b/qd+s *5hvcxy-sg (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When y+i dw*jry6e 5o2.km .msky:k a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whi52jioye+kym mrwk d.y k:*s.6le.
(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 364l*:9aloqb ;nsl o zu92 Hz (G) and 440 Hz (A 4 b9qnl:l6o o;l*zsua).
(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 traveling1j rtpu* ;i 29gqrvi;c down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) i tq2u 9i rgv1pr;*;cjIs the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequencuqw(jbt7kl/dl c / 6l)y of 264 Hz, and the tip of each prong moves 1.8 mm to either side of centerju)( tdl/ b7lq/c6wlk. 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 e0g,cg)iwm81( qy )guky drh2harmonic motion of frequency 1.5 cycles per second. What is the maximum amplithg)gdg, muir y82k 0)cywe1( qude 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 6 hjc kcv81u4vend is attached to a ring that can slide without fv v1hj4cu6ck8riction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing tak,5 5b fhotlz-xes 1.000-obftl , xzh55 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 vertical direction ory q h*9hi7a6rw can swing as a pendulum of small amplitude, but not both97y a6irw hq*h 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 fwxur,;x kd94ovg+,h a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a su94x w, fvd,o +;grkxhecond pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspend2rlj5 gnfruyrr : x67m97t5 ined from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum jr:r 2rny55gt7 7xf96lr unimamplitude 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 :jj3c:q yae -ee3y nece(8p3ejunkyard. The steel crane cable is 22 m long 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 boun(aeye je -eye:p3 cq38:3jc necing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in d* e-.)/uihsqy),yahnp)4 u z*rlapb Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–4)ay)-ls )/. dzpybp,qenhuhiuar**5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz