Give some examples of everyday vibrating objects. Which exhibit SHM,nghr(gq0hvkq d; 3;g9 at least approximatqrh;;3g h n0kv 9g(dqgely?

Is the acceleration of a simple sc dl)4asint4a *:w+:do 5dmfharmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an kfgx5m /hf adx+/ l,dr3 x7f9a8e t4spautomobile engine is approximately simple hld5gmx8/ f93 d efax/ ,xfkra+7s 4ptharmonic.

Real springs have mass. kx*6um;3k r3mvhiy xnz91j2kWill the true period and frequency be larger or smaller than given by the 9x2 muj;3k6ih xrm k13yzvkn* equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (4hrn82 lgp,s qSHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale r2r-t-mev* mg, and then is released. Describe the scale rea2-evt rg*-rmm ding as a function of time.

If a pendulum clock is accurate at sea level, will it gaixf510oa a ld-rn or lose time when taken to high51da lfa0xr-o altitude? Why?

A tire swing hanging from a branch reaches nearly to the groub0pp/2 6:uewrwmwh m- nd (Fig. 11–48). How could you estimate the height of the branch using only a stopwatchb/ rm up:6hwwe p2wm0-?

Why can you make water)uxb9 yyhx 0g: slosh back and forth in a pan only if you shake the pan at a certain frex)yhb:xu9 0 gyquency?

Give several everyday examplesd2;s(f x vh2 igbgo5wzv0g 3)t of resonance.

Is a rattle in a car ever a resonance phenom oj)zdd nx - 4b*jrks.)c6k7kvenon? Explain.

Is the frequency of a simple periodic wave equal to the frequencoh6.k),v pg1 egjad *cy of its source? Why or wjpe*1d 6ha.vco,gg) khy not?

Explain the differen diq1w)sp(kd jn0l;v: ce between the speed of a transverse wave traveling down a cord and the speed of a tiny pieced 0s(wki;:pn )q1jldv of the cord.

Why do the strings used for the lowest-frequency notes on ab 7pfsq:,1ljch8on-rp a)mi4 piano normally have wire wrapped aroundjqic,-n4)8 boasm17 :lfrhp p them?

What kind of waves do you think will travel down a horizontal dvv b iz kjq87u:9c29w lrbj+;metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its leng i9vcd;8u jkw2qzr:vl b7bj9+ th?

Since the density of air decreases with an increase in 5n9 k7 0vegipatemperature, but the bulk modulus B is nearly indep kvign7a50e p9endent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water w pdp/ cv w46(x/hbh6;kpz)nrl aves decrease in amplitude as they travel away from the sourb4w6lhpvkpprcn xh)d;/(/ z 6ce.

Two linear waves have the same amplitude and speed, bi.uf. nf8bc vx7+t:sand otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By w f+ubisc:n.tx.v 8bf 7hat factor?

When a sinusoidal wave crosses the boundary between two sxix5isdzlhha:-z, yl7x9 65 iections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velxhh79zx 6ld:ii5z iayx5-, slocity do change). Explain why.

If a string is vibrating in three segments, are they6espoq : dik-ljt7b ml;+* q inm7,y;re any places you could touch it with a knife blade without disturbingpqse :lq7 *nmitm ;k,6y+ 7ji;bldy-o the motion?

When a standing wave exists on a string, the vibrations of inciden.;w 2lq(r6g6y frvdi 4avgj. zt and reflecterfi g.y ra.v z gq2d6wv(l4;j6d waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was beingzn-il(gl qqum0 6:m 1x transmitted from one place to another, how might we determine whether the energy was being carried by part1 uq0x -lzmm:il (n6gqicles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total d . ;u+ 7mcm.bvga l0-nr 6dcm3qbx7wozistance it travels in one periodxm.gu.;nzw blo70a q d7rcv6+ -3mc bm?    m

  An elastic cord is 65 cm long g(6vq rklwmf .t +f.7jwhen a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is thet6.vmf(rfk7wq. jg+l “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into q rv*zl-n cs-4the driver’s seat. If the car goes over a bump, what will be the fqc -v s*znr-l4requency of vibrations?$\approx$    Hz

  A fisherman’s scale stretche4o 96gkbm3*d. srj/0fz -a2ojtekjuys 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spfj kbm*o9js.ytr4zau60-g j2d/k o3 e ring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz whe2eyqvg) 4i8 nnn a mass of 0.60 kg is hung from it. What is its freqny4 n)8veqig 2uency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. .k9uw:zbd a+ b11–2 at times t zua9kd.+b :bw = 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 0.25 g is caught in a spider’s web. The web vibrate64emjqx 0r+ wts predominately with a frequentr e4xj 6mq0+wcy of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibratexu q91bc1evudw uor() cqq0ll:lh-*7 s with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value 9rl e: cw (1x7qo u*0dc1luulqq)vh-b of m?    kg

  A 0.60-kg mass at the end of a spring vibrates rml .m;fxc/(n 3.0 times per second with an amplitl/ .f;x(r cmmnude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maximu4 al ij:cp1ma. :x*kebm valu*c4ilp:1a :kam j.be xe?$\approx$    A

A mass attached to the end5x +0x qgfy)lu 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 stret,w ozt*a e/t wym8ke2.i8i c5wches 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 position aga,yiiwktm 58 8cw/wz*2e oea .tin?    s

  An object with mass 3.0 kg is yx(bk lm4r,t.98s,hv c: ad xwlc5oi- attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium posit4,ho.x,d:k sl(car5w-m vtyb 9 x8iclion, 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 compress the spring of a toy popgun 0zd ,vr8-x 4v0zeu iy8p.200 m to “load” a 0.180-kg ball. With what speed will the8i-v rzd ey4 x8,zpu0v ball leave the gun?    m/s

  A mass sitting on a horizont93/w mkf +xcus: l(bpmal, frictionless 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 the spring by 0.12 m. If the mass is rel3 cfu9lb +:wmm/s(px keased 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 accordingm t,euty);f - fpocjy16z. f ac1vkq,+ to the equation x = 0.45cos6.4t where x is in meters and t is ot6e au-y kfzc,+t cf.;,y1 fm1jpqv) in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement frodmk 31 fds(yq6(;op pym equilibrium is the energy of a SHO half KE and half PE? ±;16(s d(qdyokpp3y f m    A

  If one vibration has 7.0 times the energy of a second, but their frequeygx fp7 8o,alppc039b) hl+ll ncies and masses are the same, what is the rati0,)y pl3 +gl9lhxb7pcl 8afopo of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once eve7 3(xcau (l41gsfqt(3nh wkcxry 0.6x4 n3 lk((fa(1tw 7sghx3q ucc5 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 identical z51(9 - :sn*miv ixv nooivmy9parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What vzi- v9yvixsin*( o:5n o9mm1 will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5cr p33)hm5 r0fso lxg1t where x is in meters and t is in sec )por0 rhsmgf1lc53x3 onds. 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 Ajqj:*hk; wdrn7w v+m*xa- 5fraa.t ,m 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 sprin:w: ryds/ugugtyq82 bk9*t (f/ km6zog (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determin/d smwr(kg6 2ug uy:bk9 ozt*y q:t8f/e
(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 Nt1 b( mf7fr/z5pu/xww/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at5zrw/1bx wpu(/mf 7ft
(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 springk6 kx3gd(n 3ngs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontp2 q2lpq6:9skzdry2 m .v +cbq5xza/bal spring whose dcz/qmvs 2b :kr2659q.lba2pyp +zqxspring 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 bridged q pcb5j1e1z.. After reaching his lowest point, he oscillates up and down, hitting a low point eight me1.p5cj zb 1dqore 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 vibrationff67t um;rrni;(( saus in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if i 4zq8 0. kuc +leccy,+*ohxufat is to make exactly one swing per secondx.kla occ+,h8e * 0uqfu +yz4c? (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earthiy x1zgk7x/ 9d. What is its period on Mars, where the i gd 17/kx9xyzacceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pyc)ve,h6o)dg endulum 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 365uyn f;(.tjtml- m 8r6;c+veomr9k8rk grams, and it is released atv 9o r6mk8rkrt ftcj+n(e;; .m 8yulm- 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 ofi0 pf-ts/ 6x wj,-dqa length of 0.9930 m. If the clock loses half a minute per day, how should you 0jofpw/- i-x6t,qfsdadjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed kqiry;i d 5pa gk7w)g+++zdj*$v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at eht/kw5qa6 a; a frequency of 2.5 Hz. At it is released from rest starting at an aea65; wtq h/akngle 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 b:cqqx nk(im 5y u-.aze( gak42oat every 3.0 s. He measures theeq. gm : (kiyx-qau 4zn25ca(k distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz andxum(.od 1gv/ wqmx, h-6nya2) uq(amz travels with a speed of 343 m/s How f) wnq2 x1m,yuqz dx-( va/(agh 6mum.oar apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohe /ny;- 2 vgyoyz+ iajuulm.h/ho4 j7m,rtz) and travel wit-;gy 7 4n /hjzjm2uo.ymli,/yv +huaoh 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 wafv2u.j1v snyfy:qf:9 ves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have th6 x .c 0cd7+fex-9iyl:zoijfv e same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and bd c 0iifjl +xxe76yv-zof:c.9y what factor?   

  A cord of mass 0.65 kg is stretchg 2xf,brvt9 u4ed between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travelug f4vt9b,xr2 from one support to the other?    s

  A ski gondola is connecn:bh+ /abmqcd d ye*vzpnag :) 6o56*vted to 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 bump d)gc q:*h/ em aanp5:v zo*b+nyd66vbs 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 surfpvu.3k*b 6 f 7cv:hvadace of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at thib :3fpa*h.u vvdkv67 cs point?    m

  P and S waves from an earthquake travel at differentwtld mdt ohv1g -wgj/)2nir:81 5r af2 speeds, and this difference helps in l-r v2ogj5)g11aflmdwt8ti 2 dhwr/:nocating 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 k2 cr zs32f,v l4cq*icapproximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with cik*zs c2 3rf2v ,l4cqthe ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitx8 yx y57mi3m,on2c4s t9l 0x3yaarv audes, of an earthquake P wave passing through the Earth and detected at two points v8lxi x3 ay2s4y9mm3 oanyr,xac 5 7t010 km and 20 km from the source?(a)    (b)   

  The intensity of an ehe:5o :+ dzpplarthquake wave passing through the Earth is measured to be 5ppo+: z elhd:$ 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 throuo:q+i omc v.uam 9*ye2gh the same portion of the Earth, but one is carrying twice the yuo o*qma.: mv2ce9i+energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a str af qzrm3,mf;mh5n*g-etched string have the same frequency, but one transports three times the power of the other. What ig*r fh ;m,n3afm-5mzq s the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and downq8c*n 9hen/o;w;rd a h a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wnoh;e8 w 9q*ra hdcn/;ave 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. (a) Sketch thq-j c7fk8w. whgaf+xfz ne4wj- tkv4 f0u:1i4e shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a fe4q7 wgf8 .w+ ahn4f 1wfkjefu4vx-izktc- j:0w 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 vibrcp0ys wrs x5/ s4a8*4;hzdk vkates at 440 Hz as its fundamental frequency, what are the frequencies of4rwpys * dx4 ch85;az vk0sk/s the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. Aeq4hhe /h) 6ymt what frequency will it vibrate if it is fingered one-third of the way downheh 4mqh)y/6e 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. Name at lektto :e*f c6t,sza1q5yi*u1 last three other frequencies at which it will resonat*o5 61 cyl:eki1stt ,ftau*z qe. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of stab 4 1n,fpp5m y-jx w+.ezeus3anding waves is 475 Hz, how far apart arjfy.p uawnmes1+ep-45 3x b z,e two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, wha8c.d)t c*2d55lyoa gkc 5ytsnt is the frequcn dgsy*tck58. loyt5 da)52c ency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Tx1-p4tifje ds.j2 +dthe distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequenc s- jt.+12xdj tdfe4piies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to m iqff38g12rlurz 5j9vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are, j z8riqm5 g9r132uf fl   Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at c/d j)i/ooapl3j1k mo 0:7gkc 200 Hz, but it is measured to vibrate at 20 aj3m p0id:kk1c ) ocj/g7/loo5 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 at5 s+8vnzq/ y qf2st2kstached to a small-amplitude mechanical 60-Hz vibrator. The string/ tqn5ssyk2 8vz+ 2fsq’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 . f;rdg7*kiq,f dqh7kof the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different rgqf ,7kf7hk.q*idd; standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tuc kc8fblbb5 .h): fs-sb at just the right frequency, the water alternately rises and falls at each end, remc8bshk5. fcfs-b:l b )aining 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 speed of the water wave?    m/s

  An earthquake P wave travk; noea28cr hn v9bu1m *j9i8aeling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incid*1;2cj 8nuarb9v9eo kn i ah8ment 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” whv vnvjm6 ztu8(z).ej v52a3 ac2szbwp1 t-d h1ere the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave cren2tmc h j)5 .vj6t(vdaw a3z1pb8s 2 -u1vzvzests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travea;r1po: qzi)tz6;yk h o:p6h rling in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air ip; )or;a: ohq6tky6z1zhip r :nterface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rock aa;6k.gfaz2a ldp4u3x sgw9 s5t a 6sf lu.2awps kdx;g4 z39g5a a38 $^{\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 tc9 z;eu/ weurm:gjp 5rgm+1,vhe user’s manual, the dish has to be pointed in the direction of the satellite, but an error +ze,/m vju umgep:w;c91r5r gof 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 acro +7kpnz39kyosss the Pacific Ocean. As it approaches Hawaii, people observe an unusual de k+n7sy39p kozcrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness 6njwvb, *1tixbcw d+l)z(0spopf 0 n5constant of 550 kN/m Find the maximum compression of the bump,x (j5nc6 fw l*spv0wp zi dtb1)0on+ber 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 wind;m5or4qagjume44i .gpfob2)j w8w t2ow to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, andjmwguj442.m8t ; aief2p4gr 5o)qw ob
(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 spring. The mass t t:td ovtydd f9s/:2q9hen fq2:y:t9f ddt9 dtvo/ salls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sprieud9lr6c/gbe4cr;5fw 2o b,y ng at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.yfge496; ob5w ed cc/ rub,lr20 m. (a) 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 (di4c7yskfe8 6 9;fyxd owameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventuad c8 wfy7f9k4;seyx6olly it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from thejptv)kzlu8 k;bh33 7 h center of a 33-rpm phonograph record have a wavelength of 1.70;k ) hbpljh7k33ztuv8 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates acc eu y5w.+8e 0r,m4vjociupq4t ording to the equation x=0.650cos7.40t where x is in meters and 0rwq 5,pmtjv4cy4+8 uu i. eeot in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with freque,azl*ezk0 khe//jxv5 ncy f. What is its frequency if it accelerates at 0.50g (a) upward,kz,//e*jx z0h ealv5k    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When y*s9d25 gcdy g:jn a*0foh2gra 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When od*gyjg2 5*029: dfar s nycghhe 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 tuned to play at 392 Hz (G) and 440 Hz k;i*oexr29u kcrsci* (0l 8xt8 jt n:f(A80fic ;ckis n8 r:*(l u*t9oexkjtx2r).
(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 twoxmnxe) x67 a1dd3h)-p9.3jw6 ntem qp;lvo h g-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter sectimt7npo;xda.6 veq hmw31dxxhje3)p -9gl6 ) n on, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the 1t.obqufo fa c)l6*i e/rq (+jtip of each prong moves 1.8 mm to e u (at1c )boji6f.f*oq+lq/erither side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cyclao+v0g0n(oa p es per second. What is the mapaoa o0v0n(g+ximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attac8htypjnl;c rxh40 /(hhed to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonanth8jx;lnh 4t rcp 0(hy/ vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2l*v hw c-,tgp7ytdw9 pm4a6. k.000 s — each one-way swing takes 1.9*4t ywc -h,vp.w7klm dg6pta000 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 osdtin7k;iu 16c8 qw:u jcillate in the vertical direction or can swing a1cdiw8t: 7uiq; 6nkjus 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: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 .cg4nm ;6swp;j. k cmb bgu* oj;3h-omN. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meetn; mc -mk.wjgm c* u3s.oo;pbbj;g4h 6?    m

A block of mass M is suspended frodonge/9//fr u m a ceiling by a spring with spring stiffness constant k. A penny of mass m is pl r/ d/oen/gu9faced on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. Th;ty c bwh+tp4zx s - +s.4r8h3bb,vuxue steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncinbb.hs 4x8by -cs,3uwz x+uttr;4v+ ph g 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 Foxn93c* fm1a2hl-ceg jy;a ; hig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear 19jhg *n2;acha;3 ylfx e-oc mmodulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz