Give some examples of everyday vibrating objecadjp9l.xs ;0m1v alg /ts. Which exhibit SHM, at least app/x .v s1jagdlm;p l09aroximately?

Is the acceleration of a/:g nv ghg g/t7b,ofku/ ,s-rw simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobi:3p3ijao nd2 fle engine is approximately simple hajaof2:3 n pd3irmonic.

Real springs have mass. Will the true period and frequency be - gh zs gu*u8sydj4y(-larger or smaller than gi(-gsyzy4 *uh8d usjg-ven by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum spedcfb5)0x /r/ bbqsub5:q p/ha ed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attemr1yn4iaqqkq59kw-. p98t q ached to the hook of a vertical spring scale, and then is released. Desc.9ktra9m84qi q epnyw1 qq5-kribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, willfnp/ lo4d;0,dt , s wyc7c0azh it gain or lose time when taken to high w,a/dlyd40o pc ; thcz7,ns0f altitude? Why?

A tire swing hanging fctf1ff7a sir*p6 c3u.rom a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatc3tu pf.6 rficfs*71cah?

Why can you make water slosh back and forth in a pan -:a8ggka+nd7 ocwcm2/ 85i iq kpv+ qaonly if you shake the pan at a certain frequency?g5pa cv+o: 7c/ +2dwaqk- k igmqa8in8

Give several everyday examples of re; tcx kznvs*(.sonance.

Is a rattle in a car ever a res r3;lnlo5 c ygtd1)1 nd9aeo9bonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of it :,q+ ioz *r9n(nmj+okcqmme 8h-zby*s source? Why or why notq(im n* * ybq zr:-zm8ne 9hj+c,kmoo+?

Explain the difference between the speed of a transverse wave traveli+ay k2 6pq1z+wq0e jdgng down a cord and the speed of a tiny piece of ydq21w0e +g6zk +ajqpthe cord.

Why do the strings used for the low qe :;)vw;zswyest-frequency notes on a piano normally have wire wrazvwe;q y ;ws:)pped around them?

What kind of waves do you think will travel down a horizontal metlf 39a2am5p;cta :hzw al rod if you strike its end (a) vertically from3c 2;ap at9:5fmahzlw above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperaturef gbpll66t* (9ec qnk(, but the bulk modulus B is nearlkbgnpe *6 (clt 9qf6(ly independent 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 in amplit2cn/agng/ gux fh(9c1ude as they travel away from the/9cuf(2ga ggncx1/h n source.

Two linear waves have the same amplitude and speed, and otherwise are identicpw /oj0k66fu(eks k4val, except one has half the wavelength of the other.u/vw4 o ks6(k 6jp0efk Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary buk k3 p,v3sxzdd c6y+-enc,3eetween two sections of cord as in Fig. 11–33, the frequency does not change (although the ks3zcx+dce u, ,ked3 pv-yn63wavelength and velocity do change). Explain why.

If a string is vibrating i3hpc)1 nf;jrfn three segments, are there any places you could touch it with a knife blade ;p fhjcnr)13fwithout disturbing the motion?

When a standing wave exists on a string, the vibrx7/iyabc) ji(kt ay wj11*o 2;+ espjyations of incident and reflected waves cancel at the nodes. xc(a)* o1s2 j/ 17jkybte iyiaw;y p+jDoes this mean that energy was destroyed? Explain.

If we knew that energy was beink;m;2e 1:gm si wyr3-hu mle)mg transmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodies)emg;2m 3r: u;h1)-imky lswme or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance us jy8b- ou84:ctg3 :qtpdo5w it travels in ondyttq5sbw c84 3ju:up8og :o-e period?    m

  An elastic cord is 65 cm long when a weight of 75 N hhd n6nwj:u;ufvy 7e 72angs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?y6h;ue7n :jn 2udw7vf    N/m

  The springs of a 1500-kg car compress 5.0 mp 53+9j pl69zyxz ,ti eidox3rm when its 68-kg driver gets into the+ 3zo3xil tdey,9r6xp9j5 izp driver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from 2y z- (exnu.p0r um-c sznl34xit. (a) What is the spring sti.0s4rpmuzxnel-y 3u-n z c(2xffness 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 0.60 kg is hu e-zu(sikgbg 7r. 4aq0ng from it. What is its frequency if only 0.30 zgkr q4ube.a- g7(si8 kg hangs from it?    Hz

Construct a Table indicating the positiofa1 .o2xvvsj 2n x of the mass in Fig. 11–2 at times t = 0 jfa12x2o vs.v,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’s web. The web vibpf+vbco. tv5 8jzkg60rates predominat+vgzo08 j kp5vtfc.b6ely with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a smf mpb6zq b80pqjqe gr.6 09e8u3 .hqtpring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the qqrte0 09p h upqj366g eqfm .zm88.bbfrequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibratyhuqzc5 (,,6z1eyyz sup0 5bt es 3.0 times per second with an amplitude of cyy1upz, s6q0 ,y(bzezh5 tu50.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibri ,x8u;ok zop9evzh(fzo/q3grci 0s 47um is the speed of a SHO half the maximum value?zozeu 7cs r308/ookq4xg , ;ip fv(z9h$\approx$    A

A mass attached to the end of a 8ddv3;ksv.u pspring 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 pytn1uri39 un8o3 ktb/y; v(l;dzfq6spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it taki1 bop nl3/;tr; 6y3kz v(fntu8 9yqude to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with sprinox 4gyl5zsyof0m75 dw9 ;yc y4g stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m ox so9; m5c4ld 5g4fwzyy7y0yfrom 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 80.0g h: -xlqu:**p gu7*+hsbmlcq N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave*xhmhb*s-l7+qqu*pugg : c:l the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attache71b tc, .eulua:t0drgd to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to tr:., 71lgutud0ecab 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 according to d ;txnwnjr1 8gl ;8vg3the equation x = 0.45cos6.4t where x is in meters andd3x8ltnn rw; 8v jg1g; 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 equnuw u.199wggz ilibrium is the energy of a SHO half KE and half PE? g9w.9nz1 gwuu ±    A

  If one vibration has 7.0 to+zk:9 -mo a bgzr9h/jimes the energy of a second, but their frequencies and masses are the same, what is the rat m a99grk- bjoho:z/z+io of their amplitudes?   

  A 2.00-kg pumpkin oscillates frm8kwk/6ock ci14z e, vom a vertically hanging light spring once every 0.65 s. ckc m1 /e,8kk ivozw64
(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 vertical sp ;xy7o4lr 9kj,yutnl2xd-z c,rings, each with spring stiffnessydkj x4,l-ycx 2rz olu,97; tn constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sind j831w8 ha on*rlclj 85akrl-6.5t where x is in meters and t is in seconds. Deterl a88r8la3jj-1kdcw5rl* nh omine
(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 and Bv r0bk16;dxy n. 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 horizontaywah 4 (xxvd6-l spring (k = 124 N/m) is struck by a yd4xv(-hx 6aw hammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring wit:jgx jwzy2ij ;t283v gspuq96h spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes tg262:vtj98g iyu3 xs; qjwz jphrough the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springsb*9z5rwdr8m m1- m t3jra+wvs , with spring stiffness 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 horizoni (n d/mx kciuuzo64(2tal spring whose spring std 42zim(6uki cxon/(uiffness constant 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 hq s7s93ttqvg-,cq 9rlf1j6 ouigh bridge. After reaching his lowest point, he oscillates up and down, hitting aq-vj qosc76 9rq1tlgt9 3,usf 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 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 ibl cs x b)i:7p8d,ap0bts
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simples)v,bja h nj4z(cdn.4 pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exz4 jb)4vjsdcn,(. nha actly 2.0 s.)    m

  A pendulum has a periodgr hudr7(,f o, of 0.80 s on Earth. What is its period on Mars, where the accur,( do h7g,rfeleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80baxhsq x6t/ on e/cg/7/by4m3 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.7ao2fe yk/(8x9m q;st(ib8axg 60 m, the pendulum bob has a mass of 365 grams, and it2x(qga9mx/o (beas yfi ;k 8t8 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 jr5;vj2xhw3lfmsr nd3d p5 ce ;b n61*has a length of 0.9930 m. If the clock loses half a minute per dd16 m vx*f3j3d;pnnwjrer2b5l s; hc5ay, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the m sgd;o fb3zil26jy8 3vlnpc,q i/) w,saximum 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.ufyrxu./co u9;y 1nu lf*2o 6-c1un cy At it is released from restl u6rucof9/yn11 ccf. ou yy;n*x2-u u 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 thats rw9xmlz fe) )71iv-d wave crests pass the bow of his anchored boat every 3.0 s. 1-em)isrdl 9)v xfwz7He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 7 ((2eo)h.bq cvhbtkq 343 m/s How far apart are tke2 bb7voqc )qh( (t.hhe wave crests (compressions)?    m

  (a) AM radio signals have frequ 3wu--ft( dcndencies between 550 kHz and 1600 kHz (kilohertz) and 3cwdfdt- un (-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 longitudhag;0mn p lrl3-x4:zk+m:a g pvzs-9s inal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice v7.ti rp8+wmg ,i5ynzas dense as the other. In which rod will the speed of longitudinal waves be greater, antzyr,n7+5 vgmwi 8.i pd by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the)zj z+8 xivb:v tension in the cord is 150 N, how long will it take a pulse to travel from one szzv+vi) :xjb 8upport to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 6au- 1:iflda3bo69xh) eqsi:g 20 m and diameter 1.5 cm. As the gondola comes to the end of its u1 -q3:6edio9ax)bi fglh :sarun, 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 te58au)4rg* ym ojz7nrhe surface of the sea. He hearsn5jz)4ru*rg8oeaym 7 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 different speeds, and this dio wexsw,u1+:o fference helps in locating the earthquake wo,+1 sxw:ue o“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 beq )1c3 a s;chrdxq(damb7e83z0 htr 1p approximated 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 dxcdq; 1m33)z a t(pa01s8qrehh7 bcrto leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intepmwsi+3z b7l1n4 ol m q8rp)t5tgya*4nsities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and d1pnq3 *s mlr4 t4tp8i5by+ozlw7 m) agetected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing thyhg.u jk,ncv* f+qc6t.8u95icp e df* rough the Earth is measured to be 6i v yehk8q*fd+.fnj ,upc5 9gut*. cc$ 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 travezqj ;lhtyfe*ob l-373l through the same portion of the Earth, but one is carrying twice the energy. What is the ratio ;ejblhq3tlz73f -o* yof the amplitudes of the two waves?   

  Two waves traveling along a stre(; xi:ca csw:jtched string have the same frequency, but one transpo:x:c (a ;wjcsirts 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 observed to move up and doww2f rh/0;hdti)c w(y dn a total vertical distance hcy0; thw(r2iw ) fdd/of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are ua n*/y4pe m8ax 4wk7k:aqmf8 moving toward each other. (a) Sketch the shape of the st8e:8ma a*p 47/k xwmufan y4kqring 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 440 Hz as its fundamental frequev )l 6cq5slydi3nr/6+k ) i* oj lpm8vjcuad3,ncy, what are the frequencies of the first four har* l6)qp v uiv d/5 c)y8id6lokjj3rsan3,+mlcmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it viy op)/*oqwsn4 l tgp27brate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string 2* sow gyqpt7lno)4p/vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at aexd7rw 8nn50gbp(1 m m frequency of 280 Hz. Name at least three other frequenc5emmw8x 7(rn gn db1p0ies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If eknx4 1l 4oinnl-n8l4kbok*7 the frequency of standing waves is 475 Hz, how far apart are tno8o4 llk -be*nkxin4 1k74n lwo adjacent nodes?   m

  If two successive overtow l-ka yhta0*;nes of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamental?* walhytk0-a;    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dista1ay/sims(lp3 .2/j8yg kyvne nce from the bridge to a2/y kg.s(l1n38eip vjysm y/the 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 supposed to vibrate at 200 Hz, but8 wnm ji4q t.au,xnjynq5p:wq) pg:;8 it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frjit): nw,;ny .wmn 54ppqg8u x:jqqa8 equencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supp)+ m5zgvr8qnmzz5odzfd 2m 4 3osed to vibrate at 200 Hz, but it is measured to vibrate at 5f+8mg4 z3mzq5rm2nozdz vd )205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontrn5d1/uj 9u zwal string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unzd9jur 1 /nu5wit 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 ma:i0i2owo ucj 329k ascy be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 ikuac3oi9 :20 o 2scjwcm and 1.5 m?   

  When you slosh the water back and forth in gljktm5 jdja:23/b uwg) 5 gs4a tub at just the right frequency, the water alternately rises and falls at each end, m5g4bjjg2d5t lu sw:g /kj) 3aremaining 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 speed of the water wave?    m/s

  An earthquake P wave traveling at k.: gws*),(x2u e8zga7 gzlzibt 0 km/s strikes a boundary within the Earth bewzglt(8a*sg e:xuz i,z) 27bgtween 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 u)shsxq3j jo8 i(g/mmk;3l 4lsj* wwv /nderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s Ihx8g4q /wv o/mlsl*;3sk jmw(s3j)jif the 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 whe 1s8dkm ke *-hnumgwkd.--v0 gn it hits a layer of cold, dense air. If the sound wave hits the cold air inte8m hn.0ewvd1 *gukd-m kg -sk-rface 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 wg 4ikl(* 4lvmsave strikes a boundary between two types of rock at a 38 gklm l(4 vis*4$^{\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 4/k.9.*zqfx oapa sfn8zat2tv p-x ;b user’s manual, the dish has to be pointed k ;4/9 n fz.t-2 z.axopsbfqa*8xtapv 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/h travels across the lf3woj w cs4(;Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have diedswfcj; (w o3l4 during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffuebu((r*/esfqy w- d9 n.hs:hness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 15:hun *(.es-(b d/r u9wfqyehs00 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, pz; ebq(2dtv/ which stretches the net 1.1 m. Assume that the net behaves like a simple sve 2;tdbpz (/qpring, 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 plbq18 sg +kqp5waced on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscqb1w85 gps+k qillation?    Hz

  A 950-kg car strikes a huge spring at azde*kd-s3k:edkvgn9k j3 5(n speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of z*n3d:5kk(- js3gd k dve9ken 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 the *8mokyp)o n(:iy71 + oa ksumfright pace of about 1 step per sec ona8y+:f(m)uk s*ki moypo 17ond, 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 groove 10.8 cmnq)-ljleuwfc5.3s *w from the center of a 33-rpm phonograph record have a wavelength of 1.70-*njc.euww ql )sf5 3l mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t wherdq u1fc)u4y5ybts, ,qc /l9hje x is in meters a51cftl qs ) u,d4byh9c/, yujqnd t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if it s y 9nh1x+rz8 7pgcgb),debe) accelgs+hx),d)y8g ebn7c rp9z 1 beerates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft fl 8oncoy+l1 ck,md:nr:oats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the roo 1ynckl:mc: +rn8, daft 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 (G) anuwgur o,ymn4:n,t,+ od 440 Hz (A:4y wr+,t ngmun ou,o,).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig35*p sw4kugdv2apn tjl , una9)o2:ml. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that il2w )a pond9guam2nk v,43t*spuj :5ln 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:d(d4c qvn ad j)an8:p Hz, and the tip of each prong moves 1.8 mm to either side of centervad a 4n8p)j :qc(n:dd. 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 x f.8g3 *qw:eo+y ptcgsimple harmonic motion of frequency 1.5 cycles per second. What is the mq3ewp: yft+ g .xcog*8aximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can s2 ulwc9,gdq0 bpr3s4rlide without friction on a vertical pole (Fig. 11–57). Determine the wq lu9s23pwc0 r4d, bgravelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactlyc:jyl :a ho4,k 2.000 s — each one-way swing takes 1.000 :hk4oj lay,:c s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical diqg ;tk:1x2 e,-kj -kg5ppj xb)sxatc+ rection or can swing as a pendulum of small amplitude, but not both at the same time. Which onek; xx+jt 1g,s):p- jbka2kpx qe5tg -c 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 ocicf)lnd40 ,oqi9it 1s0- dhif 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite ens)i09 ncq dcoli0d 41ht,-ifid. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with s tvn)(l)ifg9u0 f9qlj pring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to j g09t lj)i(fuq)9vlfn ust stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cabl5rvg),cw zlb/0osyp (e is 22 m long and has a diarv l(),o p5bcwyg/z0smeter 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 give:xj i q7k iv4ibwz :avz9xno an83b+/-s the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulu -o v8ni:x4vii/w j3nazb9a7+zxbkq:s (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz