Give some examples of everyday vibratd,0t(hni 6jt. mrixv6 ing objects. Which exhibit SHM, at least approximair0tt6ndj,iv6 x(m .h tely?

Is the acceleration of a simple harmoniiqyv78k1 .2r4(7 kny ufyr fwrc oscillator ever zero? If so, where?

Explain why the motion of a pipp ipsyd)6m;89w;r)pqnhj m2 ston in an automobile engine is approximately simple hpdin)pp8j9 w;r yqh 2m)6mps ;armonic.

Real springs have mass. Will the true period an y5 mxin*ooh qa,4zdn+5-i/h hd frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explaiom- ,onidyx5 +4qi5h hznh*/ an.

How could you double the maximum speed of a simple harmonic oscillator (SHO )ps)orgcu7 -d)?

A 5.0-kg trout is attached to the hook of a vertical spriq maej (j.e55gt .n/hbng scale, and then is released. Describe 55(a g.hjnjb/m ete.q the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time wx +th85r fk yli.k0.+t rcf1dohen taken l .i. k1kfo 0t+d rcty8h5rf+xto high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). H: rnpa, r8sfh *ga0as7ow could you esti: grn*08p7,a fara shsmate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake od;e1y wb5f*fz;5,6 tvo(q rpbnyff*the pan at a certa**vryq1ff6 5fdwo;z (e,fn;tp b o5ybin frequency?

Give several everyday examples of)bsef e )k./7axddr iboj0x9/k4 x m/c resonance.

Is a rattle in a car e+z u3/( lx/pqx wy(zkuver a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of6(ilpg9ez h+h+ cz bmi(j;av2 its source? Why zg lv ih bhm2p(i6cj9;(zea++ or why not?

Explain the difference between the speed of a transverse wave travelinzmn6myhm fp,ik20-3g odwgsk1*l.+ ug down a cord and the speed of a tiny pi2oz g- 0m3 d,lpiwy fmm.ugn1s6+kk h*ece of the cord.

Why do the strings used for the lowest-frequency notes on a piano norma:z+:lz ( g3dpcg tztl0 lw8:ctlly have wire wrapd( : tcp g8::wgz+tztlll3z0cped around them?

What kind of waves do you think will travel down a horizontal met s h5ajzs57o bp5(uy 8dai/t1ual rod if you strike its end (a) vertically from above and (b) horipo5b7a 18atdz is5s yu(j5u/hzontally parallel to its length?

Since the density of air decreases w31lhze;sg hv- ith an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperatueh sv-h1lg3 z;re?

Give two reasons why circular water waves decreas968x mafdn v9oe in amplitude as they travel away from theo a9dmf89 nv6x source.

Two linear waves have the same amplitude and sper3hmmfor d:)8 q( o4jxthk:8 ved, and otherwise are identical, except one has hajrmt: :r83qhd() 4o8 xf kvmohlf the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of corgyw-(, kvjo7+lzuxg mq )iuvj q4 )t4*d as in Fiu7)u*( lqv,wgy4o g+z)-xjjv qimtk4 g. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three seg(7(ci0vtvs/u 1xcu oi ments, are there any places you could touch it wit/u0 c(v 1xiucvi 7o(tsh a knife blade without disturbing the motion?

When a standing wave exists on a striahjlr njy,q z79* kz55ng, the vibrations of incident and reflected waves cancel at the nodes. Does this mean thz*rjjq y5n5zhk, al7 9at energy was destroyed? Explain.

If we knew that energy was being transmitted from one placz:xw .dd58 9l6dxrn zje to another, how might we determine whether the energy was being carried by particles (matelj5 zd :6nzwd.98rxdxrial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total rr4x+ac( bpofa v)28 ovn+uts4 (7itsdistance it travels n7rx)4ro4 +u(viasfotpcasvb +28(t in one period?    m

  An elastic cord is 65 cm long wolssz 6fo5o + xfk(;u9s.po 9ohen a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this 9sk ;su.o5of(p xof+os6 l zo9elastic cord?    N/m

  The springs of a 1500-kg caxem 5)9/npgrf.i3 m fjfbcg-2r 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 fr.)xmfic3 fpebjn-gr92gm/ 5 fequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm whe1 e2z-)xqicaun a 2.7-kg fish hangs from it. (a) What is the spring stiffness co)i-cxq1 z u2aenstant $\approx$    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 3jeh tc:xun 4,9.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from i, 4uc9nthjx:e t?    Hz

Construct a Table indicate.3qli:t 1 avy4 jrsczg)68fring the position x of the mass in Fig. 11–2 at times t = 0,t .rl gt i)j 4y3rq s6z:1eafvc8= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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)cyygo)7zdur 1qg0vdn0*ky; web vibrates predominately with a frequency o1ky)y g7 d;rzqu)n00 *ycv dogf 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 0.88e/ (1unozae:wf 8oetw 7k:l8 s Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is1u:ze8/(a8 eo nektsw7owl :f the value of m?    kg

  A 0.60-kg mass at the end ofh,sc1h/ l69tqo: jh4h o syhf4 a spring vibrates 3.0 times per second with an amplitude oft hjohc/ y6 hh:s4oqls1 f9,h4 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement faq3q o nc)/) y2jfavl7rom equilibrium is the speed of a SHO half the maximum value?nq)jay)2 acq7f ol/3 v$\approx$    A

A mass attached to the 7adl*l+ w avcjbaa ) d4*t2u;9ikv-naend of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spribz-q/1 tomlo 5ng is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibo lmt qo/15-bzrium position again?    s

  An object with mass 3.0 kg is attached to a spring wij,rq4*xfc/h, gl r6a u/ hrnv/th spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object i ,qr,4 l/hgfx j/rr6 v/uc*hnas 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 com6g ri gdtbkz)i-)4pq(press the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what spg)rd46 tk)bi(-zg i qpeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface islep*khse p-5r li+*:5v a :ajq attached to one end of a spring; the other end is fixed to a wall. p-*p5 v+:ar* l5h:ileqsa jk e3.0 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 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 mo6a77 jdun; zaccording to the equation x = 0.45cos6.4t where x is in meters and t is i 7z a;md6o7jnun 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 the energy of a SHO half KE and halfifs*pdaig. t fc55su81m*wb2 PE?.*i1 2 *tw5g8sispa f5fbm dcu ±    A

  If one vibration has 7.0 times the energy of a second, buid tur1e bd*s.p/* .*yvgs* ant their frequencies and masses are the same, what is the ratio of their.*syb np1* vr/sd ged a.u**ti amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanginy/xkwr4lebk-0* 1ay4i uu27s+jl(b onr zg/bg light spring once every 0.65 s. a*( 0l+ry iyskbwblx1gzkn / ej4/br7u2u- 4o
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vetlal7q ce3e r- .t46lfrtical springs, each with spring stiffness constant k (Fig. 11–49). What will be t lf4- 7ct6rlt3.leqeahe frequency of vibration?

  A 300-g mass vibrates accoghz j6 s8 bt zx-z3+z1tgy:cj.;nmnw/rding to the equation x = 0.38sin6.5t where x is in meters and gb-t16/3 sn+jmtz w xny.zzgz:8j;ch t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A r091oijzbfn;z4xl: k 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 r iao*93mtqyt. est on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, whiotqi a39t*my. ch 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 spring stiffness constant 305 N/m vibrates wit 4sj2lvy5b i* wbu;t7eh an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the ejsb4e *2 5w 7;yuilbvtquilibrium 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 st qb b2/w cf:;j65- sw/ecvuszgiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed h+ bdaf.mzu79 jl,rt,azf nn;1 orizontal spring whose spring stiffness constantmz7 z,br1naf+ 9j; .,audtlf n 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 kb cy:(h7wni)cc.gw :f g jumps from a 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 the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bunb:c):c n wg y(fi.7wchgee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s.nb;ii8zqw t90 mn-fh- What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pen/f rxsj,v 1:7vjscqo0dulum be if it is to make exactly one swing per second? (That is, one covj:sq x/js7 1or,f vc0mplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. Whatnd3zhnh6wc /e zii6y- l:h4(t is its period on Mars, where the acceleration of gravity is about 0 63i/hyz :4h-6cezt dnwnli(h.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long 9 o. ee;o8 dakpvf+q *,0zm6xqhtd ca/
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a 5th5die(h/oa g yv1mkv tu10; mass of 365 grams, and it is released at an angl5;uk(tyoi gv/h1tmd ah0e 5 1ve 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 leng :qi3gjnb0) dbth of 0.9930 m. If the clock loses half a minute3db giq: 0)nbj per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula forhrf7d,e2m8q jsi . o qu3yue+l1vu3t * the maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. ( 17 tr4k9oaybyta7fqAt it is released from rest sta9b4tya7 ya1q(tr7 of krting 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 anchored boat every 3 q+xuan2k (wqgb7 9lc*.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves tc+g u29lxqw* nka(b 7qraveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed o1/l,,mozuowg oc 6 d*vf 343 m/s How far apart are the wave crests m,/zcv6 ulow*, dogo1(compressions)?    m

  (a) AM radio signals have frequenciesdx9.j nt-,rks between 550 kHz and 1600 kHz (kilohertz) and trav.xn -,sjtk r9del with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed n+n xgszn, 9g5n4t e8(3nej lxof longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus,0 u9lcvhpb7znfvw6je : -md;( but one is twice as dense as the othejw ud 0v;6benpv9 7cm lzh(:-fr. In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg xd-j*ctov+d- is stretched between two supports 28 m apart. If the tension+jvd * o--txcd in the cord is 150 N, how 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 hil4sljy/sn:j p59b wu)il 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 into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse 49uwi5)bys p ljn/:js 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 h l sg2.jxn ;x1zk)rj/vis ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the oce.xkj 1nz)rgvlj/x2 ;san at this point?    m

  P and S waves from an earthquake travel at different speeds, an1v2;i 0 dbjv 7lcq9lzu)m- exid this difference helps in locating the earthquake “epice7m9qc)izvxd0 jeb1 u2li;-v l nter” (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 caf,cw6e avs ,w1n be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually ina, vsw61ewf,c clude 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 intensitiesu, tg 4uq*dx) 8ezexd+, and (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? *e qxu+8xzug 4d),det(a)    (b)   

  The intensity of an earthquake wave pav7 6996c q5hepvq 1tllhukw8ossing through the Earth is measured to be w k79 1vv669lcph5eqhq 8o ult$ 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 te6hv2/d;ub7;bb huh, :7 jur0t ccrlthe same portion of the Earth, but one is carrying tw ujuuh :c;tbr l7h/0bde,rh ;6b2c7t vice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched strin iixx568oqn: vg have the same frequency, but one transports three times the power of the other. What is the ratio o 5iv 6o:8qixnxf the amplitudes of the two waves?   

  A bug on the surface of a pond is obserply4 9rtzwa1ip4 m*f4dj4 2khved to move up and down a total vertical distance of 6.0 cm, from t* azlpdp4 m4h4iwf4tr 2y9 kj1he 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 mov:)l1g 1gw9ikji odfu4ing toward each other. (a) Sketch the shap u:fgjwi4l)k1 19oi gde 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 the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 44mvby 33.2yd skvhwg( pdl8t.00 Hz as its fundamental frequency, what are the frequencies of thyy23dp ..svgvl 0tk(wd bhm83e first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency wlqetp9llmu 1z+7+cg 0 ill it vibrate if it is fingered one-third of the way down frc1 9++ umq7leltp l0zgom the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonnliu0:rf/ c,wp 0 3uxnates in four loops at a frequency of 280 Hz. Name at least three other frequencies at whiculn f0n30 p:/xcw,ir uh 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 frequ(seso/onpa+/tzx:h1qw :ym ((ue hm(ency of standing waves is 47ue:pqs(m:oem h (+ o1nw hs(zatyx/(/5 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whm,n6uegb0* ewm:gemo6;9 * r0tdvcy mat is the frequency of thewg*9*tmgy mr b u,me:;c6d0 neo0 vem6 fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fronevk w9.mliu u.5x*e6n/ e5ih5qpc) mhjar/5m the bridge to the support post is L = 62cm and the string is under a tension of 520 we)vneh 55eik muq n9jp u5l5h.i./6cxra/m*N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar stringdg89 :rejk:; kc aqbt7.y m0sa is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hzg:bymek; q .7cj k8astd:90ra. 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 f-((0aspk ouc (drw ,csa)am3 vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tensionca,os cpk0wsf3ad- ((rm)ua ( in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal se/w:wku (*1lv5 8 us1 r8r1gdl yzkacptring is attached to a small-amplitude mechanical 60-Hz vibrator. Thlw :1g5rc1vza yu*ls8/p(rkeudw 81 ke string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of tsag iry437l1ue/ol )sb+3 n jphe string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 1pbal7 s4oleijs/ 3gyr+nu )3kg, 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 tub at just the right frequency, tuc-jr:trxxe9 t 4r0+mhe water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wavc 9tx- 0m:+rrx u4ejtre 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. i +nbd(a3n+v 7iiprh9lq u-e*0 km/s strikes a boundary within the Earth ben7 9-3udi h*eav ibrp+nl(+ iqtween two kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an undyhp-+sxj:j .o erwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If thjp .jsxyh :-o+e 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 wh0aw ( ,iu xje0j0a/cozen it hits a layer of cold, dense air. If the sound wave hits the cold air inj0 a/ w0uc0xe j(iazo,terface 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 bodz.o c exhfs,h:rnj ;qu/i tif1s39 3(undary between two types of rock at a 3nezq/9thj, ifsx uds 1 ;ir.h3f:c o3(8 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the us,*e;ory b 4trqer’s manual, the dish has to be pointed in the direction of the satellite, but an ;,b *erqyt ro4error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels acrj) ngn2a.k)1xcau t b- r7l3fioss the Pacific Ocean. As it approaches Hawaii, people3aig.jfkba71 n )) u tr2cnxl- observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing cc5 via 9(epw0iar 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 oa0ii5 p(e9c wvf energy.]    m

  A 65-kg person jumps from a windm y.h :drw mjia1e4r,1ow to a fire net 18 m below, which stretches the net 1 1r 1h,jmym.dae wri:4.1 m. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a fjsfo; n9 g (ngr;chf;9reely hanging spring. The mass then falls 33 cm before cf nf9 ;;njh9sog (r;git stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sprin(w12d zy9y qtzg at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring syt29zd(q wyz1 tiffness 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 (diameterk68yv 2cnogx;xsg0kbfs7 5:c 8 cm) at just the right pace of about 1 step per secon n s:xgykg8f07 6v5 ;ccbox2ksd, the coffee sloshes 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.7zg qv r9ie-kw*1jfs groove 10.8 cm from the center of a 33-rpm phonograph record have a . r1fekiz7q*s- jvw9 gwavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to t:rk3:4*3ysrl2w dvbha2vm n r he equation x=0.650cos7.40t where x is in meters amwa2y :3n:s 43lk*rv2v rdhbrnd 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 fmub-5ahk6c )+wj y0m d. What is its frequency if it accele)jw + d6hm5uya k-0cbmrates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands onagdz;n 1b1 rmwk .7wc+ the raft, it sinznmckb 1a +gr;1wwd7 .ks 4.0 cm deeper 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 tuned to play at 392 Hz ( bbhypxg(ux4.dui5c.wbsei- d(2 h+v;j 6+hmG) and 440 Hz (A). ;(g-x x+pb(iih 2.svhdm cub4ej+ d uh6y.5wb
(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-parmf8 . . 6: iimjnltgn7ecs+4tct cord of Fig. 11–33. Determine a fo ngi4ecm+in.j 6c.t st 7fl:m8rmula (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 of cord or the lighter?

  A tuning fork vibrates at a fre1l15 s*d4n dihew6vqlquency of 264 Hz, and the tip of each prong moves 1.q5*h1 n6sl w4 d1vdlie8 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 simp7ju:w,hvrct,zmz;-- jjw zu 6 le 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 (w:;cm6h u-7ju rt- vw zjjzz,,Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free;jk)x/ej zn wv 40o57awul/vd” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other f4; v jjv)xzokl/e0u5wn7wad/ree.

  A “seconds” pendulum has a period of exactly 2.000 s — eachvso 0 i.vi5s3x one-way swing takes 1.0. 5vii0osxv 3s00 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 vertica( bd c8nmd-ty39n/z ill direction or can swing as a pendulum of small amplitude, but not bn8 dm b3y9c-/n(di tlzoth at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: 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 tensiu; uli6 zu+d0bqw2fxd(+ o-ukon of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite ex2kfd wq+d uouuu+ l0zbi6- (;nd. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with sprrfdp2.- quki cb*1ib; ing stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillationdkibi .2qp-b*c u1 f;rs 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 cavomy1ia 1b ua:2gkv i5 u2zq,8ble 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 per:v2b a82uokgq5im,1 1izuv ya iod 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 also gives th+gf yntp/8h elw(u2p,e diml/ u, +2 phfgt8pwy(neensions 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 that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz