Give some examples of everyday ox2: f1-tg.j lzt6lr nvibrating objects. Which exhibit SHM, at least approximat6n tf1glrj:l .ozx2 -tely?

Is the acceleration of a simple harmonic oscillator idc ti8f:j6-xchf4m/rv 5f.sb3/ muaever zero? If so, where?

Explain why the motion of a piston in an automox2 oh0 jiu4 -k w0ot+h5h1jloqbile engine is approximately simple harhhwjxh ooujt0-k 1ql 2+54o0imonic.

Real springs have mass. Will the true period and frlqv p+( di .tkoz)nny; cd3d,)equency be larger or smaller than given by the equations for a mass oscillating on the end of an ideaz,d(l) )+qv3 dp kdni o.nty;clized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscilla3 y*e(sof24x ohab g.utor (SHO)?

A 5.0-kg trout is attached to the hook of a vert ln,i96u/qiycm 8h2mouf. r/+ggmyb1ical spring scale, and then is released. Describe the scale reading as a function of time 6+oumi.mg q8l9rfugy,1 h nic //bmy2.

If a pendulum clock is accurate at sea level, will it gain or lose time whe2nq 2czm1zzfy o2 ,a )vxxs/6pn tak/ma2 qzcsnzp6 o1 fx2 2vz)xy,en to high altitude? Why?

A tire swing hanging from a branch reaches nearly to y928 fuhi z*tnv0+jax the ground (Fig. 11–48). How could you estimate the height of the2 h8izvy*a9+funjx 0t branch using only a stopwatch?

Why can you make water slosh back and forth in aghlfw;.*3 v8q-kg)aya enz jl2d8jp, pan only if you shake the pan at a cerdy2;* l agw8klz3.,h) vpaqf8jg -nejtain frequency?

Give several everyday examples op.k f(ga4 i*fff resonance.

Is a rattle in a car ever a resonanr2zj-nb1/nyag bpb/ n fa30tp jh4uw7) m0 n6nce phenomenon? Explain.

Is the frequency of a simple periodic wave eqc2yednv w61 1zual to the frequency of its source? Why or why vw1dzce16 ny2 not?

Explain the difference between the speed of a transverse wave traveling down q(jc3u 3-x 4z0f :abckdork/ na cord and the speed of a tiny piece o4x jof qb/ r0:c -c3kd(zaknu3f the cord.

Why do the strings used for the lowest-frequency notessrnswb; w;3 -s on a piano normally have wire 3rssw ; wsnb-;wrapped around them?

What kind of waves do yoo v09er+gkoyda,e:hys :( :l tu think will travel down a horizontal metal rod if you strike its end(e::k0e,:dyah9toyr gsv+ol (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increa3p/ r i0t z)6gqqq,lpmk:sak ;se in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to v;k3,a0tpg/)q l p:zq i qsrm6kary with temperature?

Give two reasons why circulaw (ihog*h/p8lr water waves decrease in amplitude as they travel a p(/*8hh wolgiway from the source.

Two linear waves have the same amplitude and speed, and otherwise are identica1c6 w+y(mnw g .ignnl/b20: tk kc+cxtl, except one has half the wavelength of the ot0y l( 1:g+xk6nmct.bwt n iw/c+n2ckgher. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in(1/eh e5bwplkhkt9 imh8 w c72 Fig. 11–33, the frequency does not change (although the wavelength and /ei1h9kh5e(w mltb28h7pc kw velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could touchi5pq+. v;t gzo it with a knife blade withzv .ot5qg ip;+out disturbing the motion?

When a standing wave exists on a string, the v4kf+g auwp3q5p5.f9iza)xg vibrations of incident and reflected waves cancel at the nodes. Does this mean that enerv5 .f pf4z9 3ggqa k5ip)uawx+gy was destroyed? Explain.

If we knew that energy was bmqv (y)s. r2 f4bg5 .7+od/evscyahcheing transmitted from one place to another, how might we determine whether the eyc(gvvyq2e / + )ds.ho mb h7sfcr54a.nergy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, 0ft 4bvqhp14c p(3f0a u) emanwhat is the total distance it trn c0v)3 me0 pu14(4tapbqfa hfavels in one period?    m

  An elastic cord is 65 cm long when a weight opvii h.v (pm g :qh8+we8,c nuzd0d2;xf 75 N hangs from it but is 85 cm long when a weight of 180 N hangs fromqpdv(in:;w0uxdh +vp ic h2,8.m e 8gz it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drivem-u03 ss(j pgpr gets into the driver’s seat. If the car goes over a bump, what will be the frequency of 0g-s (spujm3p vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fis)hh. mo d 19snp/yga -r2ji*dah hangs from it. (a) What is the sprinhny-.d )9api2ja1 m r*ds g/ohg 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 when a mass of 0.60 kg istt138y.*l iynfqyp-pvi)4n3 8b io q z hung from it. What is its freque 8v3*i yq8z-i p)ty1y ibf.4npl3nqtoncy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 ah yrafj,2t7+e t times t = 0,t = ear 7j2fhy+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 vj/ yu5b9-.rl; mrben dibrates predominately with a frequency of 4.0 /m j -d neyrbbrl.;9u5Hz.
(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. When an ab/hgnc05 d d5ao-e1bjj x.0eydditional 680-g mass is added to m, the frequency is 0.60 Hz. What dc o 55e0/yn.dajx1egh- bbj0is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrate,ha-lb 4xqt 9o5ewe .ws 3.0 times per second with an amplitude of 0wbq,etw 9h aox5l .e-4.13 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 ;n( /u1k91qpe ire yooq1be;lthe speed of a SHO half the maximum val1;ope/ rk;q(19eunqil y be1 oue?$\approx$    A

A mass attached to the end of a spring is stretched a distasit h )u8:.of,*t 2pga4hnudp nce $x_0$ 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 strltu gt 4t6h/* ub1)nf/gr7 rneetches 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 theutg*e 1fnrub7/ht6)/tr4n l g (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stif 4nyel -c;,vx2 w7n-9s kizibnfness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its eq4b;--wnk vz2,e xls7i cy9ninuilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the springcrg) y7s v8 wp/ow pfv(:1lu9x of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speec7:gw 1(vxp oly8 s)rvw/u9pf d will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is atxrku 6.mq v;wdp4i/3yg ywrum hn4(pm;c4,j ;tached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is rpjrdi ku;3;m/m, q w nvgh4; .xumyp(w 64rc4yequired to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibratesb)q n/0kuh -jxwx eb+: according to the equation x = 0.45cos6.4t where x is in meters and t ijqnx+b k/)uhbe -0x:ws 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 equilibrium is the energy of ;tory 8.tc5lw a SHO half KE and half PE? ± tc;rotl58w. y   A

  If one vibration has 7.0 times the energy of a second, but thei-(2qohcqxid 0ty -p3 ir frequencies and masses are the same, i0o-(c-2qt ipd x h3qywhat is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangingu 9. , ixz4tas;1t:eog*oaf xp light spring once every 0.65 t1i*zox aapgoe ;:xu9f., 4tss.
(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 support f 16n53-wm0ghcuv/xy sas3wked by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequencywys3mxc s1hv6/wk-5un 3f0g a of vibration?

  A 300-g mass vibrates accord cfktt+ po-ou8r(;hk (-ts:rs mb 35ohing to the equation x = 0.38sin6.5t where x is in meters and t is in;t5 3(ho-c:b -fo htsr+ 8tksr (okpmu seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two exampl1iq yw7qnk ocf:k9b+-es 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 =ft h1+y 5sn(fm4gfez. 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96mf ( +gz1 t4mfn5ey.fhs/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 t2+eams, .m t pg1woxnh,f )p;vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point ( 1+wgemf,hxatst ) pmo,.;np2x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness constants5u7 u9x:ems/uiyx mu : $k_1$ 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 horizontal+np)sjxd y q91 spring whose spring1sj9+)qn xp dy 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 br),j(a:t flm:se d*czu idge. 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 :juca)e d tl*z(fsm: ,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 in exactly 60 ddh d4rrjm w9 ,-7/cphs. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it isqhoirb-d1qe od/(( -8b6xqx 1oem tr1 to make exactly one swing per second? (That is, one complete vibra -qo1-q1ho qr86et xd( /xb1bmdioe( rtion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s f8bi:; fusag2/ 3adwrv a8se(on Earth. What is its period on Mars, where the accgaiwd;3 /:abar8s2 fvs uf(e8 eleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pe cj07ll;q4y+m1prd iandulum 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 365m9dpct*9q84r l n h4i6afc0py grams, and if* 6c d8 m0hryc4il9tnpqp49at 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 the c-cm .lby69ql tdf3;lrlock loses half a minute per day, how should you adjust the length of the pendulum? shortened by flcb;3l-6lm. tyq9dr    mm.

Derive a formula for a8ofj;e;g+v e the maximum 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 oscxqmq4s gi(a+2 illates at a frequency of 2.5 Hz. At it is released from rest starting at an anglqm2 +4xq (asgie 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 anchor:fr+/ 4qv9 qrav u6mxhed boat every 3.0 s. He measures the distance between tw+/rv:faq4r xhuq m9v6o crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air ha0x5, bmfxpo+s s a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compre5f0+p so,bxxmssions)?    m

  (a) AM radio signals have frequencies betwel,kq 9u* 8-zil2bazeeen 550 kHz and 1600 kHz (kilohertz) and travel 2 llz9z8ei-qe*b au, kwith 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 longitudinaa3*/9 fz egkbwih(g/yl waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulusshkr-nym. 4 1,nqkd* l, but one is twice as dense as the other. In which rod will the speed of longitudinal wadmk rs4knhn,y -1. lq*ves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betwyz 8z -o(mbh gdengp0d456v/ceen two supports 28 m apart. If the tension in the ce ygvnp/m( 46hbcd-z zd58 0goord 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 a hj3d8po 9p(v 1dmq ;0fooes;psteel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the9dm8q; o 1ohdp (fepop;3js0v 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 *aez)b(:5zt ez a6k kvhis ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below *)eka vt6z: ez(za5bk 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel k;* akxndhk;2at different speeds, and this difference helps in locating the earthquake “ khkk2x;*;dn aepicenter” (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 sah-p h-7i to5h8bqru9 inusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture o hrq -tpo5ab8 hu7-hi9f frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) k690,l.fmma x gqfl5 cthe amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 ,9k mgcqf0m. l5l6afxkm and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing th32of hc/h qn-x8w7lg4 1wn dumrough the Earth is measured to be w 2fxd1m qhhn c7wo/-lgu43n8$ 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 er p.q u(i:y;6:/q q9atnpoluthe same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplit;.npiue::o6 qp9qay ( t rluq/udes of the two waves?   

  Two waves traveling along a stretched string have the same freoyi l; 7vcz.dukk940 squency, but one transports three times the power of the other. W4 iys;u.vo7kzcl0 d9khat is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond 426ail zah(7mb q8 h*tw4dl.6 lpehmkis observed to move up and down a total vertical distance of 6.0 cm, from the lowest to them(ia pewhmbd4 24q *lllt6z7 .k6hh8a highest point, 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 movi j91 4bue/jl3 axosed)izgn1 rm /l:m5ng toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fiab/lum3i9eo gr14z 1l jesx5 jdmn):/ g. 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, what ar/ drf;pe+usoxx i2c 7waj168l e the frequencies of the first four hao1f s;6/+iwd xxpc2 jraeu7 l8rmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what fre-44;y61g xim.du*nh stlvi adquency will it vibrate if it is fingered one-third of the way down from gma.d4 -u4hisvlnxty16;d i* the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates(/sj) 5sdlmtu in four loops at a frequency of 280 Hz. Name at least three other frequencd m/j5us )l(tsies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency64akss aq wnt*65r c(bs.by;r of standing waves is 475 Hz, how far apart are tw4t5k* 6nsr6 ysbbr sw.ca ;qa(o adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what ih g) ub-aits vm4 ,8mw9o6p4jws the frequency ofb) wpivuawt4sm6jm-ho,8 g94 the fundamental?    Hz

  A guitar string is 90 cm long and hasdzz,0yzw d 6*v - 3wlzsn8npqfz.iq -5 a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string ip n,zzsd.zzl y-fi-8q5 0q zwvn6 3d*ws under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, b8nv .7zcv 3cggut it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correcvz g7n.3ccv8g t the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but qn,)z-u;y pirg+: gyfit is measured t y:)gin+,r-fgy pzu;q o vibrate at 205 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 small-amplitude mechanical 60-Hz 0/w1f8xny wknd q(jr5 vibrator. The stri nq1 k/dfnr5 8wjxy0(wng’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted 1q6p4em/nnx mby moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 6pqn e1m/xmn 4m?   

  When you slosh the water back and forth in a tub at just the rnjy80k)da d;t ight 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 i)jdn8tky0ad; s 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary wwfam7em v,: ;lxm3b )dithin the Earth between two kinds odmam:b)wmf ;vl,73 exf material. If it approaches the boundary 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” where the velocity changes fro/;qwyw,y+hvb.k ul t8 m 2.8 m/s to 2.1 m/s If qw +hu k/y;y8vtb.lw ,the 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 warm air when it hits a /r.1i9da7oe)txc w(7pt ealzlayer of cold, dense air. If the sound wava/r9xao 7 )tliet .we1pc7(dze hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquakefx1+o gc7-qsi1 q 4cvdge12kx wave strikes a boundary between two types of rock at a12c- q4xviecxd ogfgks7q+ 1 1 38 $^{\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. Acdx-fdu 9jun4,cording to the user’s manual, the x4dnd-9 fuu,jdish has to 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 and velocity ccaiu 7i .d5/byyh;q,750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of ydcc. bi y/a,i5 ;7uqhthem attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffno;hlt*aarqou2b p857 ess constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 outa8;op7qr2bl 5h*a 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, whichxym( x; /+ nv:ktrbm+v stretches the net 1.1 m. Asrbmxv+ (x:;/+knym vtsume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freelypw: laj49x ok) hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequencjx 9l)p aw:o4ky of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), c 5rn(pn ftnww 6m(.,ymompressing twn( nwm6 ,mfy np.r(5the spring 5.0 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 (diameter 8 cm) b+c5. * 70y /um4yex(hugug pmfn7quoat just the right pace of about 1 step per second05e7u7 up n4hxcuybgo. mm(u*gfqy +/, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.kqjcx zl9 -g +wfw/17qcl6gj:8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitte79+gl1kw6g cfcqxz-q lj w /j:d?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x i/jxbt-5 m*w0n -nkcgy s in metexgwyn mjc/*0 t-bn- k5rs and t 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 frequency f. What is its frequency if it acb4q mqz5+cs td)egaz9i e:zu8rr(o-( celerates agu(+zq5 cd ib :sr- oz e8(r9q4et)mzat 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft ,ngfjzp4650z3h11z clkxmr m, it sinks 4.0 cm deeper into the cpmj zk5g,0mnzh 4 61l3rzfx1 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 mus q8qbzco+fl ajy945;cical instrument are tuned to play at 392 Hz (G) and 440 Hz (A). q 4yf+z5ao98 lc;jqbc
(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 stretchedyo gyx2yky04f7b( n)9ckn s3b two-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 ratio of tnfgy03by9 kxy c2s)4(k yb7 nohe 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 frequenlg2s14a bdeq y nj4b3+cy of 264 Hz, and the tip of each prong moves 1.8+1qa4b b3dge n 4ysj2l mm to 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 harmonic motion iwgc5k 4ad(fg) 39u9e g om*ikof frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board caf9g4ckiik 5od(g* uwge)9m3 an 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 al (ef 12.i gucww*cbuia(f)dt 16bnd4 ttached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelen*(6 i ifbdu gd2b1l41( etcw) c.wufangths 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-wq-s/evmx95pj av1 8pv ay swing takes 1.00 p/-m9 s1q5xvv8vapej0 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 mjn2jd 5 -wjzg, n hqn,m6huc/78zd a/a spring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the hdw,z/ 28mn qmzdh7-,janu6gjncjh/ 5 orizontal 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( 7-8gwiwb- kh 8vtgkp32fcb y of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the oppositekgpy 8-v2-wh gkfwc7(83t bbi end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spr/ijqirs9.4a s ing with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of osasqj rs4 ii.9/cillations 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 junkyardqh 2ets/vk( )w k,io)cphsxh8-pdd+ /. The steel crane cable is 22 m long and h)p ph)x+c8s/htqhk2 i, v-e/dokws (das 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 (which also gk a/2fl3kqemldn 5 (9tives 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 (Sectk/(2ekt9 mn3aq5 fdllion 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz