Give some examples of everyday vibrating objects. Which exhibit SHM, at least +fo t1gle6 0w5yqmo+ wrsi:o) approximately:5wqt6mowof eir gyl1s 0o+ +)?

Is the acceleration of a simplg2m.* gogxhi k,c l/n9e harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approf+ r8)p,stm xbximately simple har) x8rfpst,+mbmonic.

Real springs have mass. Will the -b+w5n/04l jcaialfx true period and frequency be larger or smaller than given by the equations f45jbni+laal f- c x0/wor a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillaty vk0t5t4 o)lfor (SHO)?

A 5.0-kg trout is attac )fz u/,*6z xky5o:z9vyvcp 9nvxt3qnhed to the hook of a vertical spring scale, and then is released. Describe the scaley3 9v)p/vvkcfq5z:x 9y*n6 , uxnoztz reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time 11 aa yle.jm/mm9gyb 8when taken to higa 11aygb8y/ m.ljm 9meh altitude? Why?

A tire swing hanging d 8x1ib,sgg) yd vhgsr),*.yv from a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height,hdxv g*sb1ig8,)r d.vgy)y s of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake th onvcfnp5pu9- r3jjm3h+ t j4k-j(x,ue pan at a certain freq( -3kur 9nj cj,u-xfp+pt j4nvj5o3mhuency?

Give several everyday exampletq u3 ldjctk,+ +t3l2qs of resonance.

Is a rattle in a car ever a )w5 qk xikn )9xaeck0(wnr.,bresonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequen,hkvmnuanu.- 8*. htr cy of its source? Why or why nakuh*8uv.n h -n ,trm.ot?

Explain the difference betwee4.,aoq 6znh4m4yf ucnn the speed of a transverse wave traveling down a cord and the speed of a tiny oqn4u,h4z 4.cnfa ym6piece of the cord.

Why do the strings used for the lowest-frnthvu n.re9gn)7 89mkequency notes on a piano normally have wire.9nge9hm)rknt 7u vn 8 wrapped around them?

What kind of waves do you think will travel down a horizontal1myn*t dk;5isw1 q)hj metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its mjhq i;dkys5w 11t)*nlength?

Since the density of air decreases with an increase in temperature, but the 92jrm*v6 6 mq gxl6qpulb d(q3bulk modulus B is nearly independent of temperature, how would you expect the speed of smq vd*6 2m(u6lpxg qr j3l96qbound waves in air to vary with temperature?

Give two reasons why circular water waves s1r2fkvk5ugw 1*.t2j/ x vb)z:vvvp8qs2dts decrease in amplitude as they travel away from the source.8vuv 1v/jssf 2x5 dpvs.t)2brzq :1k*wgv2kt

Two linear waves have the same amplituf 3xcd-d78uaj k)0ocgde and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits m) fg x3kj0dc auc-7do8ore energy? By what factor?

When a sinusoidal wave crosses the boundary between tw,q x2+rn *smdho sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change).s+m *, rh2nqdx Explain why.

If a string is vibrating in three segments, are there any places you could tf6t: ok6*x kubrm 0p8souch it with a knife blade without disturbb*s8 ko6km f r6p0tu:xing the motion?

When a standing wave exists on a string, the vibratiosxij5 2dkdhgqq75p3(b6f7n b ns of incident and reflected waves cancel at 572q iqk53fd njphds7b(b6gx the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to cqf).-pilw k6another, how might we determine whether the energy was being ci. pq6 )-lwkfcarried by particles (material bodies) or by waves?

  If a particle undergoes SHM with ampdtq,ts36b4 lota rbq )+6g( zalitude 0.18 m, what is the total distance it travels i6+sg,tr3q4qa l bd6z) ota t(bn one period?    m

  An elastic cord is 65 cm long wheyvqu:9oa9pd-.lc t,j n 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” constan-cvpj 9: q.uayt9d,olt k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets int ;fqt0id d,h3ts 29;aoqj e;wbo the driver’s seat. If the car go t9dhd;j;sqb;a 3 fqo,2 wi0etes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6,kej-p q3s8w)gfqc - c cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffnegccs)we 3k8p, -jfqq-ss constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a freqe6 tpmp)i p0*i dyxxv(ce3843jq p6p/v kor,quency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from it6re xiijdqqvk(8/e ,3 3)p*p4p vco0m6 py xpt?    Hz

Construct a Table in:ouxb2 jka. y2dicating the position x of the mass in Fig. 11–2 at times t = jayuxo2 2kb:.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 b*.7wm7t-xenpn bo5 m a spider’s web. The web vibrates predominatelw*n7 petxom5bn.7-b my with a frequency 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 o k8k1b pgyz/m)f 0.88 Hz. When an additional 680-g mass is added to m, the /1g ) mkzp8ykbfrequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrateszj1tk/brcn;5pfu,sx3 uk( p/ 3.0 times per second with an amplitude of 0.j/n5u3(ukbkr,tx;zc1 /p fp s 13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speedkh*d*lfy rf ng;k 4xhc15n9 sn6f2:dl of a SHO half the maximum value? nl 4*fkh5k2dn:fd9 *hx ; n6lcgf1rsy$\approx$    A

A mass attached to the end of a spring is st)u87nf6 rdooh03,hbe t /amdfretched 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.d1*eq+sdyva - lw:0n m If the spring is stretched an additional 0.130 m and released, how longn+d sl 01d:vy*m-qaw e does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg ,m+sxvu * *kwalx.i0tii/ b z:is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonl.w0*ix x*:bs/zi ui amv+k ,tic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m 6w4.-trw zc,f5sao,6,utf z zi 1yugc to “load” a 0.180-kg c,w6tfto ,u1z-4f5 czgu6r yw , z.isaball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a h/0c4/g8admg7v ri-2ld c bytl4:x bahorizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass expe7cc / ty dvg-d l8 bgah/2bx0m4ila:4rriences 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 thea;rwr*ts2* b9: bucug equation x = 0.45cos6.4t where x is in meters and t is in se:9 ubc uws*2gr; b*tarconds. 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 equi+ocy,wb.lo ev-3i v 6llibrium is the energy of a SHO half KE and half PE?v,.wlc+ e6i3- o vloby ±    A

  If one vibration has 7.0 o2j6 ko6vewo7/ju 7n htimes the energy of a second, but their frequencies and mauno7626ohjow/ke vj7 sses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates fro hos126dq m3bo8k 1qsdqcp/7vm a vertically hanging light spring once every 0o17cq q p81hqv2m 3dss6/kbod .65 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 )i uf,)wkemk31 lcr0p9b lmk ,supported by two identical parallel vertical springs, each wc )p,bfe,)m09 k1 kk3lrumil with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrateuh4ps7u. fj;4ymp pf-:efau , s according to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determf7fpu.a m,-hpjse yu 4:;4 pufine
(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 6g 1bz ( gdpr-zm2v)azof 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 st ch-5+ j-ht+q )dhgqbtruc5b+j d qqhgtc+h)--h tk by 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 wiz((yik u2hlv. th spring stiffness constant 305 N/m vibrates with an amplitude of 28ziuylv2h(. (k.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiff,lq2v6)hh buo ness 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 attac8o-f k ,6 g89yfwvury 4lt lp*hfh6wq,hed to a fixed horizontal spring whose spring stiffness constan8u- t,ykv46w9glpql r y f ,fw8f*o6hht is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high brid.a2 (ctqgb4krb kh9p+ge. 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 42 kk9gqt+hpc a(b.rbrest 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 evhy)kfdkk0lg, mn*y. 1;n) wrr )a e(gxactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to v2 eh fk:o,-demake exactly one swing per second? :2,kfeh-edo v(That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Eauprc9xz su wu72 )zy;ot)8o (yrth. What is its period on Mars, where the acceleration of gravity is about 0.37 tc)zsx ;yp79o8zuo 2 urt)w uy(hat on Earth?    s

  What is the period of a simple p1v g0*6niqitlendulum 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, thz qi wk: wi06bamyc;h1tl4 -z*e pendulum bob has a mass of 365 grams, and itzal *06 1ii4w-w zc:tk;h byqm is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the cl 5o0icvx z83kr *3hikhcf/bw) ock loses half a 0fov 5w8 cibzi)x 3k3chrhk */minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speezqlus eb; , 7 fh5;n1)g*o8ygo *mxtaed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillatehgqih au8ul: w8(7w2. qtt(txs at a frequency of 2.5 Hz. At it is released from rest stat8 (xa: hiq.wh2utu (7q8 lwgtrting 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 oz /tbj53wir- 5vd5jkwwy3j0 kf his anchored boat every 3.0 s. He measures the distance between twokzjj 5rw/b3 0- dy55j3wkiwvt crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hzjx;06mgvadw7 i ;hsm 5 and travels with a speed of 343 m/s How far apart are th 5x6i;a7s mmg0jhdwv ;e wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kjvth0tz :laut9dr /rnd9yd07o 4( pk;Hz (kilohertz) and travel with a spe9/ jh04d :vnt 7tty9ua;k po(lzrr0dd ed 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 was ah/:mx9 o64. yumvixa bsn+2ves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, buv/lq: t zovh9:t one is twice as dense as the other. In which rod will the speed of longitudinalz9vlv:ohqt/ : waves be greater, and by what factor?   

  A cord of mass 0.65 kg is sm2:6vovy1p sbr 9e. cvtretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pe6o:p 2vrcbvy9m. vs1ulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cl7v dnvh:j+f* - pb(anbam+ b;ho5,u table of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse alf b tl7a vb;5ubv-hdm p*++:hoj (n,naong 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 tya kek-5jgb29zhwn2j no.(xjm;jt(- he surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep - b 9n ;-ejj(n5mo(hk 2jgxk.yajzt2wis the ocean at this point?    m

  P and S waves from an earthquake travel at differe+key9 xd ffh7:i.rqc w p.vbcy2 9e-3jnt speeds, and this difference helps in locating the earthquake “epicente 3wjh. +yqi2dxr cye9 ekf bcp-.f:v79r” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a siuxn1 x /1uyf r(w+o9tj( ggx;95efe vcnusoidal transverse wave. Assuming a e;xu5c nwe+1gfv 91g( 9r(ufjo/xxty 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 ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensitie;khe;phxk wl*;9e d/ ms, and (b) the amplitudes, of an earthquake P wave passing through the E; de;9p/*hwx;k lmk hearth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to be vgv59zrc vo6wuj;,kfn 7.r t5;nzj6w.kv c9ug5f v,7 v5tror$ 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 sanrb+ag +z(uqnp8ltfl/6n;8hme frequency travel through the same portion of thq a(lt p8 rb/ugnn+n8+zh;6 fle 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, but one28 gwn+-y.pteanbfuwvw4 3*w transports three times the power of the other. Whaew3pn+ 8w -abtu.wwn4y2v*f gt is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move ijy/l2 t*8x bxup and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease tojybx8/lx *t2i 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) Sketpul5g-qsyd w5)0 1sbx ch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment ty5bw xsu)1q5ds-p0l ghe pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequenc51 b6bnk4i:ticejz av: u)sa6y, what are the frequencies ofab)jczta1bs 6 6:iu4i5n: evk the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates n4z5 c x pn5ivk fxpl-/48;xneat 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibratex5- nnpz ve8n/k4xxlpcif;45 s as a standing wave.)    Hz

  A particular string resonaru2c e+um bwj4 jx,x2)tes in four loops at a frequency of 280 Hz. Name at least three other frequencies )bj,exjmw+ 24 2ucr xuat which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of s di3n)rlx )g7wtanding waves is 475 Hz, how far apart are two w)7 dnrgx)l3 iadjacent nodes?   m

  If two successive overtones of a vibrating xhz(mk5 y7u4 zstring are 280 Hz and 350 Hz, what is the frequencymk 5zu4(hzxy7 of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass o:0p1:b2ff5qpfa0 7tfm o n;ah-k b2dyaeizw0f 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is undet; idzyf:p0wf20b efba-7h1n oa2m5 f:kapq0r 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, buoo3pw)w psv 27ak1q t0t it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So thp1 oq 3 owtpsk2a7v)w0e three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string vvr ,9ir e;;:mow7bzbis supposed to vibrate 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 frequenc ;bivz mer:;v9, wor7by? decreased by    %

  One end of a horizontal string is attached to a smallg y8+ pu7m5kvxh ui fve dr93u1g8)f4d-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length i mg71fr48uvx)93eg+ puhud5i8fkdyv s $3.9 \times10^{ -4}$ 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 strine0)q a6lub ti) :4lrgkg may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.08iq6l) 0t a4b eg)lk:ur0 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a k,k2jck .o-mj 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 6m-kcok, j2jk. 5-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 within the Earth ( y9p-w(n op67z. u7ykawsqvn between two kinds of material. If it approaches the boundary at zww. 7nu q6py7 9- nko(vsyap(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 ei ,yf g 4qwv7xs*ex-sj -lo.+underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave f + *jqx-.iseelyg7-s4wox,vcrests 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 hj:tm-6d kh)j vyzv-r f z2h8 ww.yjh+;its a layer of cold, dense air. If the sound wave hits the co j t.+h vz6)w8 hr:--fjyhk w2djmzy;vld 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 earthqudpa 43n.a )azjzph0 c6ake wave strikes a boundary between two types of rock at a 3z4nh)jd. cap p6 za0a38 $^{\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 diowb4lib7 2mp ,*jugd 0sh1o) iameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of abomu2bod p i1g7* low,b4js)hi0ut 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelengtz9 zpl9*nc uf v5wne8.h 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 harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamiznu9zfv5*ec nl. pw 98s, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper lq+ xt(p q9al:has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car9lxqap t(+:ql , 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 nrt2w6fkpo88 xpa :* rzet 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, and ko6wf*tpax8:rp r28z
(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 6/,h uv mhksel 91-mzwthe end of a freely hanging spring. The mass then falls 9 kz, h6w-smulhe1mv /33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at)o ;9y:5r hamjp rr7d,s ls7wh a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) Wh rahs7)w yspl,mr5: r;d7 jho9at 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 gg16)gmp4 -dvgo3lhs 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 top (Fig. 11–55). Estim-)h dgoglgpsm6gv1 43ate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonhpuv :qd5g7g )ograph record have a wavelength of 1.70 mm. g :7ugd5qv) hpWhat will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation y;l1 ol8j(dcf x=0.650cos7.40t where x is in meters dl(j1 ycl;o8 fand t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if it amb fy+) jd4d7uccelerb)yf+d u4m7jd ates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, id 3pr7).xgk bmrk2,rvz d. +cht sinks 4.0 cm deeper into the water. When he steps.pm7xdrkd)2 r3k+, .gzvcrh b 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 tune5daeejnk (ws-p. u 7q:d to play at 392 Hz (G) and 440 Hz (A). :js-n7dkqp e(ue5 .wa
(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. 11–33l9zvx,t(9-/ hjv:s:h zexmf o. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section o9h ,x/ zzj 9txsl-:h :fove(vmf cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of e.m z04weupul6wn,k lde ,,;g9e l4rxx ach prong moves 1.8 mm to either sidlrewu6d,; wl4 xgk p,e.04 z nlu,m9exe 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 cyq9 tt:,:uj xeacles per second. What is the maximum amplitude with which the end of the board cue :9j,xt q:atan 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 attachedpnz9 y/6:sucb to a ring that can slide without friction on a vertical pole (Fi z9c:pn/bu ys6g. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — eachvs*quk zq 3o fn9:hsr2z9zfj08cbz 2. one-way swing takes 1qjz2bn 3f z zz9:kf9.rhs2 0vcqou8 s*.000 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 the vertical direction or,2gs)a 1 yv dfmdtag;7 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 th2)fdv,sg7 maydt ; a1ge 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 tensionfe1;u ehsg8j;a7v+8kis z m.u of 255 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 two puls8e mu u ;+8ea.7 kgis;fh1vjzses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring g/ydpom--79iw (3 l,cavgfxu stiffness constant k. A penny of mass m is placed on top of the block. What is the maxim-oa c,/g7xi-umlp f 3(g9wydvum 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 *wjhs /;:os 1 zg.zlpkjunkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bounckswp j* oh 1z:/gs;.lzing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which als y)yid-dag ld0r; j1c5o 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 vibd -50ia1yd;j) cdrgly ration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz