Give some examples of everyday vibhh7n +r+tg,,oh+ rfp erating objects. Which exhibit SHM, at least approximatef+rn he h,og,r++hp7tly?

Is the acceleration of a simple harmonic oscmm7anua to3 i+*sl- mvnew 6:7m,uq)pillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engin g05/5ax qgwnse is approximately simple hs wq05n /gga5xarmonic.

Real springs have mass. Will the true period and frequency be larger or sm)jxpol,nxier.i i9*fk4 / )kraller than given by the equations for a mass oscillatirix,x l9rjfk)eo.i p*/ki4 )n ng on the end of an idealized massless spring? Explain.

How could you double the maximu .fev25yjdf7i6 kjn-gvv ff-1 m speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attachelu 1.3k )0ajgyvhex/ ad to the hook of a vertical spring scale, and then is released. Describe the scale reading as a function of hxj0u1)ae v3g l.ky/ atime.

If a pendulum clock is accurate at sea l ww.rv8f vb0 3u v(ogrnt 927hk+w9izaevel, will it gain or lose time when taken to high altitude? Why?9uzbg9 wka 27w.tvir+3hv fo n r80wv(

A tire swing hanging from a br *b4c cq6bxnt, 0mhw5yanch reaches nearly to the ground (Fig. 11–48). How could you estimaby nc 65cwm0q4,b*htxte the height of the branch using only a stopwatch?

Why can you make water semab o-09i1q0l tankt8u gf0 o. )4zltlosh back and forth in a pan only if you shake the pan at a cert a.q et4ut1 )lo tzml nk809-oa0igf0bain frequency?

Give several everyday examples of resonance.t;wof ni wh7ky*9 nt1/

Is a rattle in a car ever a resonance phenomenon? Explai,gdwulgov7k 9 7;/ pein.

Is the frequency of a simple periodic wave equal to tyq7x2w9j 4 cnahe frequency of its source? Why or why nn2yc 94aq7jwxot?

Explain the differenm .p4qnia8f;mt1)capv:y z w(ce between the speed of a transverse wave traveling down a cord and the speed oyacm;)qpt iazw(1n4.8fv m: pf a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piytt ;4wk7-x (f1,jju.hv iuupano normally have wire wra-.vy;uuh,ixp f471(jtktu wj pped around them?

What kind of waves do you think will travel down a horizontal metal rod ifj bs 3e:,7kfds you strike its end (a) vertically from abovd j,3fss bk7e:e and (b) horizontally parallel to its length?

Since the density of air decreases with an increase;v7hz7 e4khdt;gzs8oo 2ba6n in temperature, but the bulk modulus B is nearly independent of temt;ok 76b;gz 82v7 oza4hsn hdeperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplilv-eoi*s +ip7:ozwi 8 tude as they travel away +:o z isv7pw l-ie8io*from the source.

Two linear waves have the same amplitude and speed, and m4ambz q6 mzr c1p zrkzq4 9:(z;a6h9iotherwise are identical, exc i:zkq9;zz zmrzqb4 p6hc(41m9a 6ar mept one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cobdv jiq)s- ye4oiv):*77c ;w e gvyarzg3f5u 3rd as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explaiy-eeg wv4a7 d;f )rg3 vbq5*usvcio :jz3) 7iyn why.

If a string is vibrating in three segments, are there any places you cool uy 54npk9,iuld touch it with a knife blade without disturbing t45npu,lyo ki 9he motion?

When a standing wave exists on a string, the vibrations of incident and reflecc c9viaj, nv+)ted waves cancel at the ),vn c9icv+ janodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one plawu yd p9p d1trio0opy9(+:n(oce to another, how might we determine whether the energy was being carried by particles 9doy yp1r(tu+on:0io wd9 pp( (material bodies) or by waves?

  If a particle undergoes SHM wit9ppmb8 602 0t3 ck+1vmcgv2r hukhxuth amplitude 0.18 m, what is the total distance it travels in one peug 026rbpt28c mu ph1khm90 k3vtx c+vriod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 8n6-6r+rmttofos uo3th9q)j, p)jhp15 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of trho+3 rn 6)tt1 ot-)6ujj,pfpmqs ho9 his elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driv,nil4q q6q sb,er gets into the driver’s seat. If the car goes over a bump, wha si4,nq,ql6bq t will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7liyp)6 f-i * vf:lxeup6:3-o7 qolgi4ozjl) n-kg fish hangs from it. (a) What oien f p)u- v*f gxlq) 46ojlzp::37i ly-loi6is the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequ qf 0,fy)un2):ty mkodency of 3.0 Hz when a mass of 0.60 kg is hung from it,qy f:t0)ky 2 modfu)n. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating -pzg;0rnqk n: the position x of the mass in Fig. 11–2 at times t =r k;q-g0npzn: 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 ddpgeys9) 5o6sd .b j(in a spider’s web. The web vibrates predominately with a fds(jgsdoy 95b.pe)6 drequency 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 ahcj0 o0znmmv *3/rzsxt qr47/ spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequencyhtjm0*cr 3o v4/nm 0x sr7/qzz is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end ijceg+5 vf8mz vvg062of a spring vibrates 3.0 times per second with an amplitude of 0.1380 6gi2vm+f g vz5jvec 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 equb ni63x uf)*x)it5qwmilibrium is the speed of a SHO half the maximum valuexint) qfu)*x6w m 5ib3?$\approx$    A

A mass attached to the end of a sprin0r+mvq ff xd..g 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 stretchez(n.q7r rge0t-tr qes1r6o7p y d-,k ahdrv1 0s a vertical spring 0.315 m. If the spring is stretched an additiona.6oar-hk0(vtye1e7p , r qrt7nsd grd-0z r1q l 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is .-qqk-ip oo f,b wu7.rattached to a spring with spring stiffness constant k = 280 N/m and is executing s-.bqruk . owqpo-f,i7 imple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compre)pw,in, kx u/lo6 m0suss the spring of a toy popgun 0.200 m to “louilm),kuow, x /0nsp6ad” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictio1n4lp -g9w)mt(g q+56bm)mywh vqa9pm8f g ounless surface is attached to one end of a spring; the oth+o gq)p mmm461u)9b(5 gtqwv-gpny9wl m8hfa er end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum 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 rrcuoo;v 546z according to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determ roo4; cuzrv65ine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and half u (;:gcfgwma 3jy*,-e3jrur svzo 1;lPE?f l(r cmv;3oguej,yag:3;u j- z*s1r w ±    A

  If one vibration has 7.0 tim7:ucdu nuh5 i 74mvj1:6vhzg ees the energy of a second, but their frequencies and masses are the same, what is the ratio of their amp i :7zem hhvvcgnd6:uu457j1ulitudes?   

  A 2.00-kg pumpkin oscipyzpcf t5ok)c;/6h;vllates from a vertically hanging light spring once every 0.65 s. tp6 )fhy/ ;vk5oz c;pc
(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-v *; nrffb.. gh5yn kws5:hge springs, each with spring stiffness constant k (Fig. 11–49). What will be the frrwfngf.eb-vh;5ngy. * :hs5kequency of vibration?

  A 300-g mass vibrates according to the equation s6cy7luo60r nalfjo *-:d d-n x = 0.38sin6.5t where x is in meters and t is in seconds. Den *l6sd0n d -:co6ayo -7jurfltermine
(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, labeg. qxl bi3/8y9t*bsjj o* u)+g 1jfa(f0wkfiyled 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 = 124 N/m) is stuijau ++k(jminxx, 6*ruck b*uxix+k n(i,m6a+ juj y a 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 with spring stiffness constant (e, stmuv7smcbv */i6s*sz9c305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass pa*ue/,vcs7(v s9zbs cti m*6smsses through 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 spr +bvcy68pcnaei: b; h/7qjt +hings, 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 horizontal e zqk/a y 6tyok(/)ez;du44dyspring whose spr4 e;z d/okedk6yyau)/4t(yzq ing stiffness 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 high dxmut ev1*s)zeh 9bsw3- e*k+bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m belosh-x+)*eek s9wme v*z1 u3 tdbw 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 6z qb-c ao r7w7we.bs-*0 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 , z 2 a oxxeyb2st.vtzxm+0.6zswing per second? (That is, one complete vib0 zxx.+vembs.z6xoat2 , 2zty ration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Eara . 7si-h7owhc 5e/k:q3a d-v,rs: v gmq.cstnth. What is its period on Mars, where the acceleration of gravity is ec/s, oqsqdvt -hw7 i.nv:a:m s3g7a.r-ch k5about 0.37 that on Earth?    s

  What is the period of 2z pgq6e1vx(: yccvz2a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple : nuo2/js2 qvbpendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12.0/j:s uvo2 bnq2 $^{\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 ,3/nnfj tedg4-:pa ih loses half a minute per day, how shoud g: ef 4napn3jh,it-/ld you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum sp-f xjay,z1ya1058w6hwpzt iceed $v_{max}$ 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 od2h ru. m rv47wfbt5p/f 2.5 Hz. At it is released from rest starting at an angle of 15 h.ptdmw4f r5urv7/b 2 $^{\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 wa;0zcs *f(itye ve crests pass the bow of his anchored boat every 3.0 s. He measurez;cfy(t* i0 ses 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 frequswat))pc ;t9 ,7mdtwo ency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crestsm w;p) t,cdat79t)wos (compressions)?    m

  (a) AM radio signals have frequencies between 550 +yxjis: yz 2k5kHz and 1600 kHz (kilohertz) and travel with a spekxjy 5ysi:2 +zed 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 ofviq- ebhk68: q6v s1vd longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one l)k;w e )levq6d-.bq)cy)thu is twice as dense as the other. In which rod l) 6)) qtl)kwheqv.eub;c-y dwill the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28v u ;h1g ivu9-nix 9z4-az9p;xt4l zns m apart. If the tension in the cord is 150 N, how long will it take a pulse to traveluz-x;g;vpzsni n99v axltu9 14 - i4hz from one support to the other?    s

  A ski gondola is connected to the tj9iktumqt0 g:l, :zd 2op of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps 0m lz2jqt:ku :gd i9,tinto 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 h+tip ry;(y0dvis ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean f0;dv(+yr tpiyloor 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 :. t;qzzlaab;speeds, and this difference helps in locating the earthquakezlat.;; ba:q z “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 approximate py 48s 57ubufp9gbp +rp5q+gad 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 acceleratip 4g+b r8apub957ppu+5y fgsq on a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an i :rr awzf- 7u-bvkt8hn5bvbye j/a0).e(( zvearthquake P wave passing through the Earth and detected at two points 1tn h-r-w7 bie)(fv zbvb.rj/5kau vza0: 8ye(0 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wavkj/wfj6pr//4 h8gfq ufy :k1we passing through the Earth is measured to be h:j6kf/rk /ffqw wjy8 14/pug$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through t e9pglgzu *vf*+wy 1q9he same portion of the Earth, but o gvpyfegql z991wu+ **ne is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have -z3 pzi4m4w1inmrsas, 5f x1wthe same frequency, but one transports three times the power of the other. What is the ratio of thra,4z-si3mnw4z5f1 mi sp1x we amplitudes of the two waves?   

  A bug on the surface of a pond is observedynjc 9v8( ehq) to move up and down a total vertical distance of 6.0 cm, from the lowest te8c9jyvh ( qn)o 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 arre3 a0f9ra-pue moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is stra 0ua3aferr-9p ight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fund2ri1fl 1;tsvqf ew- p(amental frequency, what are the frequencies of tff-wpl 21ti(vq ;1reshe first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it vrrddy-mx5t)p qlgmk.k8q . k.q. ,r2eibrate if it is f5. p)2yk gqk 8mrdqde,.tr.kmx r-q. lingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at 0 za-y.w4 g9 viojkq lmz,(c0/aqk3fg a frequency of 280 Hz. Name at least three other frequen30qcov qk/-l, jwg.4fk0(9migazzay cies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves , y,p fl7u.lvion a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent nodiu vyfp,. l,l7es?   m

  If two successive overtones of a vibrating string are 280 Hz y8amml oi 6i ,e-;vw:m1xh1aw brt-)gand 350 Hz, what is the frequency of the fundamentmww ;)1l ov yg8e:-6mri x,t ihm1ab-aal?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g os(orwp:n480re x;gtn9 w dhtl5f +s-. 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 the fundamental and fir5wex (sn9w8ontt+o ;dshgl:pr4f- 0r st two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is m 4zkr9pf.bnu+yy:oa )easured to + 9uzf4)bny:o a.rykpvibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it i; .ra;g8 viqwzs measured to vibrate atr.q; gzviw8a; 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small e95;xq6shf.-f b, slzem5vyt-amplitude mechanical 60-Hz vibrator. The string’s 6 tysh eb 9zm,qflve.fx5s- 5;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 adjustedi 4t3wdsoj. a9 by moving the pulley. If the hangi4ta.w 9o3jd sing 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 and forth in b633ddp ti6fja 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 0.83 ijdpd6ft b635 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strhqf0go8zl7 u*qgjp5 c ws4 l5z lvw/8;ikes a boundary within the Earth between two kinds of material. If it approaches the boundary at ah587 ;*zljf wlqc vw 04/p loqg5usz8gn 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 velocpyn,0x2 dwaj1v k +0wnc a;*wbcjf82w ity changes from 2.8 m/s to1wwnb w,02cd2w+aj;*8 pfxjkncv y0a 2.1 m/s If 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 when it hits a layer of cold, denxhnvnblcyk r5dz :-g6 opn76 v9 u)p ds5:+z/wse air. If pdz7 b-5+6nw5/rk v)l 9o:hzdyx 6psv:ugnnc the sound wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types o5 cv ,9p3*kjy2gxqnepsyd; l3f rock at ae9sp*3qd;y, n 5gv 23kljxpc y 38 $^{\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 :4eh uzao 9 9oox/hs70 7rnqnhto the user’s manual, the dish has to be pointed in the direction of the satellit zsuqx0h /4oo:h n7 n799erhaoe, 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 an .:uhca 5; bisi (3fhfuh/fsq;d velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level infc ih.haqf bus:h i/;fsu53 (; the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing 9f+ xfhd49co9 o7ur uscar bumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, withho9u7uc rfoxsf+ 99 4d 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 windo an3.vmbh*;g;7dqrl ivey5x4 0i7scsw to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple 7;hxli47g dyn*ic3evb ;v.0 rsasqm5 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 spring. The mgggp e7r9, p o(qd1p0kass then falls 33 cm before it stops and begins to rise. What is the freq(7ggkop9qg1 pd,0r peuency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a spee34 zk0qk+rpu h)u 3bszd of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) W 0b)3k3 kuzz4usq prh+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 coffee (da//54z exyp mqiameter 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 over the top (Fig. 11–55). Estimate4//xye5 q zapm the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a iio 3xq*by29 r33-rpm phonograph record have a wavelengxbq*y9ii2 r3oth of 1.70 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 where x 03r92mf iqmqu is in uqm0riq 9f2m 3meters and 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 frequencyeipp(vooy8 1) if it accelerates at 0.50g (a) o pi(eoy)1 8vpupward,    f
(b) downward?    f

  A 220-kg wooden raft flojq) 3v9udj/c jats 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/3uvj9d qcj )j, 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 :ep d1gvx /0b2x if:etwe8bw1 392 Hz (G) and 440 Hz (Adbp/:gwv 2xi8:0fb w xe1 e1et).
(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 trav*repvl/ i .cv1,azw; xeling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is tvzp/wixve1 a;*.r,c l he 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 pro7 cvllnlv+x,3 yj bu6*mux6/yng moves 1.8 mm to either side of center. Caulvvl,cy6/ u3x6 *mlxj7 +ynblculate
(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 frequency 1.5 cycle.1a:4* j7om fbi-0sxusdlt nfs 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 nos* fsidjm1t 4l70o-:. fn uxabt lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached tk-+qi+wr h-:kalz5/k /ym :2vf yivnyo a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and-2+/fl5zk nhki r kw:ivqy-yv my:/a+ the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — eacmvo sz)uv5:ugiw ( x02dz w;s3h one-way swing takes mi 0(u3) sx5z2v;wzu gv sodw:1.000 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 verti l9kx- )kfi1 ql7vx2gqcal direction or can swing as )7ll f1gv kkx 2qiqx9-a pendulum of small amplitude, 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 o*bjh8e jw*7xq d 4drda2-c8lpf mass 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet2e*78 4p rxhc a8b djdjwld*q-?    m

A block of mass M is suspe 5wa4kt ynng;:nded 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 oscillations that will allow the penny to just stay on top of the block? (Assu4n;g kw5at :nyme $m \ll M$)

  A crane has hoisted a 120pt1u* u k ad+qeu53i5q0-kg car at the junkyard. The steel crane cable is 22 m long and has a auq3p 5i+ t1uq5 eu*kddiameter 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 Fv.m mg9qcnhm-jx c;.7ig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and thec.xjcgmn m9 hv;. q7m-n 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