Give some examples of everyday vibrating objects. Whiczaofpq zr1y,w2 9f4pml8 +c l.h exhibit SHM, at least approximately?842app roczly zl1,fmq.w f+9

Is the acceleration of a simp* 10 .lcnr 2jcbe5jvppiu *t*nle harmonic oscillator ever zero? If so, where?

Explain why the motion ofncb. 5gd)kn,i a piston in an automobile engine is approximately simple har5ik.n),ngb dcmonic.

Real springs have mass. Will the true period and frequency belic 66djg nboo65 u;w8 larger or smaller than given by the equations for a ma5glwbnud6o 8oj;66 icss oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillato, dk0;nfyh3ygr (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scal9n2an(-pp y(e;no1q7q1yhqmjxoar/n mo b- + e, and then is released. Describe the scale readi /hy o-o(on -q7pj+;ya1qebp2xmn (n qanrm91ng as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time who u.)lb1 fcs:uen taken to hio:1f ucl ub)s.gh altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48).i(w5zqy255 nhszs/ (wga+clkvu9nj/ How could you estimate the height of the branch using onwj5sa(n9(s5k zw /nz +l5ciyg/uhq 2vly a stopwatch?

Why can you make water slost6 uk2br fh,dy0w1eu4h back and forth in a pan only if you shake the pan atfrtwu 246yuk01ed b ,h a certain frequency?

Give several everyday hyap k ;42b l5bb2a8r ;l(z:ipzy3eiiexamples of resonance.

Is a rattle in a car ever a resonance phenomenon? /hoyh6dbfv9d,4/sukyyxmi2*)pc 6 . zt oxr6 Explain.

Is the frequency of a simple periodic wave equal to the frequency /8 4rk ur xib96 togc9oxg93qmof its source? Why or why nou8mqc9 /4g9 3gb ri9xx6toro kt?

Explain the difference between the speed of a transverse wave tkru joy6r;ti3/:ex; zraveling down a cor iuzr;ry/j6x3eo :t k;d and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on au,t)o u4nh 8d ya vc+ght87ny7 piano normally have wire wrapped arount) nthh7uov8cd aygu +,4y8 7nd them?

What kind of waves do you think will travel down a7bnvjf9j7nwho 7 8 ey5 horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to itw79 ehny8f 7n7o5v jjbs length?

Since the density ofc:r;-zge baiu53 jkzf* . c*lg air decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature,l;.-gzj3 5crbezk f*:*cuaig 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 thek0.:xkn wsh;f y travel away from thehk:kws.n0 x f; source.

Two linear waves have the same amplitude and speed, and othe+ uv8z .j 6q0bikpp:mxrwise are identical, except one has half the wavelength of the other. Which transkpjxqv. 8bpu:6 +z0i mmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two secti9i6s-1z y6aw f f)1sj9o xxlhnons of cord as in Fig. 11–33, 9 yn-1fix96 1lwfxz sas6ho)jthe frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could vi, ivw 3b-u4btouch it with a knife blade wi-i4bviv3w , ubthout disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and refqi ee6, arxkr7/e -m9yh9oga +lected waves cance,re7e99+eaxoa- qig6m h /yk rl at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place e,n*-qe un:zpto another, how might we determine whether the energy was being carried by paun z:pen q,e-*rticles (material bodies) or by waves?

  If a particle undergoes SHM with afa2)n5 /eo6or5vj ouls1p ;q mmplitude 0.18 m, what is the total distance it travels in/ uo6 o1m5vaqs;e2 l5)pjfonr one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hanga-, q*9j hmq )wzspokxgz 0b+0s from it but is 85 cm long when aapq0 , hxgbjzqmzsk*9o -)0+w 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 6frbh -sy6yv906)o d fz.sxzg 48-kg driver gets into the driver’s seat. If the car goes dofx. 9z6hsy sy)4gb-6vfrz0 over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches ce qr1g.-u ig43.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constant eugi 4c q1g-.r$\approx$    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 2.+wqodv q3*v*-ogr j f*dqvbwith a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs f.qb+2v*fw d*gd ojqvq3rv*o -rom it?    Hz

Construct a Table indicating the position x m+ pjmprvd 5)e9)h iju 14fqe8of the mass in Fig. 11–2 at times t =+pdi4j9 1fe) mjqhvupem8)r 5 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass )c3n3s sxq u)y0.25 g is caught in a spider’s web. The web vibrates predominately with a frequency of 4.0 Hx3u snyc)3sq)z.
(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(m 4wmr*k9 aqz; p)uth a frequency of 0.88 Hz. When an additional 680-g mass is added to m, th( 9u r4mzqhtm*) k;pwae frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of;zvjy4 1z3p7t izjj 2v a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determin 4zzyt27jipz;1 j 3vvje
(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 isivuqtj. 5bb, ) the speed of a SHO half the maximum valuj.b5iu v ),tbqe?$\approx$    A

A mass attached to the e85cceal ) 2+w uuewq)pnd 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 t n-+pm , kqw54at+opk4fnfu3xhe spring is stretched an additional 0.130 m and released, how long doe++xoptfmfq u -n nk4wpka45, 3s it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg qtlc1g;,3a ;+yo arngis attached to a spring with spring stiffness constant k = 280 N/m and igt n;r+g loq3 ;c,y1aas executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compresgh yhhb *d- h,on50cy.s the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With whay y-b*.g5hdh,0onch h t speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictm.av 44wql8uyionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress .4v4y8 lumqw athe 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 accord16ukeql(4r3zqv,3 dt5s xv*iel8u gk ing to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. (dkr 4e8 gv*1 ex56vql,u util33q kszDetermine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and half k;0sctbnyagw. ,a61*- me mb mPE?mb;at gs0 .y1m 6*,nceka mwb- ±    A

  If one vibration has 7.0 times the energy of a second, but their frer(d.ubo7a5x g(ebo3 7x0 sqcsquencies and masses are the same, o5sbx7(q (uce.roa0b3sxg7dwhat is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprinf ;gq b15pvu.vdu vk k+/-qz3qg once every 0.65 s.1q q.3 p uv zfdqkbk/u+vvg5-;
(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 para35h xeu0d;yi5. kccyk gac/ f s*+tg+ullel vertical springs, each with s/c;yu+0xggd3aks*ku .fhc 55etiy +c pring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where fzg/z p0d ya:o)m e4f6x is in meters and t is in soz0 medfz) :apf/yg6 4econds. 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 yewijl(giom yxl8 38 vdu:4+fw+oo., 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 horizh cx z+jxwg,fnq4q5whr (8d xmbw8,47ontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial7(w8 5h q,4mz,wg cq8wbdhf nxx4rx+j 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 wij-af u2u,ddc:: b qy9rth spring stiffness 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 (x=0) f -d cquua::rydj2b9,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 ha8 5;:s+cu :hz opgslspring 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 a6n9zybt3+ ezi ttached to a fixed horizontal spring whose spring sti3zn9b6ez +t yiffness 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 h3 iuatv20or +kigh bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Cto+0va ri3k u2alculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 6dbt0/fj 3/hvu0 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 swiyojm( u:z.b6g: f6eae ng per second? (That is, one complete vibration takes exactly 2.0 s yg(a6uze.:6j be mof:.)    m

  A pendulum has a period of 0.80 s on Earth. Wha6,o*i +jeya h w,vqj*xt is its period on Mars, where the acceleration of gravity is about 0.37 that on Earth?veiq6 ohy,xa+*j* wj,    s

  What is the period of a simple pendulum 80 cm longdx zs,;9espr 9
(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 3 gsx 3 -5i+qo4vctwe:g65 grams, and it is g:ecv+w4ogq 3x-5 itsreleased 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 lengt;2iace) jnxc6(l pzv/h of 0.9930 m. If the clock loses half a minn6l/ vcezap)(xji2 ;c ute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum hou r;xsu2qz,3umn 8v m/xg x*:)euv8 speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At jqsg vy; f y1:-po-zu;it is released from rest starpqgjs:v--fo1y z; u;yting 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 crests pass the bow of his anchored boijm,6;m 3xm0 v(ujiroat every 3.0 s. He measures the distance between two crests;oi v3xi,(uj 6j0mmrm to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 ;(pu b-fac8 jlHz and travels with a speed of 343 m/s How far apart are the wave crests ( c-uplb 8j;f(acompressions)?    m

  (a) AM radio signals have frequencies betwee89.f nim/2;ph9t i qkc6gwyg en 550 kHz and 1600 kHz (kilohertz) and travel with a spe9q/c6wii g8k pmtn fh;y9g2e.ed 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 longitgm a6u0;t:d zum*jz2)bix;g+ e mdde (udinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one isv3z9 yzuvnh7l,r grhy8(0)qu twice as dense as the other. In which rod will the speed of longitudinal waves be greate09 v) ly7yq 3vu(g,huh8nrzrzr, and by what factor?   

  A cord of mass 0.65 kg is s udc6fx))l+cd tretched 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 support to the othef cddu+ xl))6cr?    s

  A ski gondola is connected to the top of a hill yh u :*t, e-ql)1mixzzby 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 szy-,)qthzil me: u 1*x for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just bypn e-l -mw47nelow the surface of the sea. He hears te - ynwmp-4nl7he echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at d5h8aw .d)6xub ebpa6:q ma9yluu(dk0-b*i apifferent speeds, and this difference helps m6ehu)bp 8ayp au: bu0w ka5a.b d69ilqd-*x( in locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximah m*ikic(u1hof88q -s)/gd*: ccgghi ted by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of qh*hg)igmc8g-8f *hsi d kc1:(co /i uearthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, j(eb t7s29adgand (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km a b97(sdta2gj end 20 km from the source?(a)    (b)   

  The intensity of an r8yx+ 7aa fj;)s yu,qzearthquake wave passing through the Earth is measured to be r7y; a,axy z +f8sjqu)$ 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 through the same h;b acppej3l7 ;8esc5 portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of t5c bl ea;8;3ps7e hjpche two waves?   

  Two waves traveling along a st4sz1p ;dbj;k iu3x 4ovretched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two x4;i4 p odu1bzvj 3k;swaves?   

  A bug on the surface of a pond is observed to move up and down a t ttnh1e9fdsy w z5vr0i42o1 fbrke cn68t 5v);otal 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, by what fa55119vt ivrdc e8 ozf)kfs2tr 4wthen6n; 0ybctor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. o llkffr05i/6w(l,w h(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 stringrho/(i0l6 lwkf,w l f5 is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamcyan 8u2 b6iw;ental frequency, what are the frequencies of the first four u6bn;c 8w yia2harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 29rg5f wq8s 4+qmwt(znets1vo+-ce d 2*zhs.p94 Hz when unfingered. At what frequency will it vibrate if it i .1he( 5 +8+nrt-f*zw q 9dtcoe2swvpszgm4qss fingered one-third 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 frxc 6oplk4 zy /n04*9gr asubn-equency of 280 Hz. Name at least three other f ya* -4pu n/o9cgbn0z6skl4x rrequencies 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 wabu)py)7 +2p)v ey gcm/ ww;ofhves is 4)ww c;ge7b2y upy+h))ofm/vp 75 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, wha9 -1s,xsbwzemq2wm 0at is9za xmw 02sqes-mw1b, the frequency of the fundamental?    Hz

  A guitar string is 90 cm long a 162lp.tqdyi ikq fc9)nd has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental aq f iip)klt2y9.61qcdnd first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is m y07vre) z/cuneasured to vibrate at/)vr7cnuz 0ye 205 Hz. 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 suppose9mvua.awk3r 1 y. aoi:d 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 cam 1o a3.yw9:rviaku.orrect the frequency? decreased by    %

  One end of a horizontal string is :a3rtgy2g7w rattached to a small-amplitude mechanical 60-Hz v23ag7y rgt: rwibrator. 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 movinf2hgbuk. 5wx8g the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achievw .2bk8hxfgu5ed by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in as /e6o *ff dj)dfk0 tv4z4gyb9 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 standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speedtky6*e/ bdz0sv o)fd94 4gffj of the water wave?    m/s

  An earthquake P wave traveling at k.0w1 uft(qv4 sk2t8 t+j;d l ,jspadix9ca 8.8xr km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at ank put 8fi2lasxjd (as;48djqtr1.w+ c8 ,t9v x 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 the v f/4r xlm-,hzvpl)j6z8s0 rsto ch. 0oelocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests 6-hm08vcs/ootp,4rx0 zjfrz s)lh . lmake 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 s -u)wx;wmef9u)h8yp od3r2mair. If the sound wavsd;e-mu2rwf8x3 py ))mwhu o9e 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*a;1mgmfgkyy24 dfs 4 of rock at a 32 4;4f ykam*dg1g syfm8 $^{\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,4h) bm 6ztqya) the dish has to be pointeb)hmqya 4t6)zd 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 tf96 fymdu ms oh3..d,che 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 s umd .d69hf3f.yoc ,mabsence 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 stiffnesslz* .+fc: nv xoye8,jp 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 (approximately 5 mi/h).jy.o,+c enx:f8pv*lz [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window tnbexxzh5 ;l .kl )u5p)o a fire net 18 m below, which stretches the net 1.1 m. Assume that tzk5) lxnh). px; eu5blhe net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a fregy.e8 6 w ev-uz. r6cza5)tdceely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the osc56zywa6rc. . e8ge-cvedu t z)illation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), lyw 2rhf: fl:.ftlf1n - h48qwcompressing the spring 5.0 m. (a:l:hyr2tfnlwf14 .-lwf hqf8 ) What is 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 of coffee (diameter 8 cm) at just the. 9bhemx(8 rlqq(efc9 right pace of about 1 step per second, the coffee ql8qmcbe(f 9r( e.9xh sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certa rzl7zb/tn4v ouy +hjyxt+-.0: xtxf/in groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. Whatx 7:hu4.j t-t+ tbnfzrvx /xl zoyy+/0 will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.5waai/ ct3wxt *n o e87b y)lys0nn,l440t where x is in meters and t in seconds. D)n 5b,0 73c48/annoxl sylywt wi*ate etermine
(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 freque;38 v+e)*h tojsbzhm1xnkdb;ncy if it accelerates at 0.50g 8do;b hhsjb+tvmn3*zex 1;)k(a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands quba y l038p9w ht9yr;on the raft, it sink lrtyyh3pq99au8 ;wb0s 4.0 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 instrument *wjc5tbt8- e ware tuned to play at 392 Hz (G) and 440 Hz (jb8 cew*w-t t5A).
(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 Fip+ha z +n 1o:v7oogp-m5ij .gmg. 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 sectiv+n1oo.mzi5a mp:- gj7p+ ghoon of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prongn,6 ;0 rlrch pc gmr7v3qt e3u9c6+raq moves 1.8 mm to either side of center.n3v+h;rrq0cg7te u9 6rm6,r lpc3 aq c Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequewl 0ctf6 + i4d;mflvo1ncy 1.5 cycles per second. What is the maximum amplitude with which the end of the;dl l+f m vco61w4tif0 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 ring tmwit l-eym*0fp f p(im4i87 j2hat can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of tm0fp*f( m e7iit2-4ympwjil8he 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 one8y e( 1zyn j+paq9n5uo-way swing takes a1qo 9yej+np u(y5zn81.000 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 ,p*y1) 6gyvolg5xqx qs9 uv 2yoscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: L*x 92xvy og6g5us1 plyyvq,)qet $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tensi5 k+nbo -c1bw1/iqjlbdr1e7 ion of 255 N. A pulse is generated at one end, and 20.0 msqe+i bjnbo7rkl 5wcd/-1 bi11 later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with sprine awk qa.( e6f+gn0gh0g 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(awe h gqn ak0+6.g0ef just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at th.y-v+ r )wo5vkk xhvk8e junkyard. 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.kx5v-8h)vrv+ okky w the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown a5+c86q k lzbwwi 0sc;in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let gwsb6+ zai5 ;8kqlwcc0 o. 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