Give some examples of everydx:h7b/fy+,ppyiyb 9d 734()w l nbujq 1mksmnay vibrating objects. Which exhibit SHM, at least approximate( p w 7qsmyh9:uy7p/mnbynx bjk+4df3i),l b1ly?

Is the acceleration of a simple harmonic oscillator ever ze:e;i4l u ygfjx snbc)f3zt*13ro? If so, where?

Explain why the motion of a pistoktwjq 2t;u1fbm-h; *bn in an automobile engine is approximately simpu *;ftq-j1b k;btwh2 mle harmonic.

Real springs have mass. Will the true period and frequency be larger orcur9znq..yg-e) di -f3 ppcz2 smaller than given by the qd.2gzz p3.9uiyfnr p-c-ce)equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscf+ dc ,banu,eet6m6 1dillator (SHO)?

A 5.0-kg trout is attached to the hookqci*/ bsk qw-vxc42mt:p s3b; of a vertical spring scale, and then is released. Describe the scale reading as ap/:ckc s;wqb4bsx2ivq3- mt * function of time.

If a pendulum clock is accurate at sea evixlw0; s.m8vsm9k g *xd h(0level, will it gain or lose time when taken to high *8;s0l. 0hs( g9dmiev wmkv xxaltitude? Why?

A tire swing hanging from a branch re9 3agyt: csj/baches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stop :st3b9jgcya /watch?

Why can you make water slosh back and forthv/ bco79 t j6+0t9qjqyocmy)f in a pan only if you shake the pan at aj7qqjyto/yf)0c o6+c mt 99vb certain frequency?

Give several everyday exampl.fi k-ixl; vu3hell;b27 l f9oes of resonance.

Is a rattle in a car ever a resonance phenomenon? Explag 0 -gu6f5xw:aazmmr 4mz0asg7lr96win.

Is the frequency of a simple periodic wave equal to the (q6ptuiiq( eo-n q25sfrequency of its source? Why or why no5 toip((6 qiqq2enus- t?

Explain the difference between the speed of a transverse wave traveling dow mif rpo(rsjar b-h*8,*(z6frn a corr6(zs*o ir ffba*8 m- j(r,rhpd and the speed of a tiny piece of the cord.

Why do the strings used for thesvf1xu ki+t.17 pjk +t lowest-frequency notes on a piano normally have wire wr+j x1us+p1 .kkftti 7vapped around them?

What kind of waves do you think will aukpzdrf 9;. ,.rx k3+nwhpj(5vt n9atravel down a horizontal metal rod if you strwp 95 rajn,3zdhkvfp +9an;.x(.rt ukike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreaseoxl: e*p j(rl+s with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would +(*xor pjle:lyou expect the speed of sound waves in air to vary with temperature?

Give two reasons why circuln s9hynbun;tv ;3x(h9a55ex i ar water waves decrease in amplitude as they travel away from the sourceb;5 ns(xavn3eyith;59 ux 9n h.

Two linear waves have the same amplitude -n (/rrm5zcpq and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more /pz( -cnq5rmr energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections ofn:lrfiv 0rs 24 cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do chan2n :silr 0frv4ge). Explain why.

If a string is vibrating in three segments, are there any places you cou- .z 04yvwyngkld touch it with a knife blade witng0yy- z. v4kwhout disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflecte1 -cgomgpuv16 z+ p9b(sin yd:d waves cancel at the nd6ov-:zb+u1s pyg9cg1p( minodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was 3yjxpm m,x :lp9n0 ahbuy6uvqx 7+j) 4being transmitted from one place to another, how might we determine whether the energyjnm:q4lybx6uxm jph9 +0ux) 37y av, p was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHd.g/tm hpcj5+a f 2m1q6/a1wp- wfdasM with amplitude 0.18 m, what is the total distance it travels in jh1g -52/f+tsa6apfcqm w 1./apdwdm one period?    m

  An elastic cord is 65 cm long when a weiglfb)2me* 0v ud;l +rzsht of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” cons ) subvf z+2*m0;lreldtant k of this elastic cord?    N/m

  The springs of a 1500-kg car comp ael84erqt .d-z3 w,b+s :wfaqress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what wi aesfldqe- tz b+rq84,3waw.:ll be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm whth.r 7rf8s-gl km+o;ren a 2.7-kg fish hangs from it. (a) What is the spring stiffness constant -s7tr 8rf;k.olrhm+g $\approx$    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 94lxvrdgwe7 s c.t 49l)/8pwrgj*arna frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangsx tjwg 9l cg/ra*.48rr )esdlw4 vn97p from it?    Hz

Construct a Table indicating the cnb-1nb 1gy)oposition x of the mass in Fig. 11–2 at times t = 0,t1 oc)ng1n- ybb = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 spidecahr--liz9rjzz9(,b ea .n a7r’s web. The web vibrates predominately w, e-a 9(j bnz7.l-azzcr hi9arith a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates c6brvvcrc :em(+21mn 1i3jyn with a frequency of 0.88 Hz. When an additional 6n1v (cm 2+e1 n6:ijcr 3bvymcr80-g mass is added 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 sgbr*it xr9wwa1 b3 lwp*0;5xspring vibrates 3.0 times per second with an amplitude *xgbba0ip lx wsrw139r* t;w5of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speedwe/ u y 7lllknp7*6hfm+i *dx9 of a SHO half the maximum value?d6l+wih9 *u 7p*m7n/ xllekyf $\approx$    A

A mass attached to the a*(rzcr8vhr sv7pd8 o56 g sv.end of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stre-q 4sa icsiymr5sluq0z1 ,e32 tches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take tm lqs2c14ieui, -z5as syqr30o reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is atq*swqppf yf*/p5b y36tached 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 movin s b35q*w/ff*p6ppyyq g with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m toti8;hm8v-ecqy5 mc e 5 “load” a 0.180-kg ball. With what speed will the ball leave th c5yceh-metq8 8vm5;ie gun?    m/s

  A mass sitting on a horizontal, frictionles+ hj2gj x4szitbv 8/v.s surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is reig+xjh .bzv2/4 v js8tquired to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation 2*-t)akvw+5k gg qdqlx = 0.45cos6.4t where x is in meters and t is in*)wt5vqkdq lk +g-a g2 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 equilibriumy;.x)nb/gbs ,vnmbj (n n2wel3:.eh f is the energy of a SHO half KE and half PE? ± /hnfb)nw.(ysx.n3m ;bjv eb:2n,l ge   A

  If one vibration has 7.0 times the energy of a second, b 2jn) p: zzszl0x8m r-7u/ubxout their frequencies and masses are the same, wnr j2zx780)xz pmu- :bs ol/uzhat is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates 3cyu6/.ueu e ,l gxkn9e q+: bp3pih0xfrom a vertically hanging light spring once every 0.65 s+e3,k qy hu/e0l 3epcx9.nu 6 bux:igp.
(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 tz3ud8 7nloc+ awo identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–4odc +zu83n a7l9). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation 1+ubc 2y0t-8z hjtkho x = 0.38sin6.5t where x is in meters and t is zhb- t+h2 o80ytc kuj1in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labelqyx,hirba 82 /(4 u 2mxge3f* 9mlsmtged 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 horiz1ov0k2 -qfcz9sc 8 nnvontal spring (k = 124 N/m) is struck by a hammerk9n1- zvo0n2csfv8qc , 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/gk hk15qv:9ns7enb56(dymh vm vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilhh6gynsdv9(v k:enk71 bm5 5qibrium 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 spb 0 kga(usg9ozx06 tx1ring 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 horizono3 , -u5nwukental spring whose spring stiffness connw uoe u-,3nk5stant 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 bridge. After rjofro6+l yfx61 nuhc./2 til+;e uv c+eaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched lengt1u l ycc i6lx+f oj ;.+env62hr/fuo+th 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 vibran90/hyk yi;(jox ,fox tions in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing pgk3s,) ;mcy7y4mfqw- u ci613lwk ceeer second? (That is, one co3e1ukym 4c3secy7;kfw i c ,qg) lw6-mmplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its peri1mjz, ,n*aka aod on Mars, where the accea anz m1kj*,,aleration of gravity is about 0.37 that on Earth?    s

  What is the period of :lvllyswrk l1- -*qn+ 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, the pen-juank t( qmrf;tyz682w l9 x:dulum bob has a mass of 365 grfrj2u(xt6qly kn ; w9atm:z8-ams, 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 0.9930 m. If the clock loses h)bcaypi2pd (3 zr (-xqm9;2 g 5bxibcaalf a minu( 3mqp(x9b2pdai;zrg) -y ac bc 5x2ibte per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speem6p*e9y)) r phv 0c,m-ykjuzjki0 poh7r-u+td $v_{max}$ 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 it is pc2c3- o2p wim:wauw/oif6h /cl6: hxreleased from rest st6xwam:o/p6h cc 3ho22c:w/fwul-ipi arting 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 4oho:-,rh bk+kgg-lx wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.grog4hxkbh- k+: ol,-5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a g8hr36 i9ab/1(jj.um wq ukti frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (co 19aq/gmutb.uhriki6j( 3w 8jmpressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohe3u: bvfkfpl 0(rtz) and travel with a speedvfkf(pl 03b: u 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 3:hoa wx7,jk b
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, buy r,hd(o0owan 6h)r1afex 1/ ut one is twice as dense as the other. In which rod will the speed of longitudinal waves be greateda h1f1 ha /owoen6x(ru)y0,rr, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports sh8vzi. x sj 4:rhji8028 m apart. If the tension in the cord is 150 N, how long will it ta xzj0rss48v8:.j ih ihke 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 cabld(;rn8onv)z5g- sbq*hc0xywl ;x d4g e of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is hzd s-wd*8(q b y)c4rn5;lx ;v0onxggobserved 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 sea. He tl*q)e71rl tahears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the * l)1tqar7tleocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this differe--k; mr. h;a ywhaww,frwyr75nce helps in locating the earthquake “epicenter” (where the disturbance took place). w hk5 r- h,wawawyf.rym;7;r-
(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 sinusoidal traqeq2bat0ed -o(z- nr ( ksn34xnsverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of (es qqe -a to b2dnn3z-x(r04kfrequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intsu)5 m:djw v wq3e7l,censities, and (b) the amplitudes, of an earthquake P wave passing throughv:,el) um5wd7 jsq3wc 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*82 lor(/t d/ 7aomx8vcwbt fg the Earth is measured to be t8m2drx7v8w *t o gba/o(clf /$ 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 throu lah0yg +oo35 06irqqagh the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of t oo +q0i0rl3h6ag a5qyhe two waves?   

  Two waves traveling along a streosp5xy l45d0y3 hw wzg (wl:7htched string have the same frequency, but one transports three times the power of 734ly5:lxsow p wh05 z(hg wdythe other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of g(pxav f* , oj8w08ma* n*bwjoa pond is observed to move up and down a total vertical distance of 6.0 cm,pbxo a8wwg0(a *m8o*n v,jjf* 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 toward each other. (a) Sski/tx 2:c2qr2ekh z kbo 2012 fvdwd4ketch 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 each ofik2r42cd 2b2z1/s dk2 ew0t :kxvoh qther, 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 th3s c5hk9 oh;x-al t qon,8s9eee frequencieqh98oa5 n,; -o9x eshkt3elscs 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 frequency0p;cz5o.v2r d;lwxw t will it vibrate if it is fingered one-third of the ovx ;lrc .w2z5;tpwd0way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four l -t)bosez:gk973k ybt oops at a frequency of 280 Hz. Name at leas3o ) 9bztsy:bgke-k 7tt three other frequencies 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 theqh5cl4 q5rj,y j9ae,i 6ijbg 5vgqx. ; frequency of standing waves is 475 Hz, how far apart are two adjacentigl,j qij6cyq a9;j x.be, gr5q4vh 55 nodes?   m

  If two successive overtones of a vibrating string are 2)lhl:) xoo+u 9fwkh87ti -txw80 Hz and 350 Hz, what is the frequency of the fu8h:)holo7)tf+ w iluxk-t9xw ndamental?    Hz

  A guitar string is 90 cm long altr f8ltv uj,z *3t1(ynd has a mass of 3.6 g. The distance from the bridge to th*8,trytlzu (tjv3f 1le 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, but it ow;(4w(woih0jn /b f ris measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequenc(rb h f40oo;ijw(/wwny?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibfe ):xpfua 93at9nj:jaj3j 2orate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tens ::ajjpof3f)3at9 xjun9aj2e ion in the string be changed to correct the frequency? decreased by    %

  One end of a horizon q0z s -sdy kj-ytui4r,d .47e+3ngvhutal string is attached to a small-amplitude mechanical 60-Hz vibrator. They h e sy3q -ui+474 z-kgt0vnd,sd.ujr 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*c fz5*jb0e9(x a .m;z n agpcmaf(c/d 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 cm and 1.55amcz (ja;*gc. np* mzbf9(cxfe /0da m?   

  When you slosh the water back and forth in a6 f +2:2mmocstf6jp iu tub at just the right frequency, the water alternately rises anu+2m j:tfp66ocs2 f mid 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 speed of the water wave?    m/s

  An earthquake P wave travel 7ftq nab42w2l--wvfu i4 jqfu:g+) afing at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 4qfv7-)u4gtn:2f4 bf-+ wawl2ja uqfi 7 $^{\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 t3o3r yw c,h2k/yj )luthe velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests mc3/k ,h23 ywyour) tjlake 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 of cold, dense an 67ln4 ch4a6xn1 ,n k1lmctgi(2 krziir. If the sound wave hits the cold air interface at an angle of 24cal21,g rit46n6m1lk7(k zcn nxhin5$^{\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 typhjaj(y;o(d lh7 spw(.es of rock at a 37w;j( d.ph( o(yaljh s8 $^{\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 user’s manualxfqlp:a- h.f; , the dish has to be pointed in the direction of the satx: l -.;aqhpffellite, 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 .l.nvs/ lqwp3g42 fd htravels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how m34 g2p qs.hlf/w.vdnl uch 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/m Fin.gb(zmz(+ 4a6db vg,fkw gbp8d the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximatelypf(gbw (vd m68+ ,g4z gb.akzb 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to0pvq*4se1wdi 2hbd :9+zzylg a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a sieib14szvzqd:2pylw g 0 h9*d+mple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging s:lrckz 7r+ivz - t*0(r axvi0bpring. The mass then falls 33 cm before it stops and begins to rivr(k+7zit 0ri0lx- cvr*a zb :se. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 1twh k7um-.5r,v: oktee r:lod,) vtq( 1–54), compressing the spring 5.0 m. (a) Wh5( v,.:eu eo dkvmr-lt kqt,rw:to7)hat 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 copbf6 +deq)9 mlffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill bml6 qp+e)f9 dover the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groovervuo; be u-(b)cmtuuqt 781ljd2 q9 w+ 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?v)t;9cu umblotu( -1qw+b 8e2jr q7d u    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is a dl01 oytaz)t.*y o(cin meters and t in sec1*tlayt ) yc.az0d (ooonds. 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 wil udr:k ue)6o0 79gofrequency f. What is its frequency if it acceleratl:owk du7ou6ge 0)r i9es at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats r)lgo /osoxi hv05k1j8yy +o:on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper in yy g 8vilo :)kos/0h+roxjo51to the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) *7 ah9qw 9h ic/gflv;h2hks(tand 440 Hz (A). /;q f2hk(c7i* hghtlhswv99a
(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 eka 5/x+d ))ewun 6echof Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the x)+ e5k e6 dnehcuaw/)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 freque bg; 1ob,dv4sl;a(toency of 264 Hz, and the tip of each prong moves 1.8 mm to either4,d1v;b;o agob et(s l 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 simple harmonic motion of fp( y0mn,:30yny pmrqn requency 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 with the board during the oscillation? qy0(rmnp, 3 :y0n ypnm

A string can have a “free” eti 3/hetv ll y5g-q a81sh6c;,4ztio u3dax1 end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengththi,u/ s4ev-yi6ct3g3a x;t51l 8o a1qz hdels of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takes 2)q28 uzjg9dytq f9vu 1.000 s. dqutzq 2jv)9y2g u9 8f
(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 oscillev.acmlr2q: i7(c wu8rhy 1g7 ate in the vertical direction or can swing as a pendulum of small amplitude, but not.qlcrymiv ew1rc ga 7h872: (u 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 g0i+, obqguf8x5gob- o is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generagx g8fbo0, oq+io-5ub ted at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspfqk,kqh+ic,ja 5.6 qz ended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of os+if5jh,k.6c, a qqqkzcillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the :.cp)h;dveuhf9 vpn4 junkyard. The steel crane cable is 22 m long anuppeh;94v n .dhfcv): d 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 resz6 +1j:rtoot- gogeun 4 cc/7jts on a plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as-1 jouo7:/ c4 tzrj6oc tg+gen shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz