Give some examples of everyday vibrating objects. Which exhibit SH pis 97c dx8-5qt;nwgrM, at least approxi-qi dt; 8csnp9gw7r x5mately?

Is the acceleration of a simple harmonic oschuqv:02k:v py9 t ,weeillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engicl -x uui9i;v-u4b cj+ne is approximately simple harmon uvx iiu- 94b+cju-lc;ic.

Real springs have mass. Will the true period and frequency be larger or /.,esfx 16fp;/z xrbmz,incthe /)mnsmaller than given by the equations for a mass oscillating on the end of an idealized mas/zx)bcm h1,fz fis etmp nx;.r,//ne6sless spring? Explain.

How could you double the maximum speed of a simple harmowz -(s84ta 0xdh1ew 2jpdpj 6onic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, gsrlujbizs egd8z8*d 3n-)57and then is released. Describe the scale reading an)-ur zzls 85jd3sbi7dgg 8e *s a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose ti +u:bv 36ed to*yl2,yejck sew5v2fj ,me when taken to v5d ee,y+2j: l t uwy26scevk,fo3*bjhigh altitude? Why?

A tire swing hanging from a branch reachp3ip,t/. 0/ hw zf thxi0zs,iees nearly to the ground (Fig. 11–48). How t ,/pf0x ezshit.3z pi,iw h0/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 shakeaz0 7a,qh4jx11 yf gtf the pan at a certain frequ1fj7hx40fy ,1gazq taency?

Give several everyday examples of rlfmf 0ef/b c-;esonance.

Is a rattle in a car ever a resona5i p5h)q 6zepwnce phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequenc2rci b9*+mwt pzg eu:6y of its source? Why or why not?+pi mr9c2eb* guzt: w6

Explain the difference between th8kn(u; ftkj(tc rb mr)i k+;c*e speed of a transverse wave traveling down a cord and the spe*kfic c;)ukjt rr(n8t k b+(;med of a tiny piece of the cord.

Why do the strings used for the lowest-freque;t9qlet:nu2f mkutkz w1i( * * z1s-kgncy notes on a piano normally have wire wrapkwztuuz 2e *tqkf(kns:t-;l* gmi119ped around them?

What kind of waves do you think will travel du5*kqd mc7yx7ny- wiux31 1 jaown a horizontal metal rod if you strike its end (a) vertically from abov7x7k i3yn1wuq a*d uxc yj-51me and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in tem)r7.o5g,xjq wuzbf :kperature, but the bulk modulus B is nearly independent of temperature, how would you expect theqof.x:u krwg57z )jb , speed of sound waves in air to vary with temperature?

Give two reasons why circular qkw6vb :w t;yais 5vj82qx, g;water waves decrease in amplitude as they travel away from t k ; ;j:w,txvgs8qwavbq265iyhe source.

Two linear waves haveruzqw * 29w/k2xnkadhyj;m+p5i a2t: la8p+ v the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which;w+:k2r jxavmtd p+kap /nl 2*q8 iy h5wz9u2a transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sec l /8rq+qlgyw+tions of cord as in Fig. 11–33, the frequency does not change (although the way++q/8qw lgrl velength and velocity do change). Explain why.

If a string is vibrating in three segments, aro7o5t 8ttu ok7;*kk tlj/lcdk(f z ++le there any places you could touch it with a knife blade without disturbing the motio;k(o kt778f5zlk jk+ l outcd+/ ttl*on?

When a standing wave exists on a string, the vibrations owi),ijqe4 0cf8xhm4 w f incident and reflected waves canm 40h wwq ie8,cxfj)4icel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transm fu:xct f4r 7vk**ur h9rcv+2mitted from one place to another, how might we determine whether the energy was beingt74 :2uu+rxvrf v*rc* kc 9fhm carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the :dd2n 2 72sxd mrw5yomtotal distance it travels mm2d5sx:d2w ndo2yr 7in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but iif 0hcb6-pd)g-dlae,3 kh/ur s 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k od-,i bhc-lk gea3p)f/ u6r d0hf this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when iyu ;cjxbo.21nw4h ojmw 3(wh/ts 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be tch(w/xj w;n12u4jo.3 bhmw yohe frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs fm*nawdk (88 0l fwfd;trom it. (a) What is the spring stiffness con8dtwl(n*afm8 f0 kw;dstant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is hx+s ucb+. * nfpg)bpm5ung from it. What is its frequency if only 0.38 kg hangs from itpbsc +gp m+b 5*fu).nx?    Hz

Construct a Table indicating thew2r(h,hv (i zjljn.w * position x of the mass in Fig. 11–2 at times t = 0lz.h(v n2*wr w,ijh(j,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 0.25 g is cahmi j( erfx2+i;4ka t/ww.mk6ught in a spider’s web. The web vibrates predominately with a frequency of 44ik e;6t( awm.wx/fm+jh rk i2.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency osq6 rou1*o:zd8 mi w2zf 0.88 Hz. When an additional 680-g mass is added torwi:2qsm 16dzz8ouo * m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 tiq/zro:lor6 f 0mes per second with an amplitude of 0.13 m. Defl0/z: ro6 orqtermine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maximum eu m+kouu g1fo)7:/q hvalou1fgo) qm7ue/kuh+ :ue?$\approx$    A

A mass attached to the end of a spring is stretched alp/,x7m 7 lm7,gyzlo mat2mw(ms dr 3. 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 vertickt9jhh sgt3j7uu 4h -eg;m2(f8wqr/z,c7oxoal spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does zhfsxhj4m wcohu 2 ,g/otu3(k7;7 -rtegq 8j9it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffne-k2, aa2kgka9t; k wtess constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is movingt9 e2gka;2tkak ,wk a- with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress t5(14;uivk pfbrb d* qdhe spring of a toy popgun 0.200 m to “load” a 0.180-kg ball.bd (bv1 *4fp;rkd5qui With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to onydj4a( xp(yam8n: .dr e 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 thaj8m4r yp .(:a xddy(ne 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 th7ul mk:zc2lai w.18 ;fa sx-dse equation x = 0.45cos6.4t where x is in meters and t is in xuc 7fwaz .8d-a2s;:im1skll seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half ym9 qj*hgbc 78KE and half PE? ±8qc7gmb* 9yh j    A

  If one vibration has 7.0 times thn.prgz 5i*ie b.y/nr0luo0*le energy of a second, but their frequencies and masses are the same, what is the ratio of their amplit05/l ul .rengziinro*.b py0* udes?   

  A 2.00-kg pumpkin oscillates from a vertically hangporvwm,4e/0qmdk)2x bri-()d8 sxp eing light spring once every 0.xe)-r0bv2 rxqm sw/4d8ei m), (pkdp o65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identicaq; -j*wps a /;+kjpywul parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will;+/wuwqs py pjakj-* ; be the frequency of vibration?

  A 300-g mass vibrates according to the equation ny;qpau c o4;dsee(* 5x = 0.38sin6.5t where x is in meters and t is in se *dp4a5oqsn;e;e( cy uconds. 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 exe9y xxua3sl;df 1s 4l5amples of SHM, labeled 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 =i7+ uf6hi (1 mdnyk 8/ba9xzpv 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determineniy x 9p7v+ baukidmhf(8 6z1/
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibratesxgw72402f q 6 eq( zcotiaeu b,mv:.or with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium poq.m242b,z:7v (goqe 6t cxu fe0arw ioint (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 ti:e hdrzdsa2k :t:z61o two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-ky04fuo ta-m ;4o x3+cpp,lozhg block attached to a fixed horizontal spring who0uo to 3o-44lycp zhp+ fm,;axse spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. u5l1 bnpsvz()After reaching his lowest p) 1(vbp zu5snloint, 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 vibrations iy/pyv qe(6md 2-m19ars * oxoyn exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if iynx a56ovg r2pd*nv 90t is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 s.60vx n9o5d* g y2prnva)    m

  A pendulum has a period + j8oy2q .:ln xa,skujof 0.80 s on Earth. What is its period on Mars, where the acceleration of gravit :x2yua8nsoj,+jkq .l y is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 807p lmf jjy*.h5/xxp c+ 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 mvn m1jic8 hp6/k3*yyaass of 365 grams, 8 avyih1 /kmcy*n 36jpand it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. ldc sa09-zf7nIf the clock loses half a minute per day, how should you adjust the length of the pendulum? shor lasd07n cz9f-tened by    mm.

Derive a formula for the 6limom 3 9rb/lmaximum 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 it is released from rx0mb ;vgvv l2 3uh+k k f+at0mt7.kovb,o i(/nest starting at an angle of 1x(bnvm+g vktt/ l;.vhu7ov f,o0k3ik +2ba0m5 $^{\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 3.byr(8 g* yv /k si-ktz8hhq:*g0 s. He measures the distance between two crests to be 6.5 mb is /k yz* g-t8hvqgyr(hk:*8. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz apjr f 9d4b7wwkck;qne7hw1)7/ otf 1dnd travels with a speed of 343 m/s How far apart are the/ q194 o b)w;kjn7hwcdr kpf1et7d7 wf wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 16lpwzg ;0zw3w (00 kHz (kilohertz) and z (;zl3ww0pwgtravel 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 )g+g)cztdoe ca9l;01y uk- i1ga b7r awaves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one i yd64cpi4l.sv s twice as dense as the other. Ilc 46pvs .di4yn which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supportu+ts5f.(rodw n s*x9uhwc0r**3nadb s 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel fromw*r(*sosddcax5b 9nwt r u0u* n.hf3+ one support to the other?    s

  A ski gondola is connected to the top1wnt asv7u((1e8ma c vfn9p 7x (bmm-h of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes bs7v avpwm 7 t1axh(cme (-mn(f8n9u1to 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.
(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 surface of the sea. He hfis0hb,2y8 cj;; iwyi w) (mf3edhgl.ears the echo of the wave reflected from the ocean floor directly below w 8ebmdy,;f3isi )c;h.g0 fjiwy2(lh 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake traved rr fvs)+)u +phlz8p+l at different speeds, and this difference helps in lo z+d+s)urfv)hrpl+p 8cating 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 approximated by a sinusoq2d8il t r-prlc+ rw;/idal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actuallylrr 2c/l+qpr;t -w8di 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 (aordo vda-8r 4d *2py.a) the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km p -2d8 yovro*da.4a drfrom the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to i n5rh5pymkdsse7 g4z313w.k)k e rc-be m35ge1i4zks3 he7r.rkckyw5dp sn-) $ 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 portib51)idt 86 t: ontj nvl3jhv0bon of the Earth, but one is ca)d:tvi8o n 35lbhb n60t1jvtjrrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, bbj*:.sx ,q m rh*w/usjut one transports threex/brqu*w.s j :,hsmj* 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 mozcyovu3m. 2ys up36b n )92zsave up and down a total vertical distance of 6.0 cm, from the lowest to the highest s omsy3 c n6.9pu ayvb3u2z2)zpoint, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. xaffjs/typ4 a0 ur)31(a) Sketch the shape of the string at a xs 1y4t)j fa0ru/f3pthe 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 frequency, what4c+/ua l z)kvaxc kq.8b:2bgn are the frequencies of the first four ha+:c g 8quxlcb2 v/4.kk)bnazarmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency wil-7 qe mwoymlwm1-li8 wh(fs-;l it vibrate if it is fingered one-third of the way down from the end? (That is, h;y- lmoif8sqm(ww -ew71m -l 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. Name at lxaqlp9+fn(lifismti 31 6* ,keast three other frequencies at which it willxpllm n36ifia, k1 tfs9i (q+* resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waved,fu/y ipo t5 8h-ap f.2dsvt*s on a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart afdh/ atop2t8vyp-,i.5* f dsu re two adjacent nodes?   m

  If two successive overtones of a vibrating string are 2(;j0hb abnh;aphkk) 380 Hz and 350 Hz, what is the frep;nkh hb)aa;khjb0 (3quency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of bkz m4e 4h:vm7s.f g gm*(nl0h3.6 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 fv:*sb( m4l7m4nz.e mgfhhgk 0requencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, b u9j yna hr5k..nf.u sxam*u-+ut it is measured to vibrate at 2 uyju.f+nk9xn m-.h.usa5 r*a05 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 supposed to vibrate at 20k;6o +qo; vxkw*vx5dv0 Hz, but it is measured to vibrate at 205 5qvo;+ 6wox;vxdk*vk Hz. By what 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 smalq -d(gag0t 6g:dhc pdv 77a+x u5adzt7l-amplitude mechanical 60-Hz vibrator. The string’s mass per daqaz txutch5 ga vp7d 7g-+06d7 d(g:unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pulleyp:ht45u y.zywgl3w f6. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achitulhy36.yf4z :pwgw5eved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the qqvzw)e 9 nhsu;n 90t9right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose h9w;09 9znsq)nu tveqthe 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 va1e93 92 wyxyh7 pfkovvvc7dh5 8gy :at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident9589h2737 :f1vkpeyc owyvd vy h xgav 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 chang-rup :(o g),fpxvgbd0u46vki es from 2.8 m/s to 2.1 m/s If the incident wave ciu) rp,: boug0x-vg( 6fv4dp krests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dens1nj6 l17xepcrqos zg *q; plhp-yh.v 5,oo -0ae air. If the sound wave hits -6 oz,ohnrcq*v1;pe phll 0qx. -yaj5 7pso1g 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 betwer37 tiubfn;vt(r- asel-.9 /hcq b(ipen two types of rock at a 38 b.a7r ruiep; 3( 9clvihqst f/ -(nbt-$^{\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 man2bo.yr8 dbdl,ual, the dish has to be pointed in the direcbbo.8d, 2 lrdytion 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 Pact4 co:imi 2g7yific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea lemocyi 2it:4 7gvel 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 constan ;r.wcg+ 2lyeht of 550 kN/m Find the maximum compression of the w.+r;hl g e2cybumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretch2zrvb3n l(s 2o6p j*4.t(6k + wn vi0lzqocvqqes the net 1.1 m. Assume that the net 6osnwoq 4qtvvljk c lz6pq 0nrbv2+zi3*2 ((.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 opjz,rs,;m9y6cl+c pr f a freely hanging spring. The mass then falls 33 cm before it sy9m cc+lr ,, 6pjz;rpstops and begins to rise. 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), o at)t4n7xxtzmz+ ) 7fcompressing the spring 5.0 m. (a) What is the spring stiffne+ )amzfno7tx)z txt74ss 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 ju*d+ rvmai8n/e psq9 -ist the right pace of about 1 step per second, the coffee sloshes more and more until eventually it start- */d ns+a v9r8mieqips to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove/rvw. 73b qomhb-j-jv 10.8 cm from the center of a 33-rpm phonograph record have a wavelrvjmwj7-v3/ bh.qo - bength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.73u. nn/rp ioi650cos7.40t where x is in meters and t in secondsp3n7 inoi r./u. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency hz6 cr,icq-xwmy 0: 5-tv;5bjkx js-hif it accelerates at 0.50g (am-:6k;x-tr0hv 5s 5, yqjczji xhw-bc) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Wu u.y j pme62 lkrq+q52pfe2toiw46z6hen a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for2 .2uwt qekz5 l4of+2iqe 6mp6ruyjp6 a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play q ey,b.)yhrvf(hlagi-h0-tfnq9p (0at 392 Hz (G) and 440 Hz (Arh a(,fvp0eb .hl0ty ygn -q(9q-hif)).
(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.;c pik-r cu9,fuvd. b the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratiu ;.ucvk, 9frpci.-bd o of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at-/x fs,.on7et5yk(ke4d fv 1 gclnd,i a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of e sif(,g7e4ncn,5x/dy 1lokf.v- tdkcenter. 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 mos*j-,t8fr djegl +wwli/vs 87tion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact wi8 wj- *twl78fseidj v sl,/g+rth the board during the oscillation?

A string can have a “free” end if that end is attached to bm*d4 znmn:jsd * a/d0;x(rc b1vc)g ga ring that can slide without friction on a vertical pole (j/z4 :1;0g*b*nmc(g nrbdd )xcas vmdFig. 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 ae2e6-cedvq *5i*d n8anr .paf period of exactly 2.000 s — each one-way swing takes 1.0cqnrfne68a e*e*d2ip 5 -vd.a00 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 tk7fb wkyq (4/she 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 peri bqk 7ykwfs(/4od 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 sfj2jobb-od g+gp3z ( 6tretched 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 2-djj+ fgog(o zb 63bpend. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spgiw/ant,b2n4yjt8 wo+d 4 pd2 ring stiffness constant k. A penny of mass m is placed on top of the block. What iwy 2/ng4jb tio ,8+nptd2wa 4ds the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junm+wd 7negey(.j: 1wiykyard. 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 7 en:my( wig+.dw1jey 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 als8 *eq ::f prg0v6fu3qe4 wsicgo 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 :u8*3sr 06i w:fpeqvg 4g fqce9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz