Give some examples of everyday vibratiww3- 2z6cfa y9(mxxqe kc( g+6iva 5gvng objects. Which exhibit SHM, at least approximateve w6g 3wc+2i(xkq5 fc(vmg - a6xayz9ly?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where ,st4 kucr8rj/?

Explain why the motion of a piston in an automobile engine is apkqy8rppgqepdx8 q 7g -6p:- k-proximately simple harmonic.6xpp -p:8y8d-qrgk kq q7-e gp

Real springs have mass. Will the true period and frequefc cf92p8l.el.d ta s2ncy be larger or smaller than given by the equations for a mass oscillating on the end 8ft. dl 9fa2ec. 2clspof an idealized massless spring? Explain.

How could you double the maximum speed of a simple hl* f5g6t8 jndi )dt;nd 4qgx4rarmonic oscillator (SHO)?

A 5.0-kg trout is attache; 0g,*voacvtfg: xk* id to the hook of a vertical spring scale, and then is released. Describe the scalfgt* :v0g oa*kc vi;,xe reading as a function of time.

If a pendulum clock iq-h8/9ia wni fs accurate at sea level, will it gain or lose time when taken to high altitua nw/iqi-h98f de? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48)33 nefb;g7yk( / xjxyt. How could you estimate the height of the branch using only a stopwaek g/3nxt 7b yj;xf3(ytch?

Why can you make water slosh back and forth in a pan only if youkm hm.a nuwd+j7s0+p 5 shake the pan at aj5nhs+p.m k+d uwam07 certain frequency?

Give several everyday ez wpq2 zjm83.mu+vt rkpn6i *)xamples of resonance.

Is a rattle in a car ever a resonance phenomenon? 7ck-jw4)nva axpaf -a9k ,e ,sExplain.

Is the frequency of a simple periodic wave equal to the frequency of its z a3gklrc5v:-2 gl(exsource? Why ze-v(3c5g glrlk2 ax: or why not?

Explain the difference between tyt a:(86j;1v pus afcg +t)rrthe speed of a transverse wave traveling down a cord and the speed of a tiny piece of t+:6rj8yvu t;() gpt af1tcrashe cord.

Why do the strings used for the lowest-frhhz0*n:i7r r 8g(rpjgequency notes on a piano normally have wire wrapped arounn7ipg:zg* (rh0r8 hrjd them?

What kind of waves do you think will travelz3l1h i5h (qye down a horizontal metal rod if you strike its end (a) vertically from 1hq(3ezyhil5 above and (b) horizontally parallel to its length?

Since the density of air decreases with an incre,6npe) q8 27 fjs)bzj uef1a;0rtjodz ase in temperature, but the bulk modulus B is nearly independentaj) 2sju q8f bfeedz,7o 6 0np;zr)1jt of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease i p4+rd+ ur3sufn amplitude as they travel away from td3r4p+u srfu +he source.

Two linear waves have the same amplitude and s 7xnle08ey- xr9 u1uefpeed, and otherwise are identical, except one has half the wavelength u e-ue7xyr1fn98 0lxeof the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boun cb8 /lxwh-ipn2.x /;dm8hy3pycge7bdary between two sections of cord as in Fig. 11–33, the frequency does not change (al w7 3b y.n/gby x2icmxhcdhp;pe88l-/though the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could touknexztjrdu2 : t3 ,)wx1d)2deb6 z/p lch it with a knife blade without disturbing the moti6x: rdt,2wnp1 )dt xd/uj2e l)z3ekbzon?

When a standing wave exists on a strin.+ oag*5 zenoqx hucfgw1b,ot1:o g, 1g, the vibrations of incident and reflected waves cancel tzno*ao1 1b5x wg +g egof:oqh.,1,cuat the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmit4ch d iaxf(7hz e)a-g1ted from one place to another, how might we det7a1h-d e( fzgc4ia)h xermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SH2(dd,ket4pih e l3fi a po/v+/wq-ff(M with amplitude 0.18 m, what is the total distance it travfwio+(/dlfv4pidpe a2q3,f/(t - kheels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 c.x9w50 i4cfwhwsyk n 0m long when a weight of 180 N hangs from it. What is the “spring” constant k of this elaw9cnx.0yikh4ww f 50sstic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mp3 3e esy/9dftm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the freds/ety3f 9 e3pquency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3. l)qt j aoheu 1-;b9-xyoa7kx8g .epr16 cm when a 2.7-kg fish hangs from it. (a) What is the s-e-1yr xp7tbo a. je9q8 ghu )k1o;laxpring stiffness 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 frequency of 3.0 Hz when a mass of 0sc64tnb 1jls *.60 kg is hung from itn stj1scb *l46. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicati36q 1/ecxs sl4lsf ;kcooi6-kng the position x of the mass in Fig. 11–2 at times t = 0,t = k6q3sfl oks1c4x;o-sei6 /cl $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates predom0qn 8 +/llj- qckrs,nuinately with a frequency ofnl/l s-juck,r8q0 +q n 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 vibra8i 9: wyuvr,fptes with a frequency of 0.88 Hz. When an additional 680-g mass is added,u:8 iwpyv9 rf 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 per 3fd ;iddue azr9v qjd9l7 9+2fsecond with an amplitude of 0.13 m. vzi9d9u;9erf+d 7 qaddf23jlDetermine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maximq7 ,bj.* jptpdum val7 qjp jt.,*dbpue?$\approx$    A

A mass attached to the end of a spring is str. zm dwo/;,4dol8b)ap-g czgl etched 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 veyd3qg7. 9yfovrtical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to r9dvf 3.y q7goyeach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is ati.4amjkz0/ ci7kkjl878n pb s5 x1pbftached to 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 moving with a speed of 0zbx1i747/ 50k.lmi8bcpkkfs 8jnjpa.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 0.2eqq5,6/m.v 7 rrrwo pof+s *wf00 m to “load” a 0.180-kg ball. With what speed wifefow w,r*sq6/ 5. + vm7qporrll the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictiowpm 2x sd5b4yvkxu0 ciy.-/f7 nless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum accelp/ b yvci72w4y x50.ufkm-dxs eration 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 equatiu:n8x:w 5m r9c uui7htip 4rb0on x = 0.45cos6.4t where x is in meters and t is in seconds. D0p5ni b9tx 84umw :ru :7criuhetermine
(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 ismufbnn(6 v :n* the energy of a SHO half KE and half PE? ±*n (f:u vmbnn6    A

  If one vibration has 7.0 times the energy of a second, but the5 -voanv,tb ,e4qo aa-ir frequencies and masses are the same, what is the ratio of their ampli,, aeavq t5oab-n- ov4tudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lig4f19rla;0cvh .jan8 gtz zwz5 ht spring once every 0.65 s. 90 cjz g w5aln ;4hvz.rza8t1f
(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 verticalyks; b1+k+7r; vdbfv z springs, each with spring stiffness constant k+17 vkb+; kdvyrzfb;s (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to 0tjn* x)3 lu kqfrlx)zux. r29the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determi)z )rrx.j2*fl0n3ul uxqx k9t ne
(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, labeleddy8d f*qx 8v4e 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 = 1b0uwty/nok/t o49cm ; 24 N/m) is struck by a hammer, which gives the mass an initial o/uk4/ty;ctbmnwo0 9speed 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 stiffosu , h8ah1f ir10zea+ness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the oha0i+hfa1r, sz u8e 1equilibrium 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 constae0 sw )(l/hi5rj s9bafnts $k_1$ 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 horu h;onf u)-3tiizontal spring whose spring stiffness ch3tuifn )o u-;onstant 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 froiipje) idz/f1,xuw4da 6*n - o4*y nxbm 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 thef* eiduyobn- 1*izdx/ j4wx)6ai, p4n spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. Wha3ugm (fb2cxf:p 2u7nrt is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be ifec i8el4.uvd sc2.g/v it is to make exactly one swing per second? (That i g/c d.8ve24.cisluve s, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. rzj1y( sc6 2p-lj,k-ggk xq0koc9g3pWhat is its period on Mars, where the acc g0z pyso(jxj- rgc-g k 1,k6qcpk9l32eleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lonxe . cc)w6aiw:)a pry4g
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.7zcedi5 q/jqom:x+k 3360 m, the pendulum bob has a mass of 365 gq35+ ezcdxqikjom3:/ rams, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pky8l+ d 7pb,jiendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of th8p+ b7ldykji, e pendulum? shortened by    mm.

Derive a formula for the maxim u hmzkt ,(k90)-t yil,tsj4ps9kh,o rum 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. At i*j7wchfwr cw;1 vp,wg5dvz* 3t is released from rest starting at an angw1v jccwg7wv,wh ;p r5 zf3**dle 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 dp.yzt 1alf-ej n ,lew419 ey0that wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 t.9 enw-eyjlpal, ye4f 1d 10zm. How fast are the waves traveling?    m/s

  A sound wave in air has a freq5vva+frm 3mmlb5c:4 0bc r ih4uency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave ih3 a5crcmr+ b5mf4b lm4v:0v crests (compressions)?    m

  (a) AM radio signals have frequencies 9ss;r8xhj9psx64d ob between 550 kHz and 1600 kHz (kilohertz) an x p49s; shbsdr698xojd travel 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 of longitudinal waves in : r3,f hst7xqi 0y2by9 vdl,so
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have th,fh0aq;3+fdpke k2 zae same elastic modulus, but one is twice as dense as the other. In which rod will the speed +zkafa;,3kq2fdhp 0e of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg isb o0irr.bpjs *1/, pdo*k:* wqfqwt2g stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the owj qkbop*0gd.srbpt /*f 1w o:*,r2 qither?    s

  A ski gondola is connected to the top of a hill9r8aawpkksteqkz 1: i:7 f/x: by a steel cable of length 620 m and diameter 1.5 c78k/1 ::s :a zrakipxef wtq9km. 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 to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface okq1m cugt -h. ep+v3y-f the sea. He heary1p gh3m -. q-ekcu+tvs the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at differentj; sprjeh*o4:z12 q hoyljq84htjv 21 speeds, and this difference helps in locating the earthquake “epicente12jro4l*hj8yh oht4zq v sq ;jp21j:er” (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 nt *chpiy+z.f yvs s.(+l70oyv. s +uesinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what ampli+cyvv f *s u +0.ye7sphli.on.zy+(tstude 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 intensitiedh 1/tp2 opnb(s, and (b) the amplitudes, of an earthquake P wave passing thr1np(o h/ dpb2tough the Earth 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 measuredx 1q3zdj wkt.t5mmc (lxv+6z3 to be xzm +w5 z3t63(j.qx vlmdck1t$ 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(1l. lve6h y0en;v :,sxgttbo the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes xte b(6l:s 10loe,v.vy n;tg hof the two waves?   

  Two waves traveling along a stretched string have the same frequency, buv1ftd +y6f4r 7wv g9vcollx. aiqr0 94t one transports three 9 v y744 twlg9o0+vdxcrr af1ifv6 l.qtimes 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 observed to move up and dowz0z m4 cc,r.phn a total vertical distance of 6.0 cm, c4cz.0p r,hzm 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 toward3w v51qtqeqx,wpfu z 0j21.s33v bs* ( pzvcie each other. (a) Sketch 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 the pulses pass esvu. piw33 jfq11qzpt we5 q zs20ce,*vx3v b(ach 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 frequen a x9;9h qcn(sp8sz)tocy, what are the x(z ssqncha9 )o98t;pfrequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequep6dgyvi;f-,lsw,2 ,g hyb hd, ncy will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds ;s-,fwdph, 2blv h g d,,yy6igof the string vibrates as a standing wave.)    Hz

  A particular string resonates in f t7vx0*djo mg-,ik,o four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will ,kvx0,ogtj - 7fmo id*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 4p: ruij)t-y;cz* mqiof standing waves is 475 Hz, how far apart are two adc; jt *pm-qyu):4i izrjacent nodes?   m

  If two successive overtones of a vibratin rtw.u-eu9q(h l.bhzgn: e p2;g string are 280 Hz and 350 Hz, what is the freque.l;uqurw.9 e:(hbpteh zn g 2-ncy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Tar1 m:y mmvz)6he distance from the bridge to :ayvmz1 )6 rmmthe support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suppog7wz4ur1nb5bn-5lk2f ,tl l hsed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tenslwf ghbu451 tk7zbl 2 rn,-l5nion 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 v1- dgslu08f tsibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct8ldss-utg0 f1 the frequency? decreased by    %

  One end of a horizontal ex81cia1 n7hm string is attached to a small-amplitude mechanical 60-Hz v1 78xacmeh1in ibrator. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the :iss8nac po74 aga/)g pulley. If the hanging mass m is fixed at 0.080 kg, ho/a i48)sog:7gaacsnpw 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 j svqshqx3mou5 av.+6xn1s+.r ust the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequv.n mv+ x1rqsq5.aos6shx 3 +uency 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 witvqt ,5-.vin*byqlnn6 hin the Earth be.vyqqt ,6l nbn*vi5n-tween 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 underwater “shelf” where 8/ b/bsda+agz3tvng.the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crenggbdtsb.zv//3+ aa 8sts make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer vyp 9ypux-. tl*o.5z9rokhh/of cold, dense air. If the sound wave vkurlpx5 .9. 9t/hhzy*-oyo phits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rocjl. fzyf-o-vn -;ti r2k at a 3ztj2nfov;f l-i.r y- -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 . a v;olmk25nethe user’s manual, the dish has to be pointed i.2mkva le5 on;n the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h tr6ly c 4 uw:.uo:0oeld) ih+pjravels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do theyr ip:y oul ecj.u 4:d6w+o0lh) have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a al02 e sqs,h5 bw4d/mtspring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with maqse0w/m a2 hdt4bs,l5ss 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 fro mtdqb6zteu- 8l8g, k;m a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaz;6tklq 8, g dmb8uet-ves 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 plmwyex:ah (g 3fxp6y )8aced on the end of a freely hanging spring. The mass then falls 33 cm before it stops fyax yem g3p68:w hx()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 (Fi5*qzkpv;, cieg. 11–54), compressing the spring 5.0 m. (vip;qce 5 *zk,a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diame ) 31 k wjozhk1m7t7guwlyk1(g mxe86oter 8 cm) at just the right pace of about 1 step per second, the xg1oym om1k)g ul 7(3h8 kjewk1 zt67wcoffee 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 groove 10.8 cm from the 4 mw+k*pg*pescenter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emittwep4k p*m+*sged?    Hz

  A 2.00-kg mass vibrates according to the eu:dbesd)i *f4quation x=0.650cos7.40t where x is in meters and t in seconid*e:b 4sf du)ds. 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 s2wtu9,fjl5a1a + wbmf. What is its frequency if it accelerates at 0.50g (s1+2u,bjwt am w95afla) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lak* zzifhn adj2s2,.j+we. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the wfaw*dzs,hz+. j n 22ijater. 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 musiqvfu bjp sj7, 1a1j;x/bzpf12cal instrument are tuned to play at 392 Hz (G) and 440 Hz (ja s7pv2b11 1 juz;,fbqj/fxpA).
(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 scx:gsl 0 0 2-wrgxa/ntvs,t4ztretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter sectiog/0-tlg vxr40 t:aczw ,2s sxnn, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, andhk7)t 0(8gnfjp, wzjc2a2z sw; ym; mb the tip of each prong moves 1.8 mmcha ys(7;2m, zk8twfzj g0p2;njbmw) 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 s:c2hr t-nsqik8, 8kwq imple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact wq88:nc h-wskr q,t k2iith the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can sljn;(rf.t5zn i-2vbo x.0gf sside without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string wfxro0( .stsg 2 j5nv;f-iz .nbith one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — eal r )4egk5 w3ybhhx14wch one-way swing takes 1.000 s. h5x4 gk4 )w1hrelby3w
(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 directicirc qkj sg5 *hhz4)qq89c-3 e;t .oymon or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillj5 ) 4 i hc8 ch93qterk;csmgzqy.oq*-ations 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 hlxk8un,bv,+a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the oppovl,uhk b,+8nxsite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with p3**hl+ xjtgw 0+qmtl09 zjimspring stiffness constant k. +mqtj* 0z3hmj li*lt +0wgx9p 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 the block? (Assume $m \ll M$)

  A crane has hoisted a 1200f9,l6xahe11*nnt u/o kpc da,-kg car at the junkyard. The steel crane cable is 22 m ,xca ,nant l*/ou1kp19fd 6ehlong and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives theiiu50z)5+afrgb+ gc4)70j mjp bpv j5ewa -py dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate-imjbp7wc +agr5 abp f j5p40igue05v+)zy )j. 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