Give some examples of everyd8frh2dac8io a4 :au +vay vibrating objects. Which exhibit SHM, at least apprc8 fiv aado2uh+ a48r:oximately?

Is the acceleration of a simple harmonic.bwy-if r+-8z2f eq)6uabsji oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approxima(a/9)*k 3 vaxswz4xqhg tm, fgtely simple harmonqs9 /(am3ggtx af*)x4hvzk w,ic.

Real springs have mass. Will the true period and frequency be larger ;jv.6c:vc4 ck zdr8q 0dyve2lor smaller than given by the equations for a mass oscillating on the end of ac2vvcjd:;4 ed.r6l8 0 yvzkc qn idealized massless spring? Explain.

How could you double the maximum speed of caq9bnet/t( gm:6d x.a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the ho** ry2 fuft jut(x+nw o/n:s-vok of a vertical spring scale, and then is released. Describe the scale reading as a functiyf(v-tw/ 2nun*xtu f* :s roj+on of time.

If a pendulum clock is accurate at sea level, will it gain o x x2)eyr+ms,ei w:-pvr lose time when taken to highysi2 vxw :-e,+xmr )pe altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). Hei ifbvbk8tt:-pru+ z 74t ) hk5kee5;ow could you estimate the height of the branc k zhfi:p5tutb8i r7)k ke4v b5;-te+eh using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shaekg;cj5jh dau+ * + kh(jq4c9pke the pan at a certain fre;e(5 dccqjg+h u*9ka+jh 4kj pquency?

Give several everyday examples .x0 icf3 xssx2uwe41w of resonance.

Is a rattle in a car ever a resonance phe jk oh y33j.4r ;l+at9frgqp*enomenon? Explain.

Is the frequency of a simple periodic wave equa; )+wy;zwqg n:on9.wem:zf co l to the frequency of its source?9; )cz .; :emo+wzyg:nww fnoq Why or why not?

Explain the difference between the speed of a transverse wave travelq+k6 j zxf18caing down a cord and the speed of 61z8 caj+qkx fa tiny piece of the cord.

Why do the strings used for the low 2c3wgq 8-tkwrest-frequency notes on a piano normally have wire wrap23k8cg w- qtrwped around them?

What kind of waves do you think will t t7 hc3up ,h;8) s0cnohm/uyydu7,s lqravel down a horizontal metal rod if you strike its en7sq;hn )7d8/ y0ytcluc,hpu u o sh3,md (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in tempep wza2ff, llh (tv+xh:m-0mo-rature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves iof0zp :-hv-lfltxw+,h(2a mm n air to vary with temperature?

Give two reasons why circularlq:xhcnam o(1rk ;t 51 water waves decrease in amplitude as they travel away from the ct1: (;akhr5xnm1l qosource.

Two linear waves have the s 88ncwtzfk.9g4gx9f 0kqyj j *ame amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy?ygc 9gj80fwftz.48 * qk9xnjk By what factor?

When a sinusoidal wave crosses the boundary between two sections1zqx uo 6og,r +:7exbc of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do o,xb+ zxo7 c6g 1:qeruchange). Explain why.

If a string is vibrating in three segments, ,2e(zyz - ch8kfsxwz nn2 7.ggare there any places you could touch it with akxz2( ,2sy ez- 78gw.zhf nngc knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of idew -v q98x:tancident and reflected wd va8:w9e xq-taves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from ob7icv n /t:5owne place to another, how might we determine whether the energy was being 7nb5ocv/wi:t carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the totx.a qy 4qb/h16jg j8voh4pjk/ al distance it travels in one periohgj486bpvjjy1. q// qk4hoxa d?    m

  An elastic cord is 65 cm long when a ucul 3m4 ,57dv( cm cejg*g4h9e xtz8fweight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “smjdeg4 uvu*8 cf7t(43xmgz, c9ehc5 lpring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gjjz*w,vda - h:n+ t)biets into the drn jwt+:-z)d,ihja *v biver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale sj km8y.r-qus*tretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring s.r8-km uy* sqjtiffness 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 when a mass of88 igl2d r+ciq5ns: 7lemyt9i 0.60 kg is hung from it. What is its frequency icltmsli5 y :87nd+ 89erg2iq if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times t nj: v*y mjgl8+ kz2yy3= *3z+myyjjk n8:g 2v yl0,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 caqwoo7hb/g zm 7a9+( qmjhh94ojm/7w lught in a spider’s web. The web vibrates predominatelj j/hlz9(bmm/m+7o w7wqo7o ah9h4 gq y with a frequency 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 vibrates with a frequency of 0.88 Hz. W4x l sdc:w+5w6v1lqbd/v zd5phen an additional 680-g mass is added to m, the frequency is 0.60 Hz.4zx1:l 5q +wbdscv6vlp dw/d5 What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 timn(5hk(qz n j/yxp+j: zes per second with an ampli5+qnn(y: jz zx p/kjh(tude 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 /l d 84xntavcq,4)et2s91 hyc9ivtms half the maximum valu1 vq 4)nxd/ ,2avtct9l 8 sces9mht4iye?$\approx$    A

A mass attached to the end of a spring is stretched a dis j-;oozwj56m0n,qew ptance $x_0$ 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.-*jx(ukt5n w2a u gl3m315 m. If the spring is stretched an additional 0.130 m and released, how long does it take ton xtla-g uu( m3jk*2w5 reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spriv 9mhcs 0k*k*bng stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is movi9sb0mv *k kh*cng 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 0.200 m to “lv)a vl krlcb6z8x(l-l7;ztw(oad” a 0.180-kg ball. With tc- r;z vb)l 7(xwlk (vzlla86what speed will the ball leave the gun?    m/s

  A mass sitting on a xvi)zh,0dpxwf,mdp+;az2 byy5w+v 7 horizontal, 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 released from rest with the spring compressed, the mass experiences a maximum acc7y,xa+,bz0vi )wpw;+ d y 52hmfvzdx peleration 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 vibratesed o,2d2b+1u sufs sro3hlj( 9 according to the equation x = 0.45cos6.4t where x is in meters and t e+dooru 2susbs2 j df 1lh(3,9is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equil(w33b vif4t ygs,pg c/ibrium is the energy of a SHO half KE and half PEtgy i4 p/v(3,wbsc3fg ? ±    A

  If one vibration has 7.0 times the energy of a second, bux0 h+2n/d xmdujyd-a 5t their frequencies and masses are the same, what is the raaxx50dd-m +2 nd hjuy/tio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertij4u02g y/v)c jcl pekmfr:; 1vcally hanging light spring once every 0.65 sk1m ejvp lj/c) 0fy2;ug:v4 cr.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, efb7g 3*y py/tkach with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibratgf/*p 7yk3ybtion?

  A 300-g mass vibrates according to 8 j:msrinu,0s88bpzt the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determi rn s,p8ziumtb0j:8s8ne
(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 A and B. For each, what is/9e+m,bn9w xo:ehqfj
(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 = 124*0biw xh +kwhk-lwm/1 N/m) is struck by a hammer, which gives the mass anw x0hw *kw-il/kmb+1h initial 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 with spring stiffness constant 305 N/m vibiy3(s d)p0 dz*)vwmp eegcm )*rates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passeppd sew3m0(id *mc*))g ev) yzs through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffnessqh dd.+xe0ehj 5h9kv:y .c hl:ienf5- 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 blodpn-m9 wy9/n, x hxtp:a 3m9hrck attached to a fixed horizontal spring whos/3px9,yrtx dn -99ah m:mh wnpe 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 withl 5 1m)s 5vvpikz(3xzx mass 65.0 kg jumps from a high 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 brid)mk5z3p xvx i(s1v5lz ge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactlyrvr )lq/9:ia/wq fd 6 wad9ts, 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum beyi6l3mgcx 2u8idr 5c5 if it is to make exactly one swing per second? (That is, one comp6l y53rd2m ci5ucgi8xlete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where thsjqmso-oou*( +.i o6ce acceleration of gravity is about 0.37(6 m-qojsi .ocs*+uoo that on Earth?    s

  What is the period of ak*o5fbrtv0wq+ 21u ju simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendu 0g v.,;lx o.*1 fdsdmi2fkhhklum bob has a mass of 365 gramlio*1dfg2sd0kv, .hfh m. kx;s, and 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. If th1 k *ljdicbx-w.g;zp; 8uoj,xe clock loses ha,g.x;xi8c u 1lz jbjp*; d-woklf a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed + y)xgiq 2d6cha)fz 3bdm0yt7$v_{max}$ 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. dz1f 5ya.wbmtn:wqz 6m9wf7l(5ke 5b At it is released from rest starting at an an5y(6 nefq5: .zfk7b9wwabwtz5 m1lm dgle 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 boat ev:ur lk t6p0i3wjh+isl v5n.r8ery 3.0 s. He measures the distance between two crests to be 6.5 m. How fastpw5k i.r+l0us8rhlv i6 :3 tnj are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travei8l ++sce zx 3 y(z y(4mgu;pqgalg83zls with a speed of 343 m/s How far apare8g3 qglz8i;( lxz suzp4 gay+m3(y+ct are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies betwee mpoah.q5;ke -0 xaim1 xie+q:n 550 kHz and 1600 kHz (kilohertz) and travel with a speed of qx5io:a .1pexq0 ekmi+;am-h$ 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 longitu fwt)mpia 4o2s+j l.t99uu ej; bqx3q*g:2bzgdinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense ipth u le:,f5 v;zph7.as the other. In which rod will the speed of longitudinal waves be greater, and by what fact 7i,hpv;p.flze:t5uh or?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the tens4 t:,/ lcrb zs7hkiz*mion in the cb/lti:c,*7 kshzzrm 4ord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by 0pp-uv w l; xq+j/n*xva 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 termina/x ;w0pqv*pxu-n j+l vl 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 gi n -)d,j5acshis ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s laterd) g5j,-sicn a. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and thia x1fhj- e.bt3j1cp5ws difference helps in locating the earthquake “epicenter” (where the disturbance toax3 cb .11pjjfewh-5 tok 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 sinusoidal t7p,vc8 d i2zar2 aa/taransverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually incid27pta r z28caa,/valude 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) ;vsdq db + /1mndx-d4nthe intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two poind1d /qxvnn;db-d+ 4 smts 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Eart 8v,zor(dycp trc n,,5h is measured to be ,rdp, (vy rco,t5nz 8c$ 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/qv,h1-b tfoak2unaqi b3 n, - through the same portion of thnv2-t3auiobqb/1a -h ,k nq,fe Earth, but one is carrying 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, l :7t jfu6dkz9but one transports three times the power of the other. What is the rk76l9t:fduzj atio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total verticf gj.1celhbdmv87k yh: 5p(+z al 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 whaj byep8dm l.7k+5 zh:vc1g(fht factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketkpo2akzn;;je k1xv 9 1ch the shape of the stri;o ;n9k j12ex1vp zkakng at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental fre- /slz48qz-c0zm7c7 q hsngbequency, what are the frequencies of the first four ha7s-4 bmez cnz0c-shzqgl q7/ 8rmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when( .ouhhcp(pd: unfingered. At what frequency will it vibrate if it .h (:uopcd(hpis 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 re(nd rid6ddm.)26 arsq sonates in four loops at a frequency of 280 Hz. Name at ledaq.dr6in6)sdrdm ( 2ast three other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a st/smsbid3k x(* rs f-/pn+c3 wgring is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent nodes?rpc+3-ssxfd n /b(3sm i*w/gk    m

  If two successive overt.( gbtf(zze7; 3sk hj)eswp3zones of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamenta 7tzgp b)h.j (zfz;3(kss3 ewel?    Hz

  A guitar string is 90 cm long and has a iyb5acg 4e 66 .l0ua-b9czesgmass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tenb 9ac6g-y u5be .4c6iea0sgzlsion of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 2 fg+y8)2cqyiwz 11z /h zhjpk*i16ooi00 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be chanc wpo 6jh 1gzz* q1h1i2+)yok/zyi8if ged to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed tdt wst ajz1j5a0 tzkkmsw/7m:*8m :+io vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percenttmmiwstd w:zm0:jjz85*a1s/ ka7+k t should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is / zp6gbm,1 uawattached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length ia/1m wbp z6,ugs $3.9 \times10^{ -4}$ 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 lengtx7/wdyik3;k(n( kg i vh of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varykwi yk7k/x g(;v n(id3ing L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just t: rrvld/kajqea g y 18ex9.)sr2x u6g(he 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 speed of the w.a/2):6g d akrx1exv9 gq(urer s8yljater wave?    m/s

  An earthquake P wave traveli0;h:) 2zrh(xmrydpe.a r 1iff ng at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundxh 2):d(pm;f1izrhf. yar e0rary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” wx5/mmeuy0qkh0xb. 6zu f/o o tmki bxpc;;5+ .here the velocity changes from 2.8 m/s to 2.1 m/s If the mpzbhu cm/x6i0o.fqo50 mb ;x uy./kt5xek;+incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in wakc q 4d)3 .jpyyqi8ny/rm air when it hits a layer of cold, dense air. If the sound wave hits the cold yqn d.3p4ykqy)/8cij air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of 9/yw3nty-x ke+ fcd3na l6oc+rock at a 3a3fednyow+ yx6 lk tcn9c -3/+8 $^{\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 +ron( cr(1+f1r8:borr hjkhbmanual, the dish has tor cn1hobj8+r+ fbrh 1rr(o: k( be pointed 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 au1/w, nbqam j)nd velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, peja/,bu)1mw nq ople observe an unusual decrease 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 constant od /2(sx4esq srf 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 eq42/( dxss rs(approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from aj u /c2j)nfck(zq9w8 msj;l8 p window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves lksfc)j98m2l;jj/w(cq z 8n puike 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 freely hanging spring. The masg 1f.re ,jvus(s then fef1, (uvjr.s galls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a n 5wh;man0jv,huge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m.,w5nmjvh0; n a (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 coffd7, 8u.m 1q iijrgiotl7zcer2+hf25z ee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Esti i,8fh2r+51 zr.goem2 zjid7 lqc 7utimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm f 5duw093bxj7h: jul/rsu(q bg4 vk g0:vb7bhdrom the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be j7b xdbg04 ru: ( 3:svqhbh9 jk70ubg/d vuwl5the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equatixx uuffdw1vd1k 0:jj )n4k.vm*qj;v.on x=0.650cos7.40t where x is in meters and t in secondsjx;jnmv.:0 4qfkv)dd *kf 1j.1uwv xu. 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 oscvhnv 0s+1 zf 2myr,z *:pec3tfillates with frequency f. What is its frequency if it accelerates3zsy mr0fp21f+ c v,:v *ehznt at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg +ierm i m7)pch4ma/z/pe7v b)man stands on the raft, it sinks 4.0 cm deeper ieim zprvai)hm / c/e+p 47m)7bnto 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 are tuned to play *n*tz-glg *wz qi5l8u(.iku 1 vijlm)at 392 Hz (G) and 440 Hz (A)l1qz muigli*)tug*l5w-(k.iv8j nz *.
(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 *d ++(i5hn*5 k/sgynfpi v3x n bjz0ectwo-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the rafn0xyg5+dhizbv j3i *skcn+*(/ n pe5tio 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 ar24xao +rbizh6id*9k frequency of 264 Hz, and the tip of each prong moves 1.8 mm to6i doa9r+i4*rkzb2x h either 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 hak l(d jdn7o30clf+vb1rmonic motion 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 losj 3c(0dvfl1dko 7bn+ le contact with the board during the oscillation?

A string can have a “free” end if thbtig,* .ut(z hat end is attached to a ring that can slide without friction on a ve. uz*t(t ,bgihrtical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takes b )jo 1+*kju k9mgl. vcpx66qm1.00jjvbk1cpl6m9qgo).6 * x+uk m0 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or can s,0nscbzq+ jb 9wing as a pendulu qcs9 bjnb0+,zm 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 xdm3xi/ s fm3,255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Whems/m dxx,f3i 3re will the two pulses first meet?    m

A block of mass M is susnv8 :th da.z o-z,tl(apended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitudd az(8to- t:hn.,a zlve 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-br v-u)3jrcj(mcb7di2f 8kvt* 4p 9iwkg car at the junkyard. The steel crane cable is 22 m lonc9jutmrrki7b-*43wvci82 (p ) d vfbjg and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (wh/ l8dge2r+6y z)mbhkt* ymq(sich also gives the dimensions of the block). You push it sideways as shb) +y2 8ey sd /qtmg*r(lkzm6hown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz