Give some examples of everyday vibrating objects.*a.n3t *yab 8ke0y ter Which exhibit SHM, at least appr8*t0 a.ya *tk3rynebe oximately?

Is the acceleration of a simple harmonic oscillawac 11 gj8izo:1w:sg jtor ever zero? If so, where?

Explain why the motion of a piston oi40; hwiblvm 10gs)oin an automobile engine is approximately simple harmonic.4b;oo 0v wlm sgh)0i1i

Real springs have mass. Winy9) 6gu)jddj ll the true period and frequency be larger or smaller than given by the equations for a mass jgd) 9uy)d nj6oscillating on the end of an idealized massless spring? Explain.

How could you double t lnc5gwx*gnl 7(hn 7w;he maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of9u de) wpo+6fs a vertical spring scale, and then is released. Describe the scale reading as ap w9s+fu6)ed o function of time.

If a pendulum clock is acc2) q i6d23ba.zbage 2vwooe;jurate at sea level, will it gain or lose time when taken to e62o bqb.e o)iav2;agzw23 jdhigh altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–4ck:q cm -.t) pt2nasqj;;.vzp 8). How could you estimate the heighct;p. 2v;kp)-.sqjq: cazmt nt of the branch using only a stopwatch?

Why can you make watoub)3rtiy(7 ier slosh back and forth in a pan only if you shake the pan at a t7bor(y)3 i uicertain frequency?

Give several everyday exam+jjt/:j*p ajv es :i0mples of resonance.

Is a rattle in a car ever a resonance phe ;l .*m0z* 82vya/t.rdhn edk5ivets zq z:3ksnomenon? Explain.

Is the frequency of a simple period/.9msek )uava: qrip :ic wave equal to the frequency of its source? Wh).rqv :m p9eai/u:aksy or why not?

Explain the difference between the speed of pk./-bv wat6 7xu4kds a transverse wave traveling down a cord and the spee-vswa u7t6d 4 bkkp.x/d of a tiny piece of the cord.

Why do the strings us zve-, 2mxt2iced for the lowest-frequency notes on a piano normally have wire wrapped around them?m,x e2 cv-z2ti

What kind of waves do you think will travel down a horizontal metal +syg*y82d-x8o )6c bxzditz erod if you strike its end (a) vertically from above and (b) horiz+ztsb 2 xycddy*86 g 8e-ix)ozontally parallel to its length?

Since the density of air decreases with an increase i7t4vc,vbo*2loqd;q z5azkt/ o4 w7x k n temperature, but the bulk modulus B is nearly independent of temperature, how woul 7z4 qzlxw74ct,b;5ok*vokao2d / tvqd you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they trav2 xrqmv(uu3dnxg- -prt73e x-el away f - uexxvtugpr xdq2-(73-nr m3rom the source.

Two linear waves have the same amplitude and speed,bwk5ed,dy6g d*ujh./ and otherwise are identical, except one has half the wavelength of the other. Which transmits more energ .u*yd 5gdh/wd,ek6jby? By what factor?

When a sinusoidal wave crgh,x-yxfc7u h( x4xb*osses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain w 7-, xc4xxfyhgux(*hbhy.

If a string is vibrating in three segments, are there any places you coe tcd-*: s jku17gl0m alur4i du64c/buld touch it with a k7 rl1cdld*4 bc im ugk4/teuj6 au:0s-nife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflecte9s iu4-jumw6jc sdw8e 1b4i6v q,oa;yd waves canu-e,j6s4 q9 w;ocmb is8ivywu a 41d6jcel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was bbftzpifx39;.m-x ;rv i*vy;x eing transmitted from one place to another, how might we determine whether the i;r39vx;xzpi -x * vf;mb.ytfenergy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 mht(a5l-9ty pjxb/3 ijw-:oah.( deo m, what is the total distance it travelsb: aje3 p/a -(mt(h-h.wylixdo5otj 9 in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fr p*q-i4m,rvtn b6res5om it but is 85 cm long when a weight of 180 N hangs from it. What iebm*pr5 n,4-rq 6v tiss the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver get+n f( ru(magj0 bls)-ls into the driver’s seat. If the car goes over a bump, wh 0ub(lsa- mnjf+) lgr(at will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2. jht9 8sdu)mp(7-kg fish hangs from it. (a) What is the spring stiffness constant8)hmps t9dj(u $\approx$    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 c)nnx e/*va9x:w an- ea frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hn/axw-c xvee 9*ann :)angs from it?    Hz

Construct a Table indicating the position x of theeh1fbg5m*q/q x dw06r b/jhh 1 mass in Fig. 11–2 at times t = 0,t rbdh110/*ebj 6/5qwh gm xfqh= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 nm8joie3-n3ps or;p/ in a spider’s web. The web vibrates predominately with a freque3/p noj rm3piens8- ;oncy of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When bg+q x/1 ;3h hvluwyua(p0gu-an additional ha-wb0 u;( u3qhxv /ylgp+g1u 680-g mass is added to m, the frequency 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 times peroy* .k kb5yr,/ gvbw-ymryx2; second with an amplitude of 0.13 m. Determbg,mxkoyy-;w / * yv5bkr2yr.ine
(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 fron ce;24lc om iu3 cg 4he*cxzb3ic4,i*m equilibrium is the speed of a SHO half the maximum value?3x4c i lio 4h2um ;3*egcnib,zecc*c4$\approx$    A

A mass attached to the end of a sp6bi*4jpavism4t x3wnb -v trvru 24-3ring 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 stretcssh rvw-) j 8hl88zb* agc82reomy:q2 hes a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it 828yz h*8g -veq sh8 )sb:2molar wcrjtake to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached us zuzzrg;(hz5lh 2.9to a spring with spring 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 movinh5zr(9z; ug.u zs 2zhlg with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgunfx(mr2f2itm (u 9jj+k 0.200 m to “load” a 0.180-kg ball. Withf2 (r+xfkmm(2jj9 uit what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached ynr f. s;ey:3g;rt;xato 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 frr x:ng;;ry.3fayst e;om 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 wp7r;t:*dc m;u po bta6r rn6-zhere x is in m;or-pt;upbrd nc z7r6 :tam6*eters and t is 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 displacementafyr 9a *,sp2r)dufb 5 from equilibrium is the energy of a SHO half KE and half PE 9u)sbd a*pr2rf,5 fya? ±    A

  If one vibration has 7.0 tim / )wa (u34mh3xha yumajg)zk0es the energy of a second, but their frequencies and m/4) auzaa3 yg hw()x0juhmm3k asses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscill2 ix nrq4qt5lw svt3e/6n 2hbfy /*ib)ates from a vertically hanging light spring once every 0.65 ssib2r/e wx5 i4 tqft3*v)nq b6l/h2 yn.
(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 idensv2co3sm5 dtk o 3,(0jqx.mg dtical parallel vertical springs, each wit0(osqo 3d2dmx g3 cvk 5m.,tsjh spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is jf ka flh doe,06qi27i0af f3g16 tld(in meters and t is in seckq ldh 1oia0,i f6( t2 jea7ffgl6f0d3onds. 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 qfl/bcx /5 3xyeeu 4nukve,8.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 (x;t5x7 qa/+hfoxc hp rest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determinpx +qxthhf7x/5c ; (aoe
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305o *2tn m2c)zuc N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes thr 2c2*znc)utom ough 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 consti8w.mr3m.j-k0g(5r0qhqf bgs typ(a ants $k_1$ 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 horizontall4 zcu(tj:zt( kv/r(cff: tu* spring whose spring stiffness constan ( tr/:ft*zc zu4:(cujvl(fktt 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 lu* a))hpc 20y0lzmetvy2 ja-high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below l t)vy)juap 20le2-z0*cmyah 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 jach((q0 7oa eebyt zdcq9)(/ vibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to makp+g0v:n.,q. *lly f/hg zxgq te exactly one swing per second? (That it:g,xfyv gg+l.zq* p nh.l0q /s, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is itsw3(i l cn46vi(6 saaet period on Mars, where the acceleration of gravivie 3lw ina( 6(sa6t4cty is about 0.37 that on Earth?    s

  What is the period of .o 5d1esojai25uvtwb. hbb wt8ubtu;;.h(w1a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulxhc06 x w8*j+cat ssv584re f:hv yi:eum bob has a mass of 365 grams, and it is released at an angle o:v c8s8 eeasx4 tvcrxjh0y:hi6f w+5*f 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the y,rvz x2aqi)0fuxeg3 1f b 3*rclock loses hal,3qy0*arxv2fe1 rigxfb) 3uz f a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speewfo6o-*zg;w4/u/wz5 jz iwtgd $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it)+ml.7: gl(s ffz atnc is released from rest starting at an ant7 lsn (f.f mlgcz)+a:gle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every 3.0+.+pyklg4 x ljh3,*xq nc c9qh s. He measures the distpn +.c 9jh g,xqy3h+l xk*clq4ance 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 speed o4 bdd 4zf (p;dvdywt*,f 343 m/s How far (dtbyf;4w zv4*ddd ,p apart are the wave crests (compressions)?    m

  (a) AM radio signals ha rdi(c bpfg6: 4pnb1-ave frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed of dp6-pnar big 4( f:1cb$ 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 londuqv n48(ffc4zrxfd c a8* 0*pgitudinal 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 the okbm92mrr*6r2fpy(jn,z0xa)5st az n ther. 0nk mf), j atzs9rn6ax 52yz(*2rmpbr In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched bet9yrskg 7 h)zodx:4 fp0ween two supports 28 m apart. If the tension in the cord is 150 N, howzx0 k):g9d 7yr f4ohsp long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cablmp6 ogd61ts* oe of length 620 m and diameter 1.5 cm. As the gondoodtm 1*so g66pla comes 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 surfaceql*c* en+4 l tocxa(-m of the sea. He hears the echo of the wave reflected fron+o meq4-(*x acl* cltm 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 different speeds, andwm.l: f*z wrmmm2io x4z3l h.0 this difference helps in locating the earthquake “epicenter” (where the disturbance took plz*lh rw fo.m0wm.l24i:x m3zmace).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by bl 0zxlrh:vj9 5jeuyr-6 0m4 um3z8vva 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 thj 3jvvh 5ll r8zuu4mbxz-0er6:v9m 0ye ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, anv fpk ual82.4achm8h *;)ongzd (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)fnhm*c8av ugl.; zak2o p8 )4h    (b)   

  The intensity of an earthquake wave passing through the Earth is ma31f hf 0xo7mz((sj t2 x iqq(0wszuu;easured to be z;zhm 1s(2 (so(tu3q fa0jxw fi0xu q7$ 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 s xpxx.v*fi (be pf8ri0 m.wm6.ame frequency travel through the same portion of thriffx(p 6wve0p .immb.x*x 8.e Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, of om( )5g8fwwk: b9licbjg/ 5but one transportsc8 9) o(5w: 5moikjf/lwggfbb three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is r;/0sv , drklf) c6 ;o+z uutb7h)xkpfobserved to move up and down a total vertical distance of 6vzcu07+ ,pfld/)xorf;t6 s )bhu kkr;.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch7c7cn6 hiv* qa :5hjyr the shape of the string at the moment they directly overlap. (b)hi*ncqav6jc577h:y r 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 itrgcinbr; sb,b 1z tj,)446icfs fundamental frequency, what are the freqf41i,gncz i6 ,)rbj rs4tc;bbuencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 29212 jt gm( *9ruzxkm 8rqck8ie4 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That isxz9 tr1u8( 8mmj g*ce2rqkki2, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonyt / 0nkhg0vnhq8u 3cd1m+tqb1 p,-ysates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonate. mskh-p+qtc1 g0y3 ntb y8d, hqv1/0nu $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves+;x)vlakq.nh t/ uwcn84-tyz/snzi6 on a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart arez;wntun/h )kyl +i-ta ns 4/c.x6qz8v two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and po76j5cz m*plgjl99 q350 Hz, what is the frequency of tmpc5lq96 j9 opg j7z*lhe fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the b8- obu nds: 9y; 2t+bjnapgw3zridge to the +nbb 8at2yuw9j;:opg zdn-3 ssupport 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 0;sz;glswgi p6bfy)0 it is measured to vibrate at f;w s 6pbil)yg; z00gs205 Hz. By what percent 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 vibrate aiz8. u 1lx2 upv5kyup)t 200 Hz, but it is measured to)5k p8upvy21zuuixl. vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string i h(q,n2 dogu6)xy 5p1kauy8ct gvyb7,s attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass perk yu6v x, 21)yqayh5nu 78 (cgdpot,bg 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 s8ay9tqo(3 iz itring may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many differ yi9z3t8oqi(a ent 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 tub at just the 5xuij 1x2 fx*aright frequency, the water alternately rises and falls at each end, remaining relatively calmf25 *xax ujix1 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 boundary withias04dgzqtgu/ a47 if;n the Earth between two kinu74g /gf4 zsdqa ita0;ds 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 underwater “shelf” whivny ic3x z+:( fn)0zcere the velocity changes from 2.8 m/s to 2.1 in+n: yi3 (fvxzc0c)z m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelidgd 1m,5uk41+ ujaju kng in warm air when it hits a layer of cold, dense air. If the sound wave 1u,+ m5jkd4uagu1 jkd 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 jl;/lt jgb+u) between two types of rock at a 38 bl l /u+;j)gtj$^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s manual, td)i 90fa.tjt9 awgxr4he dish has to be pointed in the direction of the satellite, but an error of about ar)w4x. 9afij09tg d t2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelen5+4lrtmmy 8wl gth 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the har4m+w5m8 rllty bors. 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 ur38w5ea .o ij 1g*ktn ivc8j0car bumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of enejiw8te 1kcu.oj vn rg508a*3irgy.]    m

  A 65-kg person jumps f3t1hk vely sl pqq7hl7yanl *wx2).6 .rom a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple sl qn3 )qk26yp ex1ahw. 7yth *.7llslvpring, 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 aom7bl9ywv vc1+ 9n7x of a freely hanging spring. The mass then falls 33 cxw77v+y mv9b1cao nl9 m before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), comprm/k(a .-f36yc oqfpm xez z:)hessing the spring 5.0 m. (a) What is the spring stiffnesk cq x:-fz hemmf)zyo3ap .6/(s 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 (diameterqg.ze d.:ix(kxo *b-u 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the tu*qi d(:g.-xe.bo kz xop (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certyk8u5, :x grdyain groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the souxgu r:dyy,8k5nd emitted?    Hz

  A 2.00-kg mass vibrates according to the equatixs h5 udw :5d/yog)e:aon x=0.650cos7.40t where x is in meteos5w)h:5 dau/: dgxyers and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its freqxqu+i2/s8m8)z 8rve( fvzaww uency if it accelerates at 0.50g (a) upwarr fqsw28i8a w xemz)z(u 8+vv/d,    f
(b) downward?    f

  A 220-kg wooden raft flo 2aen., t;vhfpl:a)np ats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into tnenp. ap,aflv t:2) h;he water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play atwtv;71y c lbq- 392 Hz (G) and 440 Hz (A)wq -tv 71b;cyl.
(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 i 3h8xqh5h5 s0z vs;srFig. 11–33. Determine a formula (a) for the ratio of t8 vrshxsizh0h53qs5 ;he 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 aynhu:vlgqz -6 2oq , c;aqif33 frequency of 264 Hz, and the tip of each prong moves 1.8 mm to eit-v3quqo2i n6,3af z:c gqhl; yher side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cycles pe w / fn3zpz9r k(s9mww47,rwtnr second. What is the maximum amplitude with which the end of tr zt/34wwrznmnpw979ksf(, w he board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached t1uqghi1prh-;ql 4q0mo a ring that can slide without friction on a vertical pole (Fig. 11–57). Determqgh il1-rup0qq14h ;mine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period ofuwh s ovb(()0dh 6t;:dttkq rk0conl9+ /f y(b exactly 2.000 s — each one-way swing takes 1.000 s. 6 +b(thtdr()k0/(f; odo9wb v uhyslqckn:t0
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the verticajdah8u/wd0* gpefs 6/g3 o65-il izck l direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the pegulep5 i803 6d-jd/f zca* k6/sgiwohriod 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 255 N. A pulovyh 9,hh -.kiki k7li8 *+ni ytsk-l/se is generated at one end, and 20.0 ms later a second pulse is k8 t.n kk+vl/i*7s yilhykh9i,o-h i-generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sprimtk,)886ir ;hfrumqmhtcqu0 u38j * vng 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 q3 h0k6urm*t8rv i,;fhmmq8uu8jt)c the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable iag;p33 m xxsd1s 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the e md;1gxapx3 s3nd of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (prrqr( :7ni g:60jir;2k uzxmfb-ly9which 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 to a mass vibrating on a spring, estimate the frequency of this vibration, given t0mq;j6kb-rfr g9zi x:rl: 7nyuir p2(hat the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz