Give some examples of eve n( sy79e9gcugryday vibrating objects. Which exhibit SHM, at least approximately?s9gg 79u ec(yn

Is the acceleration m q.sz)lbt: /grbe+ta 9fz+7oof a simple harmonic oscillator ever zero? If so, where?

Explain why the motidu * cns0o*-yatg7l a5on of a piston in an automobile engine is approximately simple harnu7*dclaa s- yog5t* 0monic.

Real springs have mass. lq7dvpmmgz gd2 0-0c3 Will the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Expla3pdm0gcm2- ldgqv70 z in.

How could you double the maximum speed of a sg k2)tt va5kmw -ac7c0y )yim8imple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and the jy: 10kp- ya:dgopj1en is released. Describe thdkjag0:- jy1p y1:pe oe scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it ga+8z7e.tlyq0e f pb7sh in or lose time when taken to high altitude? Why?l+ 0.zphf7ybst8e 7eq

A tire swing hanging from a branch reaches nearly um1/end3d3ao,z zop/ojusry02/lj ; to the ground (Fig. 11–48). Howoj3j/2/sudm;o, /lzoze 130pnu aryd could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the 9mc g4jdl /f;upan amc 9ugjdf;4/l t a certain frequency?

Give several everyday examplesn+6 6 a4bysfsx of resonance.

Is a rattle in a car ever a resonance phenomenon? En09nnq0/,drkr2ml6qjbx4e, fld sq1xplain.

Is the frequency of a simple periodic wave equal to the :ur *cuak,f 0cfrequency of its source?f* :0urcucka, Why or why not?

Explain the difference between the speed of a trvivv5ol ekx )/4sm4 l-ansverse wave traveling down a cord and the speed of a tiny piece ofv4 om l-kl4 ei)vx/vs5 the cord.

Why do the strings used for the lowed,z boj,gxh5+ st-frequency notes on a piano normally have wire wrapped arj ox, bd,g5+zhound them?

What kind of waves do you think will travel down a horizontal met7b )qj2n pp+clal rod if you strike its end (a) vertically fromb2q+ cp7nlp)j above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature,tx e s4zley( 6.(e.axw but the bulk modulus B is nearly independent of temperature, how would you expwlsa.x( e .(ex4eyzt6 ect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water wa7 5ghqfim u2mbfj (qtkjb; b ll2(3g+7ves decrease in amplitude as they travel away from the sogbbj7 bg3 5lmmqu 7l+j2tf2((khi;fqurce.

Two linear waves have the same amplitude and speed, and otherwise are identi;zmp:h dl p: p9v22gbical, except one has half the wavelength of the other. Which transmits morehdil2m 9 ::bv;pg pzp2 energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections v8fapzfh+8n: l:xby- of cord as in Fig. 11–33, the frequency does not change z8yx f 8hvpln:+ :ba-f(although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any pl/q;5/sq - 7sh*v dmqj gs,zj1ytr/ bpzaces you could touch it with a knife blade without disturbing the mg psbh7q5q z/d*1-,rv/sj; /yt ms zqjotion?

When a standing wave exists on a string, the vibrations of incident and reflecc 9vk w7hv.4vrted waves cancel at k.vr9c47v wvh the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitt :zp.tf hk8)7g 9q bff*p*b thxh38wqbed from one place to another, how might we determine whether the energy7zx*p bbg) 8qt9wpfq:8.k 3hhbffh *t was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amyow jn0;)o7py vi1i /1uval2aplitude 0.18 m, what is the total distance it travels in one periuyvj/ 27 )ao ypav01l i1nwo;iod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs 5juaahhcji/( 1qp9 (ifrom it but is 85 cm long when a weight of 180 N hangs from i/j 5j hqa achpu1(9i(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 2.l (mt9o+skvy1/a;qy py vpaits 68-kg driver gets into the driver’qy+2vapm/1s o tlp; v yy(9k.as seat. 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 eie/1x0.. shbz(idm wfrom it. (a) What is the spring s ii/1 sw(medeh.z.0xbtiffness 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 frequency of 3.0 Hz -bq, wxa imd504i1yyp when a mass of 0.60 kg is hung from it. 5y p b,0q1 imyi4daxw-What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table ind,mejkbhd f (wslk53eu7- qi8l p1q:s 3icating the position x of the mass in Fig. 11–2 at times t = 0,t = wuse 13l7k8s :hild -qp5(ejfm3k, bq$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spn,am w++x)9lvp dj9 evider’s web. The web vibrates predominately with a frequency of 4.0 m+vj+ ad9e nl)vx,9wpHz.
(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 (2xd ;oqspy l.Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. 2pl;syd x (.oqWhat is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 timui-0q r xu46ghes per second with an amplitui 6xrq- 0uhu4gde 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 3ou,2w hxar5iof a SHO half the maximum valu3 xhi,w5 rao2ue?$\approx$    A

A mass attached to the end of a spring is strnnl19*,y 1wqrflv5fq etched 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 str- j*qz9nygh(gg9uf 8e gef/6tetches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium p 9ggqn-(uth9ggfe 8 6*zje yf/osition again?    s

  An object with mass 3.0 kg is attached to a qom3zw (:w-f8+jt ysn spring with 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 8qwfy t:o-zws (m3+n jof 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 spri5*tedi4h2qscs dv:d6m hbvhy;d88 (yng of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball l*h h dsb4ctdved6s8my;(v 5q :d2h iy8eave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to on;e5vdhmks6bqke;qaj,- .f t, e end of a spring; the other enfke, 6t.saj 5medqh;bqv - ;,kd 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 according to the equation x = 0.45cos6.4t whereugnzv h.(q*bj5 w)d2 s x is in meters and t is in seconds. Determinq.j(g) z dnu5vw2h*bse
(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 Sjih bs8x4 ( 2)no48hm-uercc qHO half KE and half PE? 4uiho)-82j4m(nxq8sb hec r c±    A

  If one vibration has 7.0 times the energy of a second, but their fre, 6zpo2eh0k s* iw0s;4 no qjrwpbdog63oe j/,quencies and masses are the same, what isw,q0z ;k62 pjre sb43seh o*oi6wodjn/og,0p the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a verticalx(rnpmf . s5:ely hanging light spring once every 0.65 sx: frs.(emp 5n.
(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 is7w41oh-q0vr8f 7b)- / tlemnxmntbzjsz) b/a supported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49)7nxt - a/nebts4hzl)mr bo 1w0 f8j7mzqb/-v) . What will be the frequency of vibration?

  A 300-g mass vibrates accor8,diy j rt/p a:y7rzs3ding to the equation x = 0.38sin6.5t where x is in meters and t is in8i7ayyz/ rrd j:3sp,t 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, labqadwz g.luliul:4w1 7p 1s8 .geled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on t.-jxt4a3p 77y *ohkmonf 1)6 yfp jmxthe end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Dj7)76tfp kym3xoy aj*o-1np.xhf tm4etermine
(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 8vw,3epc x+r c305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through vw+cxcpe, r38the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness const2kyq( kxoi/; kants $k_1$ 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 strik 3qv3q fveo6r2es a 0.600-kg block attached to a fixed horizontal spring whose spring stifq rev 3o26q3vffness 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 reachiny4sv nn t8nd9i*ul+r+g his lowesiy4*9n+ 8 nnl+ dsrutvt point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched 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 vibratiksn,+ :qv .ibnons 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 one swqok lno3.9v 1 pfc)on ./i 3(efwgg*zwing per second? (That is, one complete vibration takes exactl9(fp1ngcv ozeqi. )g.n w*oko3 flw/3 y 2.0 s.)    m

  A pendulum has a period of 0.80 s e-pb (i. l6wm nomcp0 1b(qrg9on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Ea l1gmwr(p0m .pnc(b qi 9ob-6erth?    s

  What is the period of c)on,byg 5:n na simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of 365 i);h 7zta0ghi grams, and it is released at an angg0ih7zti;)a h le 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 pgg/xu(o/kzlrl .(v6 of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the (prx/(lluk /o. vzgg 6pendulum? shortened by    mm.

Derive a formula for the maq77l)bhod+1zaik iy x 8kth2,ximum 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 oscillatestgx q2t q+:9zc-6skmz at a frequency of 2.5 Hz. At it is released from rest starting at an angle of zs-t :qm+cx g6tqk9z2 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every c()cfp ht0 ) w;a sa(kchhuk;p2dn,s ,3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wass;p aa(uchhthc)( ,2kdf pn); ,c0 kwves traveling?    m/s

  A sound wave in air 4ly nt7; pcjz0has a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compre 0l ;p74ycjtnzssions)?    m

  (a) AM radio signals have frequencies .,xs5be -a j jek3gun+between 550 kHz and 1600 kHz (kilohertz) and travel with a speed of g,eu +je3n5 jsa- .bkx$ 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 lv*/0wn9zn )afhhlm6songitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elg.t fejt ax p0s/49k;hastic modulus, but one is twice as dense as the other. In which rod wi4es 9tftj0h;x/ kpa.gll the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretchedimk b1 (u5ac1z between two supports 28 m apart. If the tension ink1z15iam u bc( the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected +pn hc q35r ha:d+ )9ytw.zljnto the top of a hill 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 c+l n jw r5.)np9ta3h+hy:zqd 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 4:rwwtxt.v27/em(jc5 j gqt bsurface of the sea. He hears the echo of the wave reflected from the ocean floor directlebg j( t572/t4 wvwjcx:qrtm. y below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthqua1z r9q+fxy8u9g21bkp akpk , oke travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance tooy k+gf1uzka1 2 ,8kxb9rp poq9k 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 ap n n8rz s4qe0*qyv;cf :ovc4b:proximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, whyszq e4qn:: c8* n4o0vrcfb ;vich actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and -u)fboxpgjy-y2o m2f/*xx4l (b) the amplitudes, of an earthquake P wave passing through the Earth and d xu mj o)4fx-yy*gpob2x/fl2-etected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave p wl 99 :.te;ea8npf9rxc n/( .fmlzhaxassing through the Earth is measured to be n wcle8plez:hnm9f/ta. 99xa fx;. ( r$ 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 thr:ah-hjwir2ui ix;dqp gt*cf-u q4 ;1. ough the same portion of the Earth, bu-.j2i1rw: hi;;x* qq dc tpug-u4fhia t one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling a .dy8wqz+aa d7long a stretched string have the same frequency, but one transports 7w da+8q az.dythree times 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 dowc5xij;xkwf1*x ad:,d v28v lmn a total vertical distance of 6.0 cm, from the lowest to the highest point, a2*v1xliaf5cjdd x; ,v k:mx8ws 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. 11jk 5o3xdak5h;c e .us-–52 are moving 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 has happened to the energy . h xku;jk3de5as5o-c at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what ar 5n8gduzd/c1(qyy*v se the frequencies of the fiqz/5udvy 8yd1(*sgc nrst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz 02yx*ubln e rzu)u *o1when unfingered. At what frequency will it vibrate if it is fingered one-th*2euyulb ron) xuz *10ird of the way down from 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. Nam9u/mn9psy8 b ,6 gmlljfw +l7se at least three other frequencies n 8+6l9 ,7wps9bgs /ufm ymlljat 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 h:yk hgl-sf()h t/z8gof standing waves is 475 Hz, how h z-8h(: gt/lf)ksy ghfar apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, w syc66n5wdbt4wqy z; 8hat is theb64zw5ytws8c6yn q ;d frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from thn +q5me fvvex+dqv s/r: 18oqcmc4r18e bridge to the support post is L = 62cm and the string is under a tenose/f5+v:mccrqn m81 vr q+1q4xdv8e sion of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vib85i5 sju eu jv5clu: :rkzx2x9rate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to co:zx: s5je2r8i 955c uukuxj vlrrect the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibr/ alb/,bw p ,1 6j8+uxjqcny8y oc)yogate at 200 Hz, but it is measured to vibrate at 205 Hz. By w ayun /6+gb1qwcy , 8jxp)8cbooyj /l,hat percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-ampbxg )5.nflx f64zdka ;litude mechanical 60-Hz vibr.)d 5; xfblgfa4 kz6nxator. 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 lengthoo8hgmsswkvg ) 9 i/0* of the string may be adjusted by moving the pulley. If the hanging mass ov98 *mgisws0/hgko) 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 forthb3x- 2vinx wo) in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center.vno) i3-xx2wb 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 boundaryet jmoi f23d k 8jws,f8*y(bi; within the Earth between two kinds of material. If it approaches the boundary at an i*f ( t2;i 3jyf 8wobsd,ejikm8ncident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes t0d93 /crio1rj41 kkecgkr n,) 2i/ b+dlmjcpfrom 2.8 m/s to 2.1 m/s If the incidl tcji mi/) rd bg3knk/k9rc4cp1jdo2r, 10e+ent 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 531q zdgn 8r:gl l1cp8orvvo(it hits a layer of cold, dense air. If the sound wave hits the covcv3(o881:llnp q1orz5g gdrld 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 rockokbg7h9s zndnyu37 -2irs- .a at a 3zu -.k 2ry7ssb3oh7i9-g ndan8 $^{\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. pv;e 4(:hgyuaAccording to the user’s manual, the dish has to be pointed in the direction of the satellite, but :e(4 aup yv;ghan 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 thqtz4hg;p vwhu w63-:re Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea leve 4gzt -vruwh;h6wqp 3:l in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/mrfd ,kguc3hx wu ,ge26z f1fj )04p6fu 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 (approximately 5 mi/h). [Hint: Use conservation of4wgr)jfguz32 e ,fk fu 16fp0dchxu,6 energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which -7 u - smknzj3bwo.uazrav8:5 stretches the net 1.1 m. Assume that the net behaves like a s m-jzzvw83rnoba.5ku: sa-7 u imple 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 sprinc;z fb ell-20cg. The mass then falls 33 cm before it stops and begins to riselc0zlcb f;-2e. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compresqpoeel j-yx.7c)5 j /gsing the spring 5.0 m. (a) What is the spring stiffn o -epqj/g).l7ceyx 5jess 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 right pao- *s.zogc8q(ekp07 so5bgi wce 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 coffeew.-ios 5g80co(bk q z* sgope7.    cm/s

  The ripples in a certain groove 10.8 cm from the center of aqmtflqj.ey/05c k9 qrvt7;+ d 33-rpm phonograph record have a wavelength q5+q trvck;9mtq7y0l.fd/jeof 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is in ih,cj- fy+me)a /(bulmeters and t in seconc(h-mle+y )/f b,ujaids. 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 osn)v. -l-myx wmcillates with frequency f. What is its frequency if it accelerates at 0.50g (av-l.w xnmmy )-) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on i y0, :ru+nnh)u0uuqj the raft, it sinks 4.0 cm deeper into the wateuhyun0 +jrq , u0)u:nir. 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 instrument are 053l/vprdgs2z4 0 d6f lvkigbc*oy9d tuned to play at 392 Hz (G) and 440 Hz (A vb*rfdygk2g /l9 0dpli0z6o3vc 4s5 d).
(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-part cord of Figyxjw bu, to 0tg;l/(e1rmco+fi lu296. 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) Is the wavelength greater in the heavier secticw0 t+rulif6lb2(;omtue ,9/xy ojg1on of cord or the lighter?

  A tuning fork vibratescmf..rs/)03 md98dev str ydbg d4,je at a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculate e/tyr 3c4 dvmb ,d. )rssmf.j0gd8d9e
(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 motio);ik f;/dx ftsgodf:;-do-jl n of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibgs ;xfk;fi):djdft o l-/;- odrate 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 c-:l,vy y0fah 5 2sbu/xmg hmia rg(2(a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the hxy2gsy(avc m(glb 0 uir-2/ 5fha,m: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 7itl ;* /*bs avioqco:one-way swing takes :stc7*/oibaoivq; * l 1.000 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 the vertical ltbpqum3 3okm. rg 68 dhi96.rdirection or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, th69b3 . mrl8.63hmoid utprkg qe 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 p se(d.mdw w6(mm )dkhgu1o4 -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 opposite end. Whewm(ks d).mmud16h(do 4pgw e -re will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sox- huny5w2t 2pring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on to u25 txyow2hn-p of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane c; eb;f6ij9ds--mw gmtable is 22 m long and has a diameter of 6.4 mm. A bre e-jidt; sg9;-wmb6mf eze 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 plate as shown in Fig. 11–58 (which also gives t8 2poyx0om ct18j1oe9 bv vbo)he dimensions of the block)08 y1pbvt ev1j9bo)oxo 82com . 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 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz