Give some examples of everyday vibrating objects. Which exhibi*-e23byrc(f yqn9ytvt SHM, at least approxima*q2( y b3tcn9fyyre v-tely?

Is the acceleration of4f,f x2 xg6 xuyb0drjqt 47xs2 a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is bw:c-3 hum fz1approximately simplec ubm-h f:z13w harmonic.

Real springs have mass. Will the true pw m20kk 6mtw1(ml*wqw eriod and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explam0w1mw6 q(k*2w tl mkwin.

How could you double the maximum speed of a simple harmonic0-z o jcl0y+wd oscillator (SHO)?

A 5.0-kg trout is attached to tyrx, u.ufu 2mkvl(2j; he hook of a vertical spring scale, and then is relejru;yu2 (,u vl2kmx.fased. Describe the scale reading as a function of time.

If a pendulum clock is ac nvp l7(fwh r3v+9yy/ qpve1b3curate at sea level, will it gain or lose time when taken to high altitud h /791bwlqp3y3pvyr ev+(n vfe? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fts m2q6dwhbu-1uhn4n j-dt- 0ig. 11–48). How could you estimate the height of the branch using only a sto0-24t st unqhhmdn6db1ujw-- pwatch?

Why can you make water slosh back and forth in a pan only if you s0i6 b8g3; um aw/p23bnyqhsx hhake the pan at a certain frequency3 q8amn3yh6;/hg iw b2 xb0spu?

Give several everyday examplexhzc x. anzf0;vm* 4:os of resonance.

Is a rattle in a car ever a resonance ph ketafz17-ke e.z/,zqcq*gg -enomenon? Explain.

Is the frequency of a simple periodic rzt8c2x iqq3v38u jp hly73 .bwave equal to the frequency of its source? Why or v h.8c3byir3jl8qxp3qu7z 2 t why not?

Explain the difference between the speed oax6g5tj2* r7sexhw)im b3,; clg-l eoaj1jz8f a transverse wave traveling down a cord and the speed of a tiny piece of the cordmb ;ieg,6a*3ohx t rc jsw1l28ag-xjz)e75l j.

Why do the strings used for the lowest-frequency notes on a piano normally laxwq c4 3a+mt;qt2w1 have wireqw2wa4mc ;xt +lt 13qa wrapped around them?

What kind of waves do you think will travel down a horizontal metal rod if you p fsg4n7g+ bfcio*rw;l*x,:dstrike its end (a) vertically from above and (b) horizontally parallel g f*l rw 4:gpi;n7 db+x,*csfoto its length?

Since the density of air decreases w4m,az9 /qupn+wfgn lka+2ff620al dmsy68k gith an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?6knwyg,nf4 / a+mqm zaldlkp608fgu 922sf+a

Give two reasons why circular water waves decrease in amplitude as they travel a7 l6vfw/9ml d b6b,fakwa 6m a/k9d,bwlvf76fbl y from the source.

Two linear waves have the same amplitude and speed, and otherwisv(aqjk fys 1a-u is)+)e are identical, except one has half the wafi)+uysvj)1kq- a (sa velength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary bv uq+mmfs51u 2/w4graetween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelen mv/25w1gm+r uuafqs4 gth and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places y: pu9i.ejk2zcou could touch it with p kuj 9icz2.e:a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and refl /k,.btcv4+ij .q8 7egef sqdqected waves cancel at the nod7+e / b, vjqdk4qsq8cf.ge.t ies. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place tgvnmyi70eb a a ,9zy0/,67 1atrsfpqpo another, how might we determine whether the energy was being carried by particles (material bodies7aa 0z76tbpvnmiy, rsf0/9 pea,gy q1) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, w+ww h4+9apsc;zu:26 rb v(wkb/kjdn)bucq b1hat is the total distance it travels ib;(bkkh6 d9 bp sc w uj)r+wwz:2u nc/b+v4q1an one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cm ldpusw ( 2m-c6qong when a weight of 180 N hangs from it. s(d-mu6 c2pqw What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 15037z+a5vwx+m iw5 svhf0-kg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what wilx mz5iva +5hfs w7wv+3l be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fq;0jgj.ngi x;3x6wi mish hangs from it. (a) What is the spring stiffnei;3mjw.jx0xq; nggi 6ss 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 whenvren 4di1 +h2)l1b:s+ cly (inbsoexut)4bh: a mass of 0.60 kg is hung from it. What is its f )y4rei)h ( :1d+blu4thenxnibo+s:blc 2vs1requency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at timeo.wkx 1b(r/ yss t = 0,t =bxyr 1 o/w(ks. $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibrates pred :wozmm vr6w5.vq8*g:tch( ryominately with a frequency5g*8 qmr vw.(wvm:hrot cz 6y: 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 vibrat6; fky*ed1 zpc 01keymes with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequencdez1c 61*0kepfkmy y;y is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0+ irt wu2s8t* fo/pgp:ql,xfx7.i d-o times per second with an amplitude otxr 8 :if p+ w*-l,dtq/2pu7fi.sog oxf 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 equil8zlvb *9lh2igibrium is the speed of a SHO half the maximum value?9blil8hgz* v2$\approx$    A

A mass attached to the end of a springfxpq0e;lj(l ah(1 o1g is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a verti1u 5f icss/(/1qaoeekcal 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) eq 1o15qs e ki(u/ceas/fuilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring sti w 8n.g74nriluffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium posit ng4li8wu nr.7ion, 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.f dj)s.. r *y;mx8y:)( z/sqa jk1lt ncah;gig0 N to compress the spring of a toy popgun 0.200 m to “load” a ; l*.kjcsdasxgy zfy.g)h( jin /)8:q;tm 1ra0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizo/pan9g lt.f1wlxv1k+ ntal, 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 relea9/pn vl kwx.tg1af l+1sed 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 *5 8j6on n5ywflzm.cquz nc ::according to the equation x = 0.45cos6.4t where x is in meters and t is in se nnu fyo65z cw* cmnj:z.5:8qlconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SH qw+mozc.1ucll7k+t * O half KE and half PE?k+ q*l7cotlz wuc1 m+. ±    A

  If one vibration has 7.0 times the pu wykuhrq 13y3l;06p energy of a second, but their frequencies and masses are tph;yuwrq ulp k3630 y1he same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin osk0as7 i. +nrmxzd z.r4cillates from a vertically hanging light spring once every 0.65 s.mr.k7xa4z sd +r i0nz.
(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, e, nb006doosk ohky(r8ach with spring stiffness constant k (Fig. 11ro,oobsk6k0 (y0nh8 d–49). What will be the frequency of vibration?

  A 300-g mass vibrates according tl1j x)9dvv/1nbq i)h fo the equation x = 0.38sin6.5t where x is in meters and t is in second1dl)ijqb v )xn/9 1vhfs. 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 A and B. For each,6 d)eyv : 0mj2vaf00xdm65 (kzvs o9wqof vq8m 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 horizo)ttofr02z8 ),slqgy gntal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2trz))oq g8l,0yf gst 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 cons q)nnoy-x434zyj hyd 7w4g*qltant 305 N/m vibrates with an amplitude7ynj4 l*qgy zh-4dq nxwoy3)4 of 28.0 cm when 0.260 kg hangs from it. The mass passes 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 stiffness co9fos :gqey:45txi2 a tnstants $k_1$ 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 blocmr0b8uru bo(.f ok82ak attached to a fixed horizontal spring whose spr8om8oraufr bu.0 kb2(ing stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching et xtavip 5vb8uxb6 2mj19*njbd071nhis lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculatee87u x*vt 0nxp j2vdbbbj61ma ni59t1 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 s. What i)0 9sg8a5 gs/yzsbaj0vu-y z ns its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exac.9 )c nk(mwyknk-(qsvf mi+ +f2k7ywftly one swing per second? (That is, one complete vibration takes exactly 2.0 s.)9kv c -m+nf.wm((k+wsiqk72y k) yfnf    m

  A pendulum has a period of0 7jfjpp;h,xv 5g nyw. 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on E5gfp wv;j0.7 jxyn,p harth?    s

  What is the period of a simple pendulum 80 cm lonzu-c aj3 ic(g-g
(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 h+ob ck 5.i.oy3xms.iyd-6s xvxc((j ras a mass of 365 grams, and it is ri+ob3(cxs.ms xjx -r5 kv6 .(y.dc yoieleased 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 p;ajs;z rwz f-1r+x:la length of 0.9930 m. If the clock loses half a minute per day, how should you+srz- : l;ja;p1xzwr f adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxf lj7chhj6-oqg 2.n8z8als 5 fimum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequep1j 6s0o 7inyk ejc7*dq:2q mhncy of 2.5 Hz. At it is released from rest starting at ak : q6*oe7ijp0q1jd csmhy7n 2n angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that waxs3z/ tq6 8ndj d t33/vqwa:kvve crests pass the bow of his anchored boat every 3.0 s. He measures the distance bx/zq3 dtt 38 /3v 6qajsdvknw:etween 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 9 8//rpyn+y fcgefp s9Hz and travels with a speed of 343 m/s How far apart are tsg e9 9n/ ycppfy8/fr+he wave crests (compressions)?    m

  (a) AM radio signals have freq9-qs4j7p e+t3p yo8 uamlliu5uencies between 550 kHz and 1600 kHz (kilohertz) and travey3jl us 7ea8pul4i9q+p- ot5ml with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in ij d1,v 09gfcx
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic rb 3l55t xt7uakh:7 kmmodulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater,3hmubaxt7l5 5k:t kr7 and by what factor?   

  A cord of mass 0.65 kg is strue)fl /m tbt1r m2jr8,8aqi1ndf,,fdetched between two supports 28 m apart. If the tension in the cord is 150 N, how lor1 /fnm)a, f 28d uer1j,dlmti 8,tfqbng 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 steel cab r z6uma//uvh2sc-cub.w w*(ple of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the c/ (r2b *uauv s6.pu/h-mwcwczable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the .o - v2x4ifebwsea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at -ib .2efxwo 4vthis point?    m

  P and S waves from an earthquake travel at differe9d g9; hisvfze(sc) ;lnt speeds, and this difference helps in locating the earthquake “epicenter” (where the ehsi (9 l9zvdfg;s;c) 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 s3apl m;/rx0lo*qe- zrurface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplir;plr3zexqm / - *ao0ltude 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) the amplitudebbq,k) )bu3wfs, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the b,f )) wbb3kuqsource?(a)    (b)   

  The intensity of an earthquake wave passing ow-8zhz5 - fvu 07eleqmx(ib 1through the Earth is measured to be z(vequx7z 1lh ei-8w5m-fob0$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portion ge rgcx5,7s2 z3lx u5lfbk -z3of the Earth, but one is carrying twice the energy. What is t,s53r zz3f l5cb gxle-7xu2 kghe ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have,rf2ll53sg9iy ukg* if, x/:c-hwh q s the same frequency, but one transports three times the power of the other. What is thlqif2rig5f3 x,,g h:ckylu/s s-w9h *e ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond i3yg2bqy j,n mc,( ik2 r;tv:mqs observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the hi2 i:ym,2c y (q b3kmtv;gqjn,rghest 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 moving toward each other. (a) (l6-qdp* ols ks52.ed6cw4i whciw6mSketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few2qd hl4w(6-6op wsd6i ewc* sclk.i5m moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what ar1 l nw0h uz+-1vnm4,4hlqjl kme the frequencies of t,mw104 + j-lh nuq4lv1 lmhnzkhe first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At whpl9os4n :nk 5k:puid +at frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wavep5dopuk:s ni nl4:k+9.)    Hz

  A particular string resonates in x;b vsvfy x,k0csj q l)-q10 bm:ecjorr q,)1;four loops at a frequency of 280 Hz. Name at least three other frequencies at which it wills;ocqqvxr;)1el jbcm)kj-,:r fv,yb x010 s q 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 frequekf:i vs:eg1 to1wv4uz+:q + hrncy of standing waves is 475 Hz, how far apart are two aoz1qsh1v: erk4 gi+::tfv+uw djacent nodes?   m

  If two successive overtones of a vibrating string afp -cc/qwau0;8bl sy7re 280 Hz and 350 Hz, what is the frequency of the fun 7 q0-c;upw y/bclaf8sdamental?    Hz

  A guitar string is 90 cm lonaefrl)oyr z/ob5b,+k u ,8m0tg and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two eyk ,8azr0,)l5obb+rto fu /m overtones?    Hz

  A particular guitar strinzjklh*e16jy5d0al ax,w5 vcvp36t e 2g is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tenjyv5dz 1vl6x phlw*k6 j,ec3t5ea20 asion in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, bu )qcm ; ro(w2c68bcpayt it is measured to vibrate at 205 Hz. By what percent should the tension in the mrc);y( cqoap86wbc2 string be changed to correct the frequency? decreased by    %

  One end of a horizontalb/7ar7d n j(yhvam74d string is attached to a small-amplitude mechanical 60-Hz vibrator. The stri 4d7ra7a (m7dyn/h bjvng’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 len qvn18 )9vsyffgth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed aty1nqvs) 89ff v 0.080 kg, how many different 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 31mb1iow9 zyntub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave ininz yom31b19 w a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave trhcdq: kiuz1 o(k84cseo:o+j0 v( go g,aveling at k.0 km/s strikes a boundary within the Earth between two kinds of materiju8 qeok ,og(k+ h o:1i:d(oc vc4zs0gal. 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” rcn6+o duh/ys)c s vf8jx/l,8where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a 3uoch8r)/6j ,fv /+xc ys8sndl4$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm al.qywp :k4k1b/a0j ea 6ifs/ oir when it hits a layer of cold, dense air. If the sound wave1 fla4i0b/ aqy/ow6ekjs. p:k hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary betwe) vp fln9pf39ven two types of rock at a 38)nplffv 9p9v3 $^{\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 tp1qne x k((v9)7sqwu lcvs ,c,o the user’s manual, the di 9usv7q1w,vcx)(,en(q l ckps sh 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 750 km/h travels acrost (oye 7vm4j;ew)x jq2q3mky 6s the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do3 mt 746me2y(k;)jeqjyqovwx 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 of 550 kN/m Find cucxjoip0lw68*47 vethe maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conserv 4l c0vup6ec 8ji*wx7oation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whm15lp*i 5u:i8o vzw sxich stretches the net 1.1 m.uwp omv5li :s5i1zx8* Assume 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 freely hanging sprg +rj7c ,o5 t30 c,ihwbs5ohtu4z )hwoing. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillat5outr) +zj htgw ch3h bowc0 s57oi4,,ion?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compresshu 14vm6ga:tting the spring 5.0 m. (a) What is the spring stif a:tt1h4uv6mgfness 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 (mhm40gl6psrc90 o 8wndiameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it w4srhngp 9 006mc 8mlostarts 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 f(e(e cc 4rdn,von g0)qiy(5w8rrni( rrom the center of a 33-rpm phonograph record have a wavelength of rn 85r(vie 4dn,oi ne((r qrc()y0cgw 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the )umki ,zxp (r)u+bqgox7g d*k) ad11k8v bmw6equation x=0.650cos7.40t where x is in meters and t ink g xb1idv+aq u)kw p*o(7x u1g)8)kdrm6zm,b 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. Whaq1lr. ob/l5w ,it n 7vx;czor(t is its frequency if it accelerates at lnw(xb 7 c/ rtiv5,lq rz.o1o;0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a p/qht;p04byw75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whilepq;p ht/by 0w4.
(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 arek;lih *x0kh2n,r +2 gdlgxf - ccl60re tuned to play at 392 Hz (G) and 440 Hz (Ah2ein6*lr+ x,dfh kl; gg20kr-xlcc0).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. igrl1eim;/d( z f/ui u6x8mp9 11–33. Determine a formula (a) for the ratio of thex986fld eiz /um/;1gimu (i pr speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong mwu5 7lp+5dzpt oves 1.8z5lp5wp+ dtu7 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 wiihvh. yd /p+s7th simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vib/hv7 ip+s.dy hrate 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” eh 61wxsc 2v s+ 52kw70fa oyvajzktf25nd if that end is attached to a ring that can slide without friction on a vertical pole (Fj7kz h w0f6 +5cvv25s2o2awyakf1x st ig. 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 selandmzc ; 919 — each one-way swing takes 1.000;cnaz1 le9d9 m 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 aj2 va8wg6/7sm au q6tthe vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: L t68 aawm67gs/ uq2ajvet $l_0$ 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 tensie;a+ rxmb((kvd2. tpefp6z ;ion of 255 N. A pulse is generated at one end, and 20.0 ms later a 2 ;art x(ip;. pe+ k(vzfd6mebsecond pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a cei8*xcf vm z+ib,f6hm z1t5a23v7 a0mvtot.q gnling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the btv76mz*x5o0 t h+fnfm1 aav3 tvcmz28qg bi .,lock? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the jdnebv*.t5hpy p4m**kunkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the m.yt*d*v*bn5ep hkp 4 period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–dx ;bh+x vfc88 w))-hp uh1krj58 (which also gives the dimensions of the block). You push it sideways as shown, and thchvj- x8f rhdx; +1))uhkpw b8en 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