Give some examples of everyday vibrating objects. Which exhibit SHM, at de-8uyyw9e7kd6 krdxv/ ;tz 3q)v xt/least approximatez9 u ;deqxwyk ky3 x/vevt6-rddt) 8/7ly?

Is the acceleration of a simple harmonic oscillator ever zero? If slvc( 6y:iw wjm;,amv;o, where?

Explain why the motion of a pistonprb*e).cie t,nk2*ak n..f, p xwyu- q in an automobile engine is approximately simple hau 2p f.bwtn.pi. ,qekrn-, y*akxe)*crmonic.

Real springs have mass. Will w52cvxdl bw ()the true period and frequency be larger or smaller than given by the equa2(xbw ldc) wv5tions for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator nfvj e5f gk 2eanpi9ks/4;9*y(SHO)?

A 5.0-kg trout is attached to the pnycn,y k731y0bij*z5 agk,x hook of a vertical spring scale, and then is r *5k1zycbxajg k7,i y0n3p ,nyeleased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time4w8xi vgujna :;j 80ne when taken to high altitude? W0:njx8ue8ji4n ;va gwhy?

A tire swing hanging from a brancx2kgp;92ge ukac m:z5 h reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch usi2 ax;g:km5p9kc2zuegng only a stopwatch?

Why can you make water slosh back rdn- zsw-,k0vsdbr2qe9 z(77*aw x/ tjgno,b and forth in a pan only if you shake the pan at a certain frv ,z(ng b-s2 rj*wdwn/ z,qd9eak-0o7b st7xrequency?

Give several everyday examples of reg j/.m5c9g4iv3wz bqzsonance.

Is a rattle in a car ever ak e8,vl vn1t 5(ca3s kpeikf)6 resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of er. xgg4ctl06its source? Why or why l ggxc60 er4.tnot?

Explain the difference between the sor0 3bnt 9iob- )up1fb/fhj2 ypeed of a transverse wave traveling down a cord an 1hbob 3jff)r9pt-2yi/o b0und the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequenc:/gqkubf q yf ( 0thmpp/)e0w6y notes on a piano normally have wirefp)6 wpu/my/:0 h(tf bq0qegk wrapped around them?

What kind of waves do you think n fhg. ttwf5415bqy3n will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its length?fy53gf 5tn4 ntwq h1b.

Since the density of air decreases with an increase in temperature, but the bulkr3rwe.n /vq 0f modulus B is nearly independent of n0q.f3er vrw/temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waj)bs hk 6 wsal pht;+5t)e35laves decrease in amplitude as they travel al) asb553h 6tewhtkpja ; +l)sway from the source.

Two linear waves have k,km ,w6mq60kk1aq5kxfe, guthe same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factor?,kg6 ,fm1k6 w,ak qkqku 5m0ex

When a sinusoidal wave crosses the boundary be5,9 ychjiz** wet vhz0tween two sections of cord as in Fig. 11–33, the frequency y5*i e*0 ztvw9c,hzjhdoes not change (although the wavelength and velocity do change). Explain why.

If a string is vibra,fpen)x2hi ,etrl0mh;qhd * 2ting in three segments, are there any places you could touch it with a knife blade without distur he *2ehft2mi)lq,d0nx;p,hrbing the motion?

When a standing wave exists on a string, the vibrations of inci8toim/*rpc8 z 6 1siwwdent and reflected waves cancel at the nodes. Does tw is8/ 1c* mpt68izrwohis mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another,psm/qrnq6pb3:u 8 sy i-vl2) j how might we determine whether the energy was being carried by partibvlp:q)6i2ujpq/r3 sy-m 8 ns cles (material bodies) or by waves?

  If a particle undergoes SH(va21an--cppua+a y gM with amplitude 0.18 m, what is the total distance it travels in one periodppy- 2caa -+ng1auav( ?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fromykeu,)c orn)9 it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elask) cyoe)urn 9,tic cord?    N/m

  The springs of a 1500-kg c*; s9xy6w6j- hp omhs* t*pvw kxg)6fgar compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibrations?h6xk*wsmxovt h9p- *; sg6g)fwy6 * pj$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (z*td( b7ca imec dv633a) What is the spring stiffness const b37d cd zv3im(*e6atcant $\approx$    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 tcm j/zyz/eg35 t(l h)kg is hung frol 3e jc zz(/hm/yg5tt)m it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at timetcio 5w y sz:c+sc* , dr8.:fk/exw4wts t = 0y 8:s ,k:ot.ctwrc*4 e/czsiwxdw+ f5,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 vibr+s0altctjy7/h u4 vp.ates predominately with a freq lpjtcsa7uy0/ht.+4vuency 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 h)ude6g( juq2spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is ej)gqu6uh (d20.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a sp0+afu 9xs tg*st xakp-) kq-7fring vibrates 3.0 times per second with an amplitude of 0.13 m. Determinutqk-+0s9 gfa p)f7-xktsxa * e
(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 55*s 6rl5hw wnx6d- rdh4arelis the speed of a SHO half the maximum vall45 6sd dw-l rhx65r5 wner*haue?$\approx$    A

A mass attached to the end of a spring is strerk4 g:-go rne*tched 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 vertical spring 0.315 m. If the sb5 ht4xh. dt80 v4va4tf k/keipring is stretched an additional 0.130 m and released, how long does it take to reach th0hi/vett48b4v hkx k .fd54tae (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring x x7gd)w.a/:s, 3bjqnnbq iusje36e- stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is movis6 gbij.a)s 3 dqeqxb:-x7 wu n/,j3enng 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 they;ctenp p(mr a962d( r-2qvg p spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what sprcappp;-dr e2v9m n6qg(y( 2teed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictioe/wdo9pf 0 k+4v2oez,,dffnfnless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum accelerat29/feo4on ,0+vdp,kff wefz d ion 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 where x is in wr6yuu ng3- 1. fb 8te4mg m4.wu;txuhmeters and t is i83guyemuxwn-;u b61gu wt hm4 frt4..n 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 ths7c jm/ 1jvme)e energy of a SHO half KE and half PE? )jj1 mevm7/ sc±    A

  If one vibration has 7.0 times the energy of a second, but their frequencdvc -im*j gh-5mybyw.f: sy-8b/)yas ies and masses are the same, what-/w ay. f:*sh-m5i8)cg mbysv-j yy bd is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertical2 ui(*733.avgv mjv/wfripezly hanging light spring once every 0.65r*7 .zeuajvv /i p2(3 iwmvgf3 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identic4j:vkllow +; n ookp 4xcx-y-4al parallel vertical springs, each with spring stiff k4;4xx-c-k l+nvo4o jo ylp:wness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sisr6 ho 0buq+e8j ,ws ;gnfxz7tg:fh02 n6.5t where x is in meters and t is in sohs xf0f,wgz:;r7u8nej t0 q2g+sb6h econds. 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 o4b3: dh8 z486mceckdxmpv/ blf 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 = 124 N/m) is sn ys3kpodjy -8zz .6d8truck by 8j yz8z6dk.3dypos n -a hammer, which 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 sprin jz9eo5(wleg h9b/ w r:dle3z3g stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium pointo /rw eb3(93eh9eg :w5ldljz z (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 constants iu+wwm kgr6)9 $k_1$ 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 bh,xzy+r +, bdwypm8;s lock attached to a fixed horizontal spring whose spring stiffness constant is s+myy,h, +pr;dz 8wbx$ 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 bridgevu 4c3 4zhz ,.eoc6rje. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 4cehvjz3 6oc,z ru4e. 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 vig 2 9d vljr(airw 5b(24jdqj2;z wg0r p)oveu*brations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum ya2 26c ag-nu0 m6johbbe if it is to make exactly one swing per second? (That is, one complete vibration takes exactl02bun 62hg mo aja-6cyy 2.0 s.)    m

  A pendulum has a period of 0.cof3qrj0(6d 3r24 npy q6hqbl8w6vye80 s on Earth. What is its period on Mars, where the acceleration of grhr8cb6 w d 63opn2y(eqjl06yqrfv4 3 qavity is about 0.37 that on Earth?    s

  What is the period of a simpxfyb )5rqk.f3le pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the cd /)/fo* r+gstkam y5pendulum bob has a mass of 365 grams, and it is releaseds *d5 ao+mtrfcyg/)k/ 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(*3ohvr eujjovvn2 n4t; 4p6b a length of 0.9930 m. If the clock loses half a mjvj voropuh3t 2nb 4*4nv(6e;inute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speedwoxy ,dx: woiamq981 , $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillda1kb8 ww/.l6p- r8jtopph8eates at a frequency of 2.5 Hz. At it is released from rest startiw 8ra8w . pd -hje/ktp8op1l6bng at an 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 wave crests pass the bow of his anchorez3y kg-p a oi*)monkcy2r.:2 vd boat every 3.0 s. He mpo 2: a.gony)2r-cyki3mkv * zeasures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speeckb m0w. rr4j;3 -4lselv7 ne9nf2m,9 l sylbld of 343 m/s How 4sb n,m2l 9re .vw;fl4lklrly03cj7n 9b-mesfar apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kkxa7pyn)f6c7ivx ,z -Hz and 1600 kHz (kilohertz) and travel with a 7f6zxx a)7n p-yc i,kvspeed 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 longit1f8dl/6sifu2zm* u6 9 /o iynnynsc8judinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as thek(hl r*n+n.gbjqtg9 ppz+/ a;0ecx;s other. In which rod will the speed of longitudinal waves be greater, and by what fsg nb;0+/ jzh(+ncagp.x*peqrltk;9actor?   

  A cord of mass 0.65 kg is l4fi0kyv 3r/ez2 o/hs 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 supph rv0 l 3oke//4fi2syzort to the other?    s

  A ski gondola is conx9(i4h bh8. grzto9lpgo; 2zqnected to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps p;4ot 9h8o9g(2zilbrxq.g zh 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 juse4s1x(j 5zjcmoegy y8jaj)1.t below the surface of the sea. He hears the echo of the wave)14(jeozx jge.1jyscmj8 5ya 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 th cjhul2m2*7 travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took l7h 2mj t2huc*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 q+cjzw48b f9p 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 freque8b j zwf9q4p+cncies), 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 a 4 ;l;zqash:*9jrem jv0+wxk(b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from t;xk mj0 ralewj azqsv9:;h +*4he source?(a)    (b)   

  The intensity of an eart3kc -u xxq;z/ahquake wave passing through the Earth is measured to be 3 /xaxqu;k- cz$ 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 ob;2c /w *diq/ njns*4gq26go6wfutk ev 9lhu0 f the Earth, but one is carrying twice the energy. What lnghb;tws/v9i g 4qjc0 knu/ *quw d62f6e*2o is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretchmg/thn0b-1xz3 nujnnnf 2 cl3uz 3p*5ed string have the same frequency, but one transports three times the power of the other. What5z1f ln/cn x-*bg3mp2 nnhtu30jnz3 u is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and doihe k*x-vg/)oc kte;qo9nlm6l0/ j1qwn a total 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, by what fag/q0;n eo ltm lxei*-h6j91qk/)ovkcctor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (lly b2kxydl0e4,/lv)/bq w 6ia) Sketch the shape of the string at the momen/6ev xl24q y l)wlydb b/ki,l0t they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates a3 a:i07*idmdcrm9vfm w; lx2pt 440 Hz as its fundamental frequency, what are the frequencies of the first four harmonics?l27 ca;vf*:p9mir i0m dxwm3d$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered./*1/ :rrsy)c b eacxmbjpy8 3p At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, cjy8 / ea3/)bmcbpyr:s*rxp1 only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a fc oyrye :g40q:requency of 280 Hz. Name at least three other frequencies at which it will resona0yg:rq 4c:eyote. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the f .4vcqry .,4 4m9irnj(cqtpiu requency of standing waves is 475 Hz, how far apart are two adjacent i,umrj qri9 c(vt 4q.44pcyn.nodes?   m

  If two successive overtones of a vibrast+ o;;hsypa2ting string are 280 Hz and 350 Hz, what is the frequency+s;ay2 ho tp;s of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass .pxs2v,9s* q1x x pamqof 3.6 g. The distance from the bridge to the supv,2sax .1* sp9xqmxpqport 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, .t q:6sg-boch i sa4dklss wop*31,b-but it is measured to vibrate at 205 Hz. By what percents,b do3ts iq:po6l4a-s.1w*k hsc bg- should the tension 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 vib*z fytg .ha.)erate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decrea egz)y .afh.*tsed by    %

  One end of a horizontal string is atta3c2ekab) :bhpched to a small-amplitude mechanical 60-Hz vibrator. The strhk2: )abpb c3eing’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 ma7nihx-d4q2; nz/kty my be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and ziq/nm4 k2 yd7x -hn;t1.5 m?   

  When you slosh the watertd-b u a1*ft9e back and forth in a tub at just the right frequency, the water alternately rises and falls at t*ue1t d-9 abfeach 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 water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundaryh4;b2.b yaavwqe79nf within the Earth between two kinds of mater 7q ;92hbbfe wa.ayn4vial. 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 unwr b,x;u: 6 l0cyqw*lgderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If t*xgqy0lur6bw ;w:l ,c he 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 lr66z.vh 2by )6t)iv m6lozpvuayer of cold, dense air. If the sound wavei u)zz.vo266vymphrbt 6v)l6 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 between two types of rock ammapjn uf0(8hr xtayk );hxz;9( q3f*t a 38mfp*q ma t ;x u8x0nah3f(9h(y;j )zrk $^{\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 dia51b pc2s dxr4rmeter. According to the user’s manual, the dish has to be pointed in the directio s5p1rcdrx b24n 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 trave2 zrexw pv+y95ls across the Pacific Ocean. As it approaches Hawaii, people obsex 9epzy5wvr+2rve an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m Finduy0vmn3 y38u xy7 5i v6cqr8n zniw)uj;g:jx+ the maximum compression of the bumper if the car, with massunu8r7v n3zji 6y +3 8yxnwiu0 y5cgm:;xjqv) 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, w60wb ls5oa )efid +g/which stretches the net 1.1 m. Assume th w sg/a05b)e6widfo+lat 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 et.66 ,lh owtvnnd of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the 6vnl wt6,.htofrequency of the oscillation?    Hz

  A 950-kg car strikes a h-)hp h1qyy vh hm8;1dhuge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffnhh1yv;h ydm-hp8) q 1hess 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 h b jbi32s6+5jmrab0v 8 cm) at just the right pace of about 1 step per second, the coffee sloshesvbrj3ab 0m6 sbi25+hj 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 10.8 cm from the center of 2fle0*d uy wi)o7mc2ha 33-rpm phonograph record have a wavmcyf7o2 liwuh0) e*d2elength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to th6h/git8s ex ,:0t2josr gh)xr e equation x=0.650cos7.40t where x is in me2)6t/ ,rx x:h8srhest0 joggiters 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 frw,t f 5(wbn zk2cscl.6equency f. What is its frequency if it accelerates at 0.50g (a) u2nwtf (w ckl,.s 5czb6pward,    f
(b) downward?    f

  A 220-kg wooden raft floats on ua-5opz5w ge(a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm d geazwu-p55( oeeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are:hpe4 c ,1skzduvph ki;e9;rrw,f5 4f tuned to play at 392 Hz (G) and 440 Hz (Aru;w9kd:;ezh fhf s4c rk p4,v5p1ei,).
(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 theso4uznk7i8 g46;)sn mya 8nl 7 m4ljby stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the y sn44my7m nll gsouk 84; i)78jb6aznspeeds 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 eavi8pb6n21 e8 r bzmel)ch prong moves nb2z prl81m6bvi) ee81.8 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 u0:uqzv6obnx g5 0,wosimple 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 pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillatio6 q0w0uv5g b, oxzn:uon?

A string can have a “freem/ )yv. lsa06*a)l ruzsp+dva” end if that end is attached to a ring that can slide without friction on a verv asu pa6/lrs. 0a+yz))ld* vmtical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a -ws k9xhci1 +ywe dj-,period of exactly 2.000 s — each one-way swing takes 1.000-9,kcwywi +he 1- jsdx 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 t4leaz kd)7g3e he vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the l az)e7e3k4gd period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 2q 0gq.(oup vw ok8)r lv(k06sv55 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the tp8.lq0 gwokqk6)r ((vv sv0uo wo pulses first meet?    m

A block of mass M is suspended from a *avmt*c y 5: tv2)ezu6;zesmv ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is e )v a;vz5mv2z6mu c:tytes* *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 5sfs-e4x wub +s66 8ctoemh*vcable 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 bouncin+ 6ehf5*46svb me susotc8 -xwg? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11 eflivrb k:mukym- / 0* u/nd,o*6z2li–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy ido-/r* /mk yi0vk6*bzunl, 2:lfmeuto 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