Give some examples of everyday vibrating objects. Which exhibit SHM, at least ack6s(4scg b*n5.cccu .i ov i3ppr ncccu g.iv k3c*.645 cissb(ooximately?

Is the acceleration of a simple harmonic oscillatorj+t:1s .bwr/f i6wkize ;a7z-h bq,ag ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximateg/x/swtmr5 hld7 (6i: :b w(2negj ltaly simple harmonicjxt/lgerb(m w/das7hn:l62( iw gt5 :.

Real springs have mass. Willm7 7dz; myhcw/co j jcv8lzkl.6dg/.8 the true period and frequency be larger or smaller than given by the equatiozlj czd.j ;8g/m6vkm/yo lh 8ccdw.77ns for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harm;d7ck ev mth)mle, o3,onic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale,9(smj;f h a 4+ g9xg:srzn,ely and then is released. Describe the scale reading l g,+(4ygfj9ze ;9sxsmarn h:as a function of time.

If a pendulum clock is a6a d) opvygp c,m7 j*3ff1fr1eccurate at sea level, will it gain or lose time when taken to high *p1 fmcef6g fvoa1)rpdy3 7,jaltitude? Why?

A tire swing hanging from a branch reaches near szw1 7.oa3dj4 al)oqsly to the ground (Fig. 11–48). How could you estimate the height of thl7a.)o soa4sq 3dzwj1 e branch using only a stopwatch?

Why can you make water oikq. 67j 5re) bkaz ae.osm)6slosh back and forth in a pan only if you shake the pan at .s6o j eer.kqi67a)5a bkz )moa certain frequency?

Give several everyday,ai)a th: .wvs examples of resonance.

Is a rattle in a car ever a resonance phenomenon? )ju52 i-zo:,e co nrwkExplain.

Is the frequency of a simple periodic wave equ whfr qj+ 9ixjoy.+ s .,m91shbx5noz8al to the frequency of its source? Why or1q,sj5+s jnwf+9x8x ihomhzbr y..o 9 why not?

Explain the difference between the speed of a transverse wave traveling do/r62a w,sf mn4f et y:sb8g/zfhhkb2u8* j)bb wn a cord and the speed of a tiny piece of the cor*u6 yfr8: sj ,b bhzk)g2t mb2b/she4nfwa/f8d.

Why do the strings used for the lowest-frequency notes on a piano normally hp; w)bxkkme*gt5vc/q nvd ,,(ave wire wrapped arounktkxvp* ;q/vg,,(ecmd)w b5 nd them?

What kind of waves do you think will travel down a horizontal metal roj 6y:jkq6+x hod if you strike its end (a) vertically from above and (b) j6hyojq6 +x:k horizontally parallel to its length?

Since the density of air decrea -yk):x/x cdq-pk:qnises with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves ::/ -i)kc - kdnxypxqqin air to vary with temperature?

Give two reasons why circular water wavesfzs.c ,2; tvlji k83ks decrease in amplitude as they travel away from the s;k jvs3sz,2f8lk .i tcource.

Two linear waves have the same amplitude and speed, and otherwise are identicalfuv+pg(-6l5da mr7 le, except one has half the wavelength of the other. Which transmits more energy? By what fac-u e 5v7(6d+lgmpla rftor?

When a sinusoidal wave crosses the boundary between tw;(1b1ic / minlcfc;mz o sections of cord as in Fig. 11–33, the frequency does not change; cz 1nic1;(fclbim/m (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any plawe , sgdmxqu24aua7/-ces you could touch it with a knifsa-uawmg u qe2/4d, x7e blade without disturbing the motion?

When a standing wave exists on a sk; q8--r wvjxl;fpc q:tring, the vibrations of incident and reflected waves cancel at t wlpjfcqx-- qkvr:;8 ;he nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one :qlox( bp0yy3 lto/q:(pwd, iplace to another, how might weyp( lq,io (dbxly w03: q/t:op determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, wha;w2a5 z, r 8pq,f0myq0wtrg fcq+,yoot is the total distance it travels in one period? 0,f q;or cgfawzm85q2 +w y0qrt,po,y   m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but.p2) olw cnuew9 8n3ah is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of th3hl.2nw )aeuwc9pn8o is elastic cord?    N/m

  The springs of a 1500-kg car compress 5xg9 d,s5- sjbl(a ipcn rw+7hm/7rw/z.0 mm when its 68-kg driver gets into the driver’s seat. If the car mnagz h7ld5rp r/cx 7iws+(js, / w-b9goes 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) Whatr6n k-5ebeieat8g bkva+;.4 i is the spring stiffness constant kkn8 4 ;e-r5ebgv6.ibat+aie $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60gr4weopbhxx 085r3 b0 kg is hung from it. What is its frequency if only 0.38 kg hangs from h or030rbbg45w8 xxpe it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 8cdt a0ev 1z:bat times t =0v:18ce zbtad 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- bz8hbovy:7c -.zrx me8j/uc in a spider’s web. The web vibrates predominately with a frequency of 4.0 v- 8-ujb.c/7ceyo bz rx8zm: hHz.
(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 arhdc - f8+s x4kuh1.xwith a frequency of 0.88 Hz. When an additional 680-g mass is added to xxhra f-1+ 4dcu8khs.m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0ww 39 efu ,l.lkpxtuwfm9j90- times per second with an amplitude of 0.ewl-9u 9lt,.93w kjpm w0ffxu13 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 speedgv7giy ry8dt cnz34+- of a SHO half the maximum valuevcn4r+3d gyg 8iy-7zt?$\approx$    A

A mass attached to the y o(vvoz jy-.xs.sf,g:ky.w5end 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 stretc*r evn:vory-78ykouyba1 0(v hes a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m andvn:(rby7* v ovu0yye18a o- kr 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 spr zpjaxfa1z2wctmspp8z,;7c g ke54 +2 ing 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 ckc2mag7z ;w tae5x8 pz , zp4js2+pf1is 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 f0cha6kkh dsk,z60r 7yo dd);80.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball 7c6dr0)d;kha 0 ysk6zko,fdhleave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of ahmulns gh.;2+0lckk 9 hhk s k+.lcu9nm0;gl 2spring; the other 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 according t msa/hf,uxa2 lqd59q ;o the equation x = 0.45cos6.4t where x is in meters andalu2hq5 fmsx,qa ;9/ d t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from f.a *m ;vlkkm7equilibrium is the energy of a SHO half KE and half PE? ± kvalkmf*; .7m   A

  If one vibration has 7.0 timesa5hsy ux xkm/41wpk1 , the energy of a second, but their frequencies and masses are the same, what is the ratio of their amplitudes? /x11hu 5xap,4mkswyk   

  A 2.00-kg pumpkin oscillat(2ze d6vgzcob/ b)5x. 5tukbj es from a vertically hanging light spring once every 0.6 25)bu /xzgd 56kjebobv.z(ct5 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 v-))fg 5ryw*p-sm- tbq vo/ uwsupported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will yvwfqsr*ot- v))bm/ p-g u5w- be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.bv+ ;qjmnzd+k ,0,8 .s gexfmi5t where x is in metersbziq sx m,fk0dm.enj,+ 8;vg + and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what i c1yj(uxzfsm( 6uor95un 8mf.s
(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 1 cp6s;.jxrsqkd (8tvhorizontal spring (k = 124 N/m) is struck by a hammer, 1;d(jtcspsq68 rvk. xwhich 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 w 9ekq:z: snam,ith an amplitude of 28.0 cm when 0.260 kg hangsm9:zs nq:,ake 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 two springs, w8 /d7xbzn)1ix dxtr u5ith 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.:-ya *cx x1xeo0juun 3600-kg block attached to a fixed horizontal spring whoe- u3cu*o :xy n1xjax0se 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 65.0 kg jumps w jf g b5fgm)rx7* c8g1ng9nswmz/, g9from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.5mgggjnscmfg9xz/1)b w,8 f n gr7 9w*0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vqs,*3i2zl di-oz 1xxf ibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendu mp7+6;4tjwck 1rk ozvlum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 z 67 j kckpwt4morv1+;s.)    m

  A pendulum has a period of 0.80 s o: ,+s hw; aserqdxk)-pn Earth. What is its period on Mars, where the acceleration of graviepda+wk;h) q- sr, :xsty is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm l(rq f107orjw;kgd: qsong
(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 pendulum bob has a maf6)avx*gn0yxh 9q05g1 o )xbzt thje/ss of 365 grams, and iagho g5z9 h 00vxt*y))n6f1etqxb/xj t 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 0.94npkh4j7sd +g+/ev/qd r ks; z930 m. If the clock loses half a minute per daysz+q +4enkhd7psg k/r / j;d4v, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the mu j-*ou(te8n taximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is ;( by/k-ehbuvx+su-5 a*ok:m e0btm yreleased from resoxeus-/ebk+b y5t0h ma:v ;*my (kb -ut starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat everybz 4( p -3+ 9hooofqdb3qdp;ia 3.0 s. He measures the distance between 9f4poiqb( ; zq3ab 3phdoo- +dtwo crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequen,(e43 wf q:ehceaq wk: u3hr0vcy of 262 Hz and travels with a speed of 343 m/s How far apart are the wave c3w,(u:4h rhecfq0evk3 aqe w :rests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 16( (xv nczhwlew o-7.8v00 kHz (kilohertz) and travel with a speed v. 8z7cwleo- w( nhx(vof $ 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 longituhgalw;g.a2uavcs*l /3x .9 rqdinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have , ys4f(ubdhhgv b0b4 8the same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by wbh8b4h 4d vg(bf 0,usyhat factor?   

  A cord of mass 0.65 cu e tw32gj9c0ep e r02+krn/qkg is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support 2pcr0q9egk 0c3rjeu/wnet+2 to the other?    s

  A ski gondola is connected to the qb(*;()hfvsi i yv g7xtop of a hill by a steel cable of length 620 m and diameter 1.5 cm7h vigq (yib*xs)(f;v. 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 observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the sur.hll4f;5 p 3dqncqop9-h tl;mface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later..lon q4pqclld5t m3;hh fp9;- How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and thisd.e:1/aqc yb1+p mcw e difference helps in locati m p+a ye.qwd1ec/c1b:ng the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal transvey 6:vg6jgzip2 rse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixturz6j6g i: ygpv2e of frequencies), 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 an eart7oga60 jcvp ;dhquake P wave passing through the Earth and detected at two pvd7cpg6aoj 0 ;oints 10 km and 20 km from the source?(a)    (b)   

  The intensity of an ear71yxw.dj +r u5fpcz2hthquake wave passing through the Earth is measured to be hjzp 517dcu w2+fxry. $ 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 jl)f+r7 dgl7gn 9 i.nxfrequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplit gl+nln. i )9dj7x7rfgudes of the two waves?   

  Two waves traveling along a stretched strit/-jz avsa 5lr5t6z uzdvf 6p2::fe1bng have the same frequency, but one transports three times the power of the other. What is thet61z5bf j:/ zt5:davfavluep6s z2-r ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is bo im (.na/qyujl ;j.;observed to 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, byiunmj(l boy.; /j.aq ; what factor does the bug’s maximum KE change?   

The two pulses shown oz7 ih2- jk/ekin Fig. 11–52 are 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 7o- jzek k2/hiother, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fund thz. d,6jfsr0c+fe /n,:bpjxamental frequency, what are the frequencies of the first fourcjj,n e0h.f srd 6z:xfp,+t /b 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 wim x*k h*g3,hp8lnr:p fll it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)*n8 frkxpl3*,hhmp: g    Hz

  A particular string resonates in four loops at a fre( 7iq5l2tcg3 3uljt sz,wd.nlquency of 280 Hz. Name at least three other frequencies at which it2(l w. j 73g tl5n,cl3idtqsuz 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 fre5i c/x-07e4 ui os5qk s,ngep,dav)on quency of standing waves is 475 Hz, how far apart are two adjacent nodein/ -x kg5ec)i4qpoae0ods,s5 , u7v ns?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what isxnm9 xn* cjt bla.(u (jdbqw)i7 n**1s the frequency of bdns7tl(wj(1xu ac*xj **b)im n9n q. the fundamental?    Hz

  A guitar string is 90 cm long and has a a :v:j62 enqs2qw)hqzmass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the freqqvj6aez:2s) qwnh2 :quencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vbe pa5t( dru(;ibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three freq(u e;bd(tapr5uencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string isq)/rxplur,8t/p l3q q supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequeqr3ulx/t8/,lq p rqp) ncy? decreased by    %

  One end of a horizontal string is attached to a small-amprc1: nxxat o54litude mechanical 60-Hz vibrator. The string’s mass per unit lengc rtx5 a1:xno4th 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 ltj7w )1gl/for ength of the string may be adjusted by moving the pulley. If the hanging mass m is fixed atr7fol t1/j)gw 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 just the right freque7l.u wa0n-alg6e mu)p*kh:i xncy, the water alternately rises and falls at each end, remaining renplui:x.-)h7l60 kgmawaue * latively 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 km/s strikes a boundary within thef.)r.95nz7dy9 yy jkupy2+ n ft) ejrq Earth between two kinds of material. If it approaches the boundary at an incidenrqyy+kz7)n puyftjrjn2.95).d e 9f yt 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” whey pe;t ,y+oss18s u3kj6k+a xw 2l9llhre the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave cs,lwu+61k3p o lthkxl 8+aeys2jsy 9 ;rests 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, densenz/cv7. s:r nt -v(ksi air. If the soundn zntk/s vc.v s-:(7ri 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 bo(d8d q ert :u.tdt( nudb/d;i0fx6- xoundary between two types of rock at a 3 0dbd/-t u:8rt.td(uq;oxdie(6d fxn 8 $^{\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 0 t w+ix-rm;l)z gx(mznwz .1sdiameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an ew.zl)w; x0m1(z imgn +- sxrtzrror 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 k u3r8ggkw.bss( b4rh/nx)4 xxm/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. /b(hx4)rs w4uk g.g 8rsn3xbx Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m 8l;+bb( 2xhiwi5yor j1;pm; )dgn kkj 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 5phn;l j) w5+g8b; b d(i2k;omyrkj1ix mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m w ;u;t zbv-p5:rwoir 3below, which stretches the net 1.1 m. Assumw: or ubtir-v3 ;wz5;pe that the 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 the end of a freely hanging spring. Thgpdj9laz mdrz33 q5emikd d 777x+40be mass then falls 33 cm befiz3d k mrdda47 gz9d0l3 x j7mbpe57+qore it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed ofrwnd5jm: 7yosj9ixz1 m , k;x9zd*j:l 22 m/s (Fig. 11–54), compressing the spring 5.d:5j m:njd 9irl9xwk jo,*z1z s7yxm ;0 m. (a) What 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 (diameter 8 cm 0 xk,ku+9tjjv)orgg6) at just the right pace of aboug0ug9j j,ox6kv)+r tkt 1 step 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-rp/uluy*8l/k*bp + mhdw m phonograph record have a wavelength of 1.70 mm. What will be the frequency ud hk* l8//lmbpy*u+wof the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7bs(mh;-q,3 r u s7dqka.40t where x is in meters and t in seco sukamdq r q7-s,h3;(bnds. 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 wiy6 x*x9kp4vd dth frequency f. What is its frequency if it accelerates at 0.50g (a) upward, *k yx4v6xpd9d   f
(b) downward?    f

  A 220-kg wooden raft floats qi;e4.lvo u ,2p9a simon a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he stp94mslq ,ia ;e.2ov iueps 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 tunosb a c.1igto+()ht/w ed to play at 392 Hz (G) and 440 Hz (A). +ag1obh)t/i(w .tsoc
(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/qlbojfgw (5p 2m3f*:e.ke fn :nm bs2 traveling 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 sectf *g lbfkm3wj :qepsen :25n.fb/om2 (ion, 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, andk 8e qpwxbri94 fe+t*. (x6bbc the tip of each prong moves 1.8 mm to either swbbr6c(.e9b +t*xq4xe p ik8 fide 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 frequency 1.5n-v *(ypks -gc 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 g-synp(kc- v* during the oscillation?

A string can have a “free” end if that end is attached to a ring that can sli05,a3 xh,awhwm ilraajjb*; ,de without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of 0hji;3b,a xam, hwa 5w*raj l,the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum h z,j;nu:*s7oq wlc-hhas a period of exactly 2.000 s — each one-way swing takes 1.0lh7 sjowch:n,q -uz*;00 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 oscillkb8y*; dbie,4x*b a7ze nhti 1ate in the vertical direction or can swing as 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, ei etak;byzhb1n* 8 7di,x*b4and 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 tensk hi s:64 dbs,y8z0mitd,9dhlion of 255 N. A pulse is generated at one end, and 20.0 ms later a second ,s my9 sd6tbih,0 4:hl8zdidkpulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with sprq i y(9g7e2mx37xxj ising stiffness constant k. A penny of mass m i72e gmi(jx7sq93yxx 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? (Assume $m \ll M$)

  A crane has hoisted abo),tknyd9 +svg r ;e0 1200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncin9 ;ksvb+,rgtyone0 d)g at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives 5fj8 snfj*g1nthe dimensions osfn f8g1j*jn5 f the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz