Give some examples of everyday vibrating objects. Which exhibit SHM, afqa;ler,fhx di.e feq kp *4e.w5/ (k2t least apprf.p,q5ae;we k2.qkdl/e rx hf*(4efioximately?

Is the acceleration of g3y0k 0ykqu89/d1 +w g md/ncmh8fr ima simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an autoxe.p6ghf b/ +zmobile engine is approximately simple harmonic.bh/ pgzf+ x.6e

Real springs have mass. Will the true period and frequency be larger :j2zb g xt)df4d0; actor smaller than given by the equations for a mass oscillating on :;fajg b2d )c x4t0dtzthe end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple fn)fz:tw8l 2t harmonic oscillator (SHO)?

A 5.0-kg trout is attached to5l nxozai: i;ld(f 7i8 the hook of a vertical spring scale, and then is released. Describe the scale reading as a functioiozi lf;(57d8lxain: n of time.

If a pendulum clock is accurate at sea level, will it garpl lcb,v c,1tt i(- ybs7s6pj-+ npw4in or lose time when taken+,,ri7wl ltct-y- pp1 nv b c6bps4j(s to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–4iq 5k jg/l(x d u,j0+uw:z0 cs9evxhb(8). How cx,uhz((5i:kwujcv e9 qblj s +0x dg/0ould you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and c8 mhc)l;nj/f *,mnyiforth in a pan only if you shake the pan almh8; )nmj*cc ni ,yf/t a certain frequency?

Give several everyday examjifw u5*:w)0wix qqm: ples of resonance.

Is a rattle in a car ever a resonance phenomenk/(yvh5 5w:a gzeqlp1on? Explain.

Is the frequency of a simple periodic wave equal to thew*seej * x*+bwcd4tg.f,+jmzl .o cv5 frequency of its source? Why orb +gvce ez.m,+t.*4*w5* ofx jwsdjcl why not?

Explain the difference between the speed of a transverse wave ,.vfblk9v;bm +*i3b bih m6obtraveling down a cord and the speed of a tiny piecefkib39. m h m6;loi*+bv ,bbvb of the cord.

Why do the strings used for the lowest-frequency notes on a piano normqiu:n.am) 2no,w;d8hsbct 1q xytzp8 )(3 mkhally have wire wrapped arouqomhws2ia8t) ,hz1; qdybtn(xc.p 8mnu: )k 3nd them?

What kind of waves do you think will travel down a horizontal metal rod 1*benye l r6g4l.u-yl if you str1b* e6 l4rl-en gyylu.ike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of0mly jh )a;bm3 air decreases with 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 temperam )lhb30 aj;myture?

Give two reasons why circular jw ))sx 5gd9:po 6yoeu/e4ey uwater waves decrease in amplitude as they travel away from the sour)p9s)ugyj y/e6 5ue4x :oweodce.

Two linear waves have the same amplitude and speeq/ij h0lccc5 l9 -efn3d, and otherwise are identical, except one has half the wavele-nh35c /fleqj90 cilcngth of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary +jx .bady+( jo*bgb1w b yhj,6n1j*plbetween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explail gpj+xwd*y.b, a+jjb( b* 1 obynjh16n why.

If a string is vibrating in three segments, are there any places you c/5-uud jgge ;sould touch it with a knife blade without disturbing the modgj-/gsu; u 5etion?

When a standing wave exists on a strin fc60,b)zwlgsz ,t8 tng, the vibrations of incident and reflected waves cancel at the not0s,f8bl zncwzg t,)6des. Does this mean that energy was destroyed? Explain.

If we knew that energy was being tr8jx svb81vhb34c5 d cz:-oj yvansmitted from one place to another, how might we determine whether the energyjv8o b31vz:5dh cxbjc-s4 8vy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, whamks t68y j+76-ppsvjct is the total distance it travels cm 8sk6ps7 6j-tjypv+ in one period?    m

  An elastic cord is 65 cm lon cv w:r-yjjsk/.6 e5cjg when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k ofy j jc5vewr:. kcsj6-/ this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm h.n swi-n +u;lwhen its 68-kg driver gets into the driver’s seat. If the nnwil us+h. -;car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cmfu3*j(bq t 4cr: nvcmyy26 1uf u7)czp when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constan 3jf7:yurc (pvcun2q tu*)z16f4 mbyc t $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is hu*-xuj+ oe5u,z xiwe 5wng from it. Wha*+5 uwxo i- e,juzwxe5t is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the masswvdc,;+fyd )e in Fig. 11–2 at times t =ed+,c)w vyf;d 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibratef)*;lh+r-kntzx /u2 ukly+ gvs predominately with a fre/)fk xk+;*t2+vgl -ulhuzr ynquency 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 m 7rbiy;d2d6m c/t9ic with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the valu cc9i2my;d 7dm r6/itbe of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times poo8,wuqz e, 3u2lp:u t ;rb8kmer second with an amplitude of 0.1328,poqu t;m8k lzwuob,:eu3 r m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half te8hvdng:a: e.b wqk0+l8 iy kt t5siwrk1b06;he maximum valu:6g ewy:aqitw1 .0ktvk5 elb8; brds8+0nkh ie?$\approx$    A

A mass attached to the end of a spring is stretched a d( 4m qjns3u)buistance $x_0$ 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 5 axe9ukog ,:92b binqxjv.p-a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it takenkuj2vx b: pqgx.5 ai,9ob e-9 to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness d 0 9 xt:i4l1e39twugzbtjc/gconstant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its ect 4 z/:0e3xtguj 1lwb99g dtiquilibrium 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 80.0t+ x8mdbzcs*(aps0( f N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball dss(mc0 z+pxaf * (8tbleave the gun?    m/s

  A mass sitting on a horizsvdg2;9;o(lwj884 kkb upx ekontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is w8u kl; gpo8( 4;dksj9bevkx2 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 acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t w+5-o;pj(iagzrki,b p9 -ccf xhere x is in meters and t isrzpioaipgj(;f cb+-9 xk, -c5 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 l8) r+xcrg yxki+r 2+tequilibrium is the energy of a SHO half KE and half PE? ± 8rlyc+t +x +grki2rx)    A

  If one vibration has 7.0 times the eg /:c-spm *evbnergy of a second, but their frequencies and masses are the same, what is the ratio of bsg-:*pev cm/ their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spuhuus* j w dftn2;9 +t w/pw8d(rigv8/ring once every 0.65 f; utwr/tvijpw hd g s/ (9w2d88+*unus.
(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 para ++n6m,f))va p i;tnxft3r zgvllel vertical springs, each with spring stiffness constant k (Ft;n3 ,vxv6i ffn gr+)t a+zpm)ig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x iss k*2*sd i nhfvk7r8zpu*u3s( in meters and t is in seconds.(7s8u dzskfn sk*u*3 i2vh *rp 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 anqbv(9g6xgs) gj6 vgm 5d 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 = 124 N/m) isa: p7fccn2a+ +3 oxglx struck by a hammer, which acag3x++l: ocn7 2fxp gives the mass an 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 spring1ei+otsnr h gziy 0;v5q4q.8en v42pq stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hq1 peq z2y4 orsvg48hv0 e+tni5ni.; qangs 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 stiffn lwdli bv*so)/f 7nc43ess constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed hl:eq /( gdce u- wb(8u omo.sghe1p*y9orizontal spring whose spring stiffo 8 e*mpob 9(:gd1weuhs-e/c ulyq( .gness 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 dxy0k a:/h +eaic0xk7mass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight a0h :ackexk/7 + xy0idmore times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is ithg6,ltmowqe -66wc/ b s
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if aay0(90 9guv76zx.cg.xr mdwc q vr,wit is to make exactly one swing per second? (That is, one complet0a97r q.v(x9w rac ucg.ym0,zvw6xg de vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is i ujniu8o.n( ajo54ut 3ts period on Mars, where the acceleration of gravity is about 0.37 that uotu 5o.i j4nj3u8n(aon Earth?    s

  What is the period of a simple peno7+ohjg9; mp 9t )fwdldulum 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 pen0xvw( egn5t(v3dv f6udulum bob has a mass of 365 graxvg3d ( u6v5f (0wtvenms, 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 0.993kogunk * t7m080 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened by nk*t 70kuo gm8   mm.

Derive a formula for the maxi1ve7 jrgnp-.dbn p9) 7g ezbb 9kn(,xumum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5yj 6 j lrv,,u-y/.3q gcafhp/;cgi q7d Hz. At it is released from rest starting at an angle oqu gcgqhdp/-/rv6y7y ,lja3.;, cf i jf 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 anchore3h4edl-5r06y lop0 g2r c 8qhvcmife) d boat every 3.0 s. He measures the distance mhc hvp6g3- lyi0r )r eecl4q5o0d2f8between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air hastx yj)(kqpicuv 8-+8c a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressions)? k c +j8i)8p-y(qvtx cu   m

  (a) AM radio signals have frequenciesw3r lh5y4 t v(8rul8pisj4o/d between 550 kHz and 1600 kHz (kilohertz) and travel with a 5y(s34l8 v4 pouwdlh rijr /t8speed 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 h l 7h/k8q-k/iaus,ww in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twico1 yobom::/s ce as dense as the other. In which rod will the speed of longitudinal waves be greater, ando :/y:sobo1c m by what factor?   

  A cord of mass 0.65 g rw zrt*ex5j5c.ens 2q0( g6lkg is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to t 5rr6.tqej(c0xnsz*wge5 l 2ghe other?    s

  A ski gondola is connected to the top of a hill by a steel cable of lu1v+r:sul k.or+) orpength 620 m and diameter 1.5 cm. As the gondola comes l:p1rvru o++ .rousk)to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. He hear0i7 s4 1nn;vy0xsrv mjzy z9e4s the echo of the ys n0mv71v y0 e zn94jxz;s4irwave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at diffwvv.p +met1+ xerent speeds, and this difference he1 pvx+.tv+ wmelps in locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated byv7qyc8s xea/( a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ysxcav 8 (7/qeground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the am;bep872 yvp 98kuvkz,3yq )w9szipakplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 yv )ekvuawkpz99k i ;8yb8 ,2pz7q3p skm and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to b; * x35-ayot svmabydo5:lk yi,ciw,s*b)8o me wliixsky,;d mb* y-*bm5syao :vc83 ,a5)t oo $ 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 travbvnb-.tm 5nt5el through the same portion of the Earth, but one is carrying twice the energyn tb5nt-5 bvm.. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, bu cn 6un-7yvdj6t one transports three times the power of the other. What is the ratio of th-7d 6nvcju 6nye amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a totxqvzi 4ty2s 021c 2v -iof;rbtal vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm,041tvt2yv; 2i2-c qor fsbi zx by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are 5kx 4(f)aitxumoving toward each other. (a) Sketch the shape of the string at the moment they directly overlai f kx4ut(x)a5p. (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 fundamentalx6d ya,6r lfdu) u-/in frequency, what are the frequenrx,a6i)6f d yuulnd/- cies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what fre2h+ko.yj6 n ypquency will it vi n26hyp.ko+jy brate 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 wave.)    Hz

  A particular string resonates in four ,8wx29so ixr, )evc-5m krpt mloops at a frequency of 280 Hz. Name at least three other frm)5sp2ix 8ke x9-,ctmrwo vr,equencies 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/+l b qt0p8ji,;*l stdqs If the frequency of standing waves is 475 Hz, how far apart a,;sdtq* qljl b t+pi80re two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz andoqa ,pb.6 ord5 350 Hz, what is the fre qpo6.bra,d o5quency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance f-y od 7pf6lu-drom the bridge ld op-- 6fd7yuto 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 overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measuj* ;hwmg ( x:diujwfi 2e,(xv7red to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequx;: j(mfid vwwig,u2*(jh ex7 encies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is4i*z4q tca0 7ur:ztrn4nz vm2 supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 uz :n47tmivqczrn 44*zr0 2atHz. 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 1zaxi *)1 jcogmechanical 60-Hz aoc1 )x*gi1 jzvibrator. The string’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 by moving the(ndw5t dk 6h(xmwr:y ) pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave pattekd( w ntrdh:wmx)y6( 5rns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water bwfi7tx ta0d-m. mab6 /ack and forth in a tub 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 in a 65-cm-wide tub is 0.85 Hz. What is the speed of the w 7aw0itt-./ad mxm6 bfater wave?    m/s

  An earthquake P wave trme y,*,.mzfao aveling at k.0 km/s strikes a boundary within the Earth between mza*m., yefo ,two kinds of 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 un.4l0vf (8bg yuyy*hsfp lg:)vderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave c4 s8(fl fyu.hp:ybv) 0v*gg ylrests 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 lvq+y;.m k e(86nuosoy ayer of cold, dense air. If the sound wave hits the cold air intmne6 ;.u+oo y kqvs8y(erface 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 1n(14gdhe/fkefzru 2between two types of rock at a 3gkeznedf12/r(f4h 1u 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 user8qxd fps-2dos 0fd 6+z’s manual, the dish has to be pointed in the direction of the satellite, but an error 0- z8d+o6sfd2 qxd psfof 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 vel., qn 6 l(fiqg9ve)zkbocity 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 them attracted to the shore to see str )l9eiq.vzk( b,fqng 6anded fishes and boats.)    min

  An energy-absorbing car bumper has a spring st;q,x4(bzrg *mgs- hr wg-o-,cmpv6 o siffness constant of 550 kN/m Find the maximum compresh 6s*;c(sgq m,p-4r,wm z -bg orvoxg-sion 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 conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below,pe6w c1fha) pv9o;vb: which stretches the net 1.1 m. Assumvp :91f6)wo;be cv hape 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 fre0g)dh bx9)48s.yzoqq v)rh ofely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of t) f0d)gqxr84o. 9ob)qhvhsz yhe oscillation?    Hz

  A 950-kg car strikes a,t+(t,l ntu7:h rn5wfl wx 9i18 xpupn huge spring at a speed of 22 m/s (Fig. 11–54), compressing the trx9 t1h:p 7u,+8fln wnwtpn(5lu,xispring 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) at just the right pace ofce5- tz 7j20wc 2d)b 3gjqmkpxswk:ef 0fe)p 3 about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves zeqfgwp)e 2cjxcw m:3 0d3j-se) ktbk70 p25f in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonogoehs0h z-el0v ze5 5o6raph record have a whz5e ze 6-0 05oshveolavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according tot, twc1.a5 mra the equation x=0.650cos7.40t where x is in meters and t , .tmw5raatc1in 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 m 3uklyy5fo pi1- 9fp(a:ed -jwith frequency f. What is its frequency if it acceleraekfpyyf 5o9umi--a1(pj3dl: tes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Whenpbey k:uui skxqq0pz+ ;.-k86mb l 2,n a 75-kg man stands on the raft, it sinks 4.0 cm deeper into mup pky 02ib.z: k6b ,ux+e;8-qnqklsthe 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 tu;ukbeqx) au,v hfp w3l*;eoj,1kn6* aned to play at 392 Hz (G) and 440 Hz (uea owhv 1l *xk*eu;n;),a,qbkpj36fA).
(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. 11–3tz:mcd or.s3*y, 0 vpm3. Determine a formula (a) fo3oc:srpd m0 m,.* tyzvr the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency ok-uj-5gxgpur- wz wdl9nf qe619l f( 3f 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculazr3u-- g q xudg 19wel9-jk l(p6fwfn5te
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscilla 408-p(h0mm7szscwe wi .ejlbfmb m18tes with simple harmonic 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 peb(p.imb10c ws80jh7f4mm s-eme 8 lbwzble 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 attached t 5qq6.zy*w v:hygyy 4xo a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string withq .gz*yyy46wvyhx q5: one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each o3m(5;):ot + kbzmv*4 avg:apzlpzpf t ne-way swing takes 1.000 + k* b3a4)zpl zt:gatpfv5 (omm zv:;ps.
(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*zmq4bd. :h r */ xtpuxcw9)m: j(wfqy 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 horizontal st hpdxc9/wujzbm *wmf.:: )(4y*qq x rwings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A h5 z /cyj-f*d vvje79tpulse is generated at one end, and 20.0 ms later a sechc v-djfjv /y t7*5z9eond pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suj- i5zkymlo w*e0,dk s)(: 90oibwhcdspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed 0boewk(l9ij5sd m :z,)oh* -iwky0d c on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable3j-sbd ys.ubkot3e4,s 2 x-du 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 period of the bouncing? [Hi-yo t2.xu,jskbd3 4su-sbde3nt: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (5t3 klzle y-lq/jy3 *b5gz px-which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. -35 zy3tllk/ qxb jlyp5-gez*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