Give some examples of everyday vibrating objects. Which exhibit SHM, at least ac2o g0ws.-fr2p s)quj(9zs v mpprzsm-s)(.s fj0 po92gvquc2w r oximately?

Is the acceleration of a simple harmonic oscillator ever zeroor/;vou1x:.yx 1j zp3n6jv je7zh o r4? If so, where?

Explain why the motion of a piston in an automobile engine is approximately swmfh3 knh90v) imple hah)k0 3nvfm9whrmonic.

Real springs have mass. Will the true wn8gfj sxl/q 7zc5u) nya; q99period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spri8/u qqy)fawz9lj gs;x7nn 95 cng? Explain.

How could you double the maximum speed of a simple harmonic oscws-ul0vo s./:2rgori illator (SHO)?

A 5.0-kg trout is attachebh38 5n9wcuirpn 0 qm;d to the hook of a vertical spring scale, and then is released. Describe the scale reading as a functq9b n nrhp80wc;m5u3 iion of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when tadixznw7j f od:/mj 9)2ken to 9)zf2wnji x/dj:o dm7high altitude? Why?

A tire swing hanging from a branch reaches nearly to th2- cg1.7;e hwqdp;xfrg h:idme ground (Fig. 11–48). How could you estimate the height of the branch using onp -127xcr:dg;gimwfhq ;d. e hly a stopwatch?

Why can you make water slosh back : fd pu8b4 r.c9wtct7oand forth in a pan only if you shake the pan at a certain fret ow:cdc4u9.f87p rbtquency?

Give several everyday: r+oaz suy(1ozrkjq ** .uv2mmj;hk 3 examples of resonance.

Is a rattle in a car ever a resonance phenoo9u +oaqyx/xlua gzn . 5)q*1qmenon? Explain.

Is the frequency of a si, ;5pqqt p+*k+ 0pbf 2ccahhl5 jvsw:jmple periodic wave equal to the frequency of its source? Why or why no 20k* a+:t , wp+5f;bsqcq5lvh jpchpjt?

Explain the difference between the speed of a transverse wave trfs(vr/ rxd2 i+aveling down a cord and the speed i/(r dr fsxv+2of a tiny piece of the cord.

Why do the strings used for the lowest-frequency noe;8 wls9 )*dm)ijs q;1tumxev tes on a piano normally have wire wrapped aroun;desv q)t 9l);*ui8w1msxem j d them?

What kind of waves do you think will travel down a horizontal metal rod if you:t5elx*g*g c o1imym6 strike its end (a) vertically from above and (b) y 5x*g1mgtlc :*ioe6m horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but tqrud-dx8ouow;j j 4yu dh7q6d f i/06.he bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wiu 6x8h/ juo.4- q 6qddy0wfjdd ur7o;aves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as thjtjl 29wl/ wr59f/rfn ey travel away from wllnrj9/j5w 9f /2rftthe source.

Two linear waves have the same amplitude and spvxn5u5* aui6c 9m)vd-mu yj) prgkv );eed, and otherwise are identical, except one has ha)pd) 96u5)5a;g nxrmuui -vvyj* vcmklf the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of c) 0wr ;ghjgr4uord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Expla0w4)j hrg g;urin why.

If a string is vibrating in three segments, are there any places you coz6xvgo t9 q/d xiv/8x6uld touch it with a knife blade without disturbing thex68/v q9x 6/o vzxigtd motion?

When a standing wave exists on a string, the vibrations of p;iz1 .mwhxc72 gzhxy76suob.f8(pcincident and reflected waves cancel at the nodes. Does this mean that en 1yh;wmzuz.7c87f6 ibx.2s cp (xohpgergy was destroyed? Explain.

If we knew that energy was beingo7oittrnnj 4k.raduo7i) )0wfw 9 q-. transmitted from one place to another, how might we determine whether the energy was being carried by particleunt4rtna)i)d9.kw7 - .or7i0qj wf oo s (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, wa x4ju *pmkuybs .m+r26m o(ask29el ,hat is the total distance it travels in one perio*ema 2akmb. ,l(musoyu+ 6 s29k4j pxrd?    m

  An elastic cord is 65 4rj 4uywo483 dxjdf9 ucm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is th3x4 jf 4ddwj9uy8r uo4e “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets int,5 macqnp6kii03vpv v9q 3 tn,lfpb8 8o the driver’s cvv 3m, 868i5vplbt nfn k 90i3apqq,pseat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm wheyx rb m.e1 ffdc1wq9;4hxf1 y:n a 2.7-kg fish hangs from it. (a) What is the spring stiffness constan ;f9.wy1:1dm yerfcbfx1h x4q t $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is huy* dnvy(q 44(:jzbne ong from it. nnj(4:vo4e(z*bd yy qWhat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the nzk i56lc. +cbkps49u mass in Fig. 11–2 at times t = kpz+ci6blk 4 n.s5u9c 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 a spider’*rrof, di5s6;uyu: r ms web. The web vibrates predominately with a frefyo5d ,ru6:rm*;i sr uquency 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 vibra3slxua 83 t-pw. rtao(tes with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. Whx(pstr -lawt8.3a u3 oat is the value of m?    kg

  A 0.60-kg mass at the end of a springg +76u qofgax( vibrates 3.0 times per second with an amplitude of 0.13 m. Determine 7g+ga6 (xoqfu
(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 maximum vq/z,.+ nj yov9daiv y)alue vqda9ov yy.n, j)zi/+?$\approx$    A

A mass attached to the end of a spring is stretche trpg tt/:c3y.d 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 06p pm2o:iiy2 x.315 m. If the spring is stretched an additional 0.130 m and released, how lon2op2i 6pmxy:ig does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is ml-iymg.w(hl;g - w q1attached 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 positi 1q.mwwlghmgyl( ;-i- on, 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 to2uyta5oy 8 jntf ::dq ho*f9n pp03mq6y popgun 0.200 m to “load” a 0.180-kg ball. With whathnt9u8aondfy:0 2mtf*:pp63qq j oy5 speed will the ball leave the gun?    m/s

  A mass sitting on a hora-dw + 5yjgct/izontal, 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 cwa -jtgd/y +5by 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 according to the equation x = 0.45cos6.4t where x is inmc.i4c ,)unewpi1o ey:85m pg meters ano,8c w.mp:1ciugi )pem 5yn4e d t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equ-0s, 6vbk7ixeqs;x5keolb. nzkb1 6e ilibrium is the energy of a SHO half KE and half PE? ±; 6x bkbxse1kli75zo v6,b 0n.seke-q    A

  If one vibration has 7.0 times the energy of a second, but their frequenl 4 c aw(nea556cvt(yucies and masses are the same, what is the ratio of their amplitudes? (a ct4cu( w5enl6v5ya   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once e- *jr.wyd 5ec/xk cp696p om .ykhoz(tvery 0.65 s.mcyrxt(*6.ydczwp.- o p6j/ he95 o kk
(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 suppoyj f w.ew- 5y8m8rgb-grted by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). Whaww gyr8b-f 8e5. mjgy-t will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t whe:1 02(eors nexrl/ cqcre x is in meters qr20x ee(cc1l o:r/ns and 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 exame3 8 jh(i6rug+4xsl -p,p xe2x wy9uuqples of 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 = 124t 3sgkub8j:i 6 N/m) is struck by a ht3 isg :bj8uk6ammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with an ambmsy -*/ho 2rzplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive ve*2rh/ s bmo-yzlocity 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 stiffn/inm68ordf a+qepyoye 1*h )0ess 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 attached0xf rsp*f6; pl2gjaxh 4z,8 df to a fixed horizontal spring whose spring stiffness const 0f fpx*62fpdh, l4ax;jg 8rzsant 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 brn6nhwkm9 j n37zvh n8z5 8r7zyidge. After reaching his lowest point, he oscillates up and down, hitting a low point eighzzj5yk h78rn 6397h8 nmv znnwt 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 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. What is iyc*vjr q- vu57ts
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple mli6 w4xrqu/y*aq,l0 pendulum be if it is to make exactly one swing per second? (That is, one complete lq*wam r,/y 6u4qxil0vibration takes exactly 2.0 s.)    m

  A pendulum has a period of e,; zkks x: 2lr4wnq:e0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 tha:kz :kn,2eqwl 4sr;x et on Earth?    s

  What is the period of ql n,oq8;7hv:r;pjcg a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m,azwp 4 ruy+d;77gp1fu the pendulum bob has a mass of 365 grams, uppyadr+7 fw4 17zu;g 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 pendulum has a length of 0.9zsg b0273zze 8 qhgkpio6th ;-rrky 2.930 m. If the clock loses half a minute per day, how should you adjust the lenehs. 2-;p b3qi6ygzgzokrzkr 2 h70t8 gth of the pendulum? shortened by    mm.

Derive a formula for the maximsit6a,y:w,ug3dr khi ,f i2;kum 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 +;z(nh 4v g)htpds8 klit is released from resth; (t zdn8pg)h k4+svl starting 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 hisfiedu09iy e;erra v0)k*v: 4 r anchored boat every 3.0 s. He measures the distance between te *e):i kadif0uv9yvr ; 0r4erwo crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with4n 7nugv;a5t .tywyl. a speed of 343 m/s How far apart54gwnyv yn7 lat.;.tu are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz andp**fa6x(, ar u r3nelw 1600 kHz (kilohertz) and travel with a x*6l(a* 3e,aupwrfr nspeed 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 longitudina c3hxstd1)1oe8;jx7*yix xn ql waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic m(+w6t5ffpxw el4r ae:odulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be grw4f:elp fa(t6 w +erx5eater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two s,j jjor;ptur7ku7.e1upports 28 m apart. If the tension in the cord is 150 N, how loorj1pru 77jkjt ,.eu;ng will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length1 1 nmoo2+wtmmp0 v/ 7u:cfbmf 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 vbofp/m mwm7 ncf:tu+1o2 1m0pulse 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 of the zsn/xto* ke20sea. He hears the echo of the wave stez/x2o0 nk *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 zwdrp, y )f:*ptravel at different speeds, and this difference helps idp,f y:prwz* )n locating the earthquake “epicenter” (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 app r 9xmw3ns)0y ynus:j(roximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the ann)ssjw x3m y9u0ry:(cceleration a>g]    m

  What is the ratio of (a) thsw-k9o; ad:dz: ign2z-1ex boe intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earthn1b:z iz-se9 gkd2oxa -w;:do 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 be7c 1lrll56:6 cvnng zk 57lln1c vlk :ng 6czr6$ 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 fre)u6ki(,l u2jl hthdr7 quency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio tdh li r7)l(,2uu 6kjhof the amplitudes of the two waves?   

  Two waves traveling along a stretched string have i1yxeqst-)en 6 .r7s dthe same frequency, but one transportsd1 ri7qty).-e x 6enss three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observe m0 a 37shjhjf5s5etk6d to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest poist0 57eh5jjsm6h3k a fnt, 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. 11–5aa 9kw;lz6 qp52 are moving toward each other. (a) Sketch the shape of the string at the w5q 9zkap ;a6lmoment 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 440 Hz as its fundamental frequency, what are tu*ac epis,e1 8he frequencic*s p e,u18aeies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates atcbd2 mma -rhwyj6(58 v 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of6-2y8hvj5dmcaw(brm the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates i7l jrd 9 whreudd 2-q:mxs30y1n four loops at a frequency of 280 Hz. Name at least three other frequencies at whichq1sud2 wedxj-rmr : 9y7hd l03 it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string i sj;34oc ku wstk:6k+ls 92m/s If the frequency of standing waves is 475 Hz, how far apart are two t w4;oskcs6:kk3l ju+adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hzl; iy e w258jatxwa9 b2clnx;. and 350 Hz, what is the fax;;2c2 8jitxwy9 a ebwnl5.lrequency of the fundamental?    Hz

  A guitar string is 90 cm long andl hsu2j2vab5. has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of j2b2alsv.hu 5the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measure 1 aiyxxkh4c3l z;8bhgv/ *kh1d to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the thre1* ky 1z3 /8vhakgc lbixxh;4he frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string 2c kabxxs d5abz3 pb,+6/o3wfis supposed to vibrate at 200 Hz, but it is measured to 6+b 23xb, 3 xo5afd /swzkapbcvibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal d k2m-a-q e(msstring is attached to a small-amplitude mechanical 60-Hz vibrator. Thds (--mqe2 mkae 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 ofom l. xdjdp35 5qyr;cix 1rj28 the string may be adjusted by moving the pulley. If thy;iojq.xdjd 1r rc82m 5 3l5xpe hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back an(tl159w pqql(xdce sw ;y- +qxd forth in a 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 65-cm-wide tub is 0.85 Hz. What is the sp 1s(wqq9- qexllc( xd+ typ5;weed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earth l7 (qjnif nz/h p1a;-fbetween two kinds of material. If it approaches the bounda 7hqfa;1p-zij /fln(nry 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 the velocity changes from 2.vofbh0ms8 f4.4j rp .1xeu)ni8 m/s to 2.1 m/s If the incident 84 o. nfrh0f.sjxe1b4impu v) wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelinw5 qb-nd ::cdxg in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold acnq d: xw:-d5bir 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 ox/ps0n9:rx irn9nx; two types of rock at a 38 9:9n0/xsron;x pin r x$^{\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. Acbf)hi ,rl*5 2gyozq:b cording to the user’s manual, the dibhgz: rqo*52lb,y f)ish has to be pointed in 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/lnr ; 1p4zlpwj5j0dl 9h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the w pl5ldj p0 j9zr1l;n4harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/mic+m wnt;0pa01i a2hd Find the maximum compression of the bumper if the car,02ad1w0;h+ m tnapcii 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 fija (my0 c9:uzlupi/9xre net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, 9/aj xl 9iu :umz(ypc0and
(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 fre-haz4y v2kh4t ely hanging spring. The mass then falls 33 cm before it4ay4h-z kh tv2 stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring 9m -buf db2 nx)y1b3ofat a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is un9m-b1od)ybb3xff 2 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 cm) at just tkj+of/dm4rka:; tdu0 he right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts takf+kjd rdmou0 4 ;:/to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain gle :+eoe2i vgxf :0f18rebk5lroove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. Whllr eke i2 5:go81e:xevb+0f fat will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates v6 f6(gmpph0i according to the equation x=0.650cos7.40t where x is in meters and t in seconds. Dhp0f(v gpm66ietermine
(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 freie p pgn-7v;ug(7z71ndqnf-b quency f. What is its frequency if it accelerates at 0.50g ( -ev n qgdpun;izfn(p g17b77-a) upward,    f
(b) downward?    f

  A 220-kg wooden raft fl+bd) +*-gagow3 4wsjghg rr)ooats on a lake. When a 75-kg man stands on the raft, it sinks 4g*gr+)o ggh4jw 3ro ab+-ws)d.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 Hgh3z ab vgq/..z (G) and 440 Hz (A). . 3bgvg/qzh a.
(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 stretx ue(,z e e1uudcs0a(7ched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the,xs1ee 07cu(au(deu z 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 frequency of 264 Hz, and the tip of each pron8cfocuoivv))+ iwd s a:v900d4 yn hz7g moves 1.8 mm to either side of center. Calcul9c :8o)dzs)fdcvn w vi0ha74+o uvi0y ate
(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*9i( mq-78 t2tn(mphj,mccowa vh j6w 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 pmwt7vt n o(28c( chpjij*qm,a-9h6 wm laced there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if thok5g qc 7n;9qeat end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths oo;g7 95cq enqkf 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+x du+jwwy t p;3f(fj0 s — each one-way swing takes 1.000 tx3f+jyw+( df0u pjw;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 9pw bvd.u )n6dspring can oscillate in the vertical direction or can swing as a pendulum of small ap vnbd9w.6)ud mplitude, but not both 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 tension of 255 N. A p +3wymf: bwxp93z in1culse is gey339cn:f z1w +ixb pmwnerated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffnesc:o izdve;s(d)33*hs ew r u4os constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow thecdh ozis3ud o:(s* w);ev4r3 e 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 cable is5g m,e03n27f6bwwk xh cvl)m y 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cach 3em n0v6kg2fx)wmb l,7 5wyble. 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 az go-6 qvnh,8 j cuv)x2cm9,xx2c1ugllso 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,c9ncvv,o lxmu6-1xjg)cq22 u g z8 hx 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