Give some examples of everyday vibrating objects. Which exhibi wx.;/r*fbhf n)/67ovejbxtg/ g wdt,t SHM, at least approg/t6nrtxdw gf7v,*. be /;jxbof h/ )wximately?

Is the acceleration of a simple harmonic oscillator ever zero? If s0w0h ;w2fws4z u el2wz58v sdjo, where?

Explain why the motion of a piston in an automobile engine is approximately simpm;s 4a20ghje8vyx t4zle h4vgex0h8a s t jz;24ymarmonic.

Real springs have maslz m+j/e:6:kjdb l2v1 b+aho fs. Will the true period and frequency be larger or smaller than given by the equations for j+::emb/kld 1b jhozf+al 6v2a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillx;w* mkocfg18ator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scala ptpa dy+jyh2pd9gj0 l w3y*f (oc(/in(f8i;e, and then is released. Describe the scale reading as a function of( f9ao/p (cijjt i ;2 y 8daylf+*npdh0w(g3yp time.

If a pendulum clock is accurate at sea level, will it gain or lose time p. -ypmrz77n +5 wtlg8eb;8sm*lypxd when taken to h sb8g 7lx*-ytzmrn5;e7+l.ypwm ppd 8igh altitude? Why?

A tire swing hanging frtl-7mwx9ne i fn7 *mb(om a branch reaches nearly to the ground (Fig. 11–48). How could you estiw 9t(e mnmi-x77n flb*mate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pcp)il8bbx+e* 0r ztso(,; culan only if you shake the pan at a certain frequency?l8 i;0xelzsc) bprc(*ob+ tu,

Give several everyday examples of re wi;2u1*jo ex/ejs8 sbsonance.

Is a rattle in a car ever a resonance phenomenon? Explain.a(ia:iv d dz/-cz9p jmat 6y*,0g*pg t

Is the frequency of a simple periodic wave equal to the frequency of it g/ie.f-rlby da rc149s source?dli-fbgr c eya.9 r41/ Why or why not?

Explain the difference between the speed omqa:u7mur6 g6 5k fq;8lg* zcpdy64w vf a transverse wave traveling down a cord aupa4 ;rf:yq* gqwv78mul65kcd m6gz 6 nd the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a pianowx6-t mkhs(wl0 x.1vc normally have wire wrapped arouw6t0-x vw.sxhc m1k( lnd them?

What kind of waves do you think will travel b,lgl(4 8- 8bdv2 xjpnjvu x)vdown a horizontal metal rod if you strike its end (a) vertivjlvxlbx)8-vb gn428 (pj,ducally from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in tet*k:h ;,hot a4t,oj xtym,gi,mperature, but the bulk modulus B is nearly indepen g:t,o,a,oy hhx4*tkmi,jtt;dent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular wa my zo 9wzlp0xwkfu;83+7 ya0(gud2knter waves decrease in amplitude as they travel away from the zlf;kw2u angdy0980x y ou p 3m(w7+kzsource.

Two linear waves have the same amplitude and ygqihy2ei p1 2llj;: +speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more ene; 21gpiyiyjel2lq: h+ rgy? By what factor?

When a sinusoidal wave crosses the boundarysi47i s66*gn8, xmg.ol um hhb between two sections of cord as in Fig. 11–33, the frequency does not ch4g7h.lu6* io xn6sm gs8bm i,hange (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you coqned-:r*qg 8s4u qp w:uld touch it with a knife blan:u rq p* :sgd-q48wqede without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident andb8sb oq*awkr*0c7 wn. reflected waves cancel at the nodes. Does this mean s cbak* ob0w.rn7q w*8that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, ho3t -q p-vof :-0aycjoew might we determine whether the energy was cfo-pq3 -t:aj0-eo yvbeing carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitul-dkkp my(ar34kro,b+.ww 4 lde 0.18 m, what is the total distance it travels in one p3 4od.bmal4rwl,yw( p-k k +kreriod?    m

  An elastic cord is 65 cm long whe;pxl azsu2.b: n a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs fro xu.sap:zb2 ;lm it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg h7ka*(1tepcut9 ngw. driver gets into the driver’s seat. If tehu tgtcpa*7k(.w n1 9he 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 it. (a) Wbn0 +t;r 2kayyhat is the spring stiy nk2y;0 b+rtaffness 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 w 3db4 r4hrrk8mith a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency br43 rmr8d4kh if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 ajr)d:s1 n(qh ct times t = 0,t = :q1dns )j c(hr$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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’sc5:ts vd /u7g tq,k*wn web. The web vibrates predomi gnu dt*c7w k,5:/svqtnately 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 spring vibrates with a frequency ofj zo g: (wxx7l*uv 74hbkc1em/ 0.88 Hz. When an additional 680-g mass is added to m, th ejg/lxu4:m1zw(*b7 7oxhcvk e frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per secz,.13 ftq1 f o qibl8 5gfnl9fa0zr*sr zfk)t-ond with an amplitufr0in 1t *zfkoslzrl)f 15 ab9.f- 8fq,3zqgtde of 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 speed v 8qhf*29b+nx/ju:tpg .g yjs of a SHO half the maximum value?buy*gq njsj/fv+2g:t8. xp9 h$\approx$    A

A mass attached to the end of a spring is stretchedsjii(d 3d+-c ue p8ne,u39,5 7dc:clmf oiqy h a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring 5 :9;qy,m(gt. s f ys0tqrfntais stretched an additional 0.130 mts59 ;rq(nq.f0ay,t:ts myg f and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a s hv 6yv4(dg2lrpring 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 irvlh(y 2gd v64s moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgu 23hyps8yot9 ef3upbi.u ,(von 0.200 m to “load” a 0.180-kg ball. With what speed will by9,s o3 e.ovuyhitupp3 8(2f the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached tl /1ylmojl9k 5o one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to ll om yl/9jk15compress 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 vibrated f:(p25f+ i2txgepmju ra6x. s according to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determin+u:m( 6e2 tdfp5 g.ixaj2rfpx e
(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 halzgkgmn:k ka4x 0.f1*gf PE? ±ag4n.kg1km: g*fx 0kz    A

  If one vibration has 7.0 times the energy of a secons.2,k kyiwjxjet t2h/gy 9 05+ i7zzoad, but their frequencies and masses are the same, what i0.t xk j5jy w+7y9oitk/e,iagz h22 szs the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lirl2k 6*h4hfsv5a bb g.ght spring once every 0.62fra6l. gs4*bh bhk 5v5 s.
(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 springib;y-57thj 2e*i y ly5d0im 8 8cswtogs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrationc7 d;88 hye0g* lw5y osjbity2 i5-tim?

  A 300-g mass vibrates according to the equatiai,wwf q) l6q2on x = 0.38sin6.5t where x is in meters and t is in seconds.a,f)q q ww2i6l 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 examplex m5j dbq32-2jnm la4es of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end4n9la )qrd(p d of a horizontal spring (k = 124 N/m) is struck by a hammer9d)q rdnal (p4, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with ny.hw9kw,1cwpxo(ef;l-2l y an amplitude of 28.0 cm when 0.260 klp2w.olw,;hky nf1e-(yc 9 wx g hangs from it. The mass passes 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 t/ q*7mzjkua :dbs,eaq g*8oj+ wo springs, 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 horizo)bi1w jahon;79lp ( 7i x3hqqdntal spring whoaiphh71jloqbi;( w73 ndxq) 9 se spring 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 65.0z)yngm a g +e:de7pg 8ja9q6)u kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness em)a8jn dgg 6g9a:p+)7 qyezuconstant 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 indcsbbb;51. ie */2g;rxt2mdcrc alc) exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum**n9eykf3egu x. j o8q be if it is to make exactly one swing per second? (That is, one c *3eqkenx.o8* yg fu9jomplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where tbq:n/f8 b+t9 sjkonaqx7 e0a /he acceleration of gravity is about 0.37 that on Eartt9k /jaaxosb qnen8f+ 7:q0/b h?    s

  What is the period of a simple pend1rb7 g5;xss9muarik ;w y7w 0gulum 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 pendu 21yvb6)bn3jop x3zr zlum bob has a mass of 365 grams, and it is release2v)o zrbz16nb 3pjx3yd 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 penoi1y; bv-m1kk;pr ( ux:b bct;dulum has a length of 0.9930 m. If the clock loses half a minute ; k b1kb: po-u(itcmv;x;1by rper day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spee3 (()pllphfhl d $v_{max}$ 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 relev ;zo 0uk4na2eased from rest starting at ana0uov k 2n4z;e angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of:5 e4* kezuv mq(b-cem his anchored boat every 3.0 s. He measures the distance between tmec e(q: be k*vu-4m5zwo 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 t tdj+7lzgz9b9 ravels with a speed of 343 m/s How far apart are t7d gz9 t9zj+lbhe wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHzt nw y(v2s-n9e (kilohertz) and travel with a speetev-n( 29nsyw d 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 +;xbr( w5sqyrof longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elas17 ,7kana8xjz +mdcugzli;n( tic modulus, but one is twice as dense as the other. In which rod will the speed of longitudi1;87ax kg7+,nzld m(jz iu ncanal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched l . 6i,tq15w5za *wgkf(:wjwl qhx-nsbetween two supports 28 m apart. If the tension in the cordknlaxwhw q* :l-ztwq5( ig15,sf6.wj is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a ho b ::vs1r k.me.5ca6zaltng6z .9d5nltc:p steel cable of length 620 m and diameter 1.5 cm. As t l.haemzzl.gv o b:tc9d.6an cnkr1:t5 6ps :5he gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side u90zv+ ua,xxa gp 15dzof his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How dpx,av gxz ad510uu +9zeep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, andqr -7/-/b(cnrgk4xg. ou zxai this difference helps in locating the earthquake “epicenter” (where the distui/arko- xn ( /xqr.bgc 74z-gurbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by aa:ymy54l8y f o 496hum/ruhz1hnes o( sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequen(s mun 8:ya u1/o46hymr9hzf leh45yocies), 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 intensities, and (b) the amplitudes, of afl4g jh;;9lymn earthquake P wave passing through the Earth and detected at two points 10 km and 20gflm ;hy 4j;l9 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing n4m1 /j z;aadsj c(n)2*nqtee through the Earth is measured to be nznaa;tdjec qme1* n) s/ 4j2($ 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 the same porb5dku6-m k-zction of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wave- -uzb ckk6d5ms?   

  Two waves traveling along a stretched string have gl lhs ea2:/ mtkn37k3the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two2sg hlkna /t: 7k33mel waves?   

  A bug on the surface of a pond is observed tm+o6o10p sv vki rysmwm;o+86jpn/2mx3: sjp o move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by whap2 0s: omm6k8s;pi +mn1s3oj+v xjv/rymp wo 6t factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketc6- * alwnwm55-jaksdwh 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 straight. What has happened to the-w j5an65kwa-s* mwl d energy at this moment?

  If a violin string vibrates at 440 Hz aoa8 +/esmfphnsr2 m*- s its fundamental frequency, what are the frequencies of the first four harmn*/p8he-a m2fs oms +ronics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrate*8o:a-l6ypr l1 ijvf o xffm;9m8*saws at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the wafvjfi-lw roly a1afxomp:*69s;*m 88y down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonatesy(-e/ooa8 flt 5c1e3jyipjxb4r s o7 ( in four loops at a frequency of 280 Hz. Name at least three other frequencies at wh pojyc4r13b 78x(jfats e- l5/(ioyoeich 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 the frequen 19qtvep7 *mohcy of standing waves is 475 Hz, how far apart arevotqmh 7 e9p1* two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, wh ob m :hpi(odxq0vywlm9 b+:95at is the frequency of the fpoxhl9wmmvob0q 5+ :( :iby 9dundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.fzuab*-63jdr/f9 a0o+cn w h g6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520c/+9a-zwob g 3h fd6f0*njaur N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vi g5 7q;bzbe0skbrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should tq 5ebbzsk;g70 he 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 ise6 -qu38ryod 3amep 5a measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct 83meeaya 35d-uo qrp6the frequency? decreased by    %

  One end of a horizontal string wy yi/5 mm e/vhx.a:h0is attached to a small-amplitude mechanical 60-Hz vibrat/hae yw.hm5v x im:/y0or. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the lengt)q.j2) hezkn1 ywrofj*b, (wyh of the string may be adjusted by moving the pulley. If the hanging massh)(.k e o,)nyy2qb*rwjf1 jwz 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 a tub at +alrmo8 +dj,yv:gb6x8vrp g( just the right frequency, the water alternately rises and falls +6l8ad p bm8xgrvrg(: j yov,+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 traveling at k.0 k9ta9zfcuj, 4 mm/s strikes a boundary within the Earth between two kinds of material. If it approachut ,f9 4zacj9mes 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 approachw,jhf 3 um;0qpzmv m um0.w43r,d*dzt an underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If wm* 0,h4. z0m3ru t3jmwv,q mz;ddupfthe incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveli0ho yd,nyu/o .fmu.e:ng in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold ue / u.,hyn.d:f ooy0mair 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 bi))qr , je)op,h;o41psry7v f)ou r/ qd qrg0aoundary between two types of rock at a 38q1f oyq,,epg )drop) s)7r4/0h roqi)va;rj u $^{\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 manual,of+(k+d d/nuwk-f 6ru the dish has to be pointed in the direct-k(r f dnuo+/fkw6u+d ion 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 an 0z6-p-s bj7opvyut)j d velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they hapz y tbj 0su)7j--6vopve 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 constantu:x xk3xpua+j;yo ze:20qod * of 550 kN/m Find 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 (approximately 5 mi/h). [Hint: Usz 03 +2d uouxyqxepxaj::*;koe conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net xv ye04(.qg jm9 pqpq.18 m below, which stretches the net 1.1 m. Assume that the j9qe.q04 .g(pqym xvp net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on)ld9(6i ixp-+nd+ o8boe fcpe the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rispend+ce6 +9x-) (8ipobl i ofde. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (/mdmlahduj h)1;)0af pxuh3) Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of u3axfd1 d)hl;a/h)m)hp0 ju mthe 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 gx5ywa tar5*tk,anbpd52: 0a just the right pace of about 1 step* dxaw0y5 krbtgta ,a2:5 a5pn per second, 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 cm from the center of a 33-rpm phonolqrjj51f 7xl.c3ui x3graph record 1ju37l5xq. xlj 3ir fchave a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates a .svbr7db w2 uftr8,t7*rda p6ccording to the equation x=0.650cos7.40t where x is in meters and t in seconspb2wftr. 87tur6bvr7,ad d*ds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. 6n pv--: immphWhat is its frequency if it accelerates at 0vm in-6- pp:hm.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the ra4.shf(wpoyu (nn(,kfn pnqk**6c o 9lbe) 3nxft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibra(e n.n(nyfq4 )k*3u pfw9 oonlnp(bh6 s,k c*xtes 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 1 id+7gd 24u8*(1eouqqp ti2iboomdv 392 Hz (G) and 440 Hz (A).o2mg t1i41iq*dpd+8ed2( viq7bo u u 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 stretcks er/ ;owpbw47lh45 ched 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, 7 cwsr/wb54;kepo hl4 and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of f:vrvigp7p/6)-p *gm*ojufs each prong moves 1.8 mm to either * *vp/fopg: uvp-frjm6s 7ig)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 frequenc93g4np:+ ljt )x tpljdy/w 7tvh t+)bdap,s1vy 1.5 cycles per second. What is the maximum amplitude with wh dlsdg+b7:1)ht) 9pj,tnya 43p jvx+tvt lwp/ich 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” e9, rflnrsr. :wauws*pyul)4 ; nd if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resrl,uf);s w saul4r n9.*wr py:onant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period z- j/xak;ncb8 9-q wo5l) qhj0op6lj gof exactly 2.000 s — each one-way swing takes 1.000 s. q6-jn-wgl)ao c;h9/lqj 80bkox j5zp
(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 oscillateki6iefgy4ph jo56)bf)6 ,t fx in the vertical direction or can swing as a pendulum of small amplitude, but not both aixy46h, 6 ei)okft 5pfgbjf 6)t the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N:gy5g6q-nd4wg je l+r . A pulse lg64gw+g5 n- q:djyreis generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring ib fk8x7on4i 0 l,+nlhwith 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 allo nhnfkll8xi+o 470ib, w the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable isx5)ovpi6 wt)k-,s 0: oy.6 hedhzn yuw 22 m long and has a diameter of 6.4 mm. A brey, .oenov6phz d)ki :u)s0wxy 6w5h t-eze 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 shosxnv-cgxk:;ms(q2 a 8 wn in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shesg2ks: -qx v n;(amxc8ar modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz