Give some examples of everyday vibrating objects. Which exhibiuhhly, jn0 :arbt1p : q12b9oit SHM, at least appryb2hn,j h o1ap::0i lb9q u1rtoximately?

Is the acceleration of a simple harmonic oscillator ever zero? If *m7uosd. 2flspm0-diuk: x9 lso, where?

Explain why the motion of a piston lut*9 qul,n) cin an automobile engine is approximately simple hn ucl9 l)tuq*,armonic.

Real springs have mass. Will the true period and frequency bzxn /;;o,ay jg(dlj+le larger or smaller than given by the equations o;x zd/nl g(yj;j,al+for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic ogfah(g1in /vp5so 7c -scillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scalecot9 mmvs 44p0, and then is release c tm9vm440sopd. Describe the scale reading as a function of time.

If a pendulum clock is accurates (m4w0oui:ie at sea level, will it gain or lose time when taken to high altitude? Whyeio4:0iw ms(u ?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48).jgrd ; )ti6n*zzm- ltg9o:6ts How could you estimate the heigsr tgj o6-lmtd:ntz96) z;*ight of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan j h(h jdrm-c01 v-c4hxonly if you shake the pan at a certain frequenc-hdhcjj 0-vxc4(r1m h y?

Give several everyday examples of resonancatlub 096rp s3e.

Is a rattle in a car ever a resonance pmsh 4 ed3r5i ,d-iiuu(henomenon? Explain.

Is the frequency of a simple periodi*t69th 2kwe4lg3p b nsc wave equal to the frequency of its source? Why k tw9e2t3g*l h n4sbp6or why not?

Explain the difference between the speed of a transvers l ev/-nuvv p3.+cpcl14;v rzde wave traveling down a cord and the speedvv.;e3 lp vc+14zuncr dv-/p l of a tiny piece of the cord.

Why do the strings used fo.yeyo u8jp-d7un-pv7 r the lowest-frequency notes on a piano normally have wire wrapped around .y7yu-ponpjvd ue8 7-them?

What kind of waves do you think will trd 5jzag-;ax3o avel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontall jaz;3 gx-ao5dy parallel to its length?

Since the density of air decrease*/;hompdibxmu -ou:,s with an increase in temperature, but the bulk mmbu,uo/mo:i; xpdh-* odulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why ciocy7c0-og5mnl mmpoj b+nf031ud 6 m8rcular water waves decrease in amplitude as they travel away frooojcuy3m6pnm5m71 og-fb0 80mn+dlcm the source.

Two linear waves have t+wcbz hg bfu(-6 si6*fhe same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? *+b- 6w6zfubh(scfgi By what factor?

When a sinusoidal wave crosses the boundaufyy n jb)ib5hhbzx:*r.7 l 15 cexh4*ry between two sections of cord as in Fig. 11–33, e54 cf7hxh*xj bzbn .h by 1*u)y5ril:the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are thezhk ,2 okh 0keyu7( 61vsax+aare any places you could touch it with a knife blade without disturbing ka,01y+z s2xoahvk(u6h e a7kthe motion?

When a standing waveslkbh 5rm3.ufrgf5(5 o, zaj. u4u*cf exists on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy 55k3ff m5,( .jzf r*uhs4c ubu.orgl awas destroyed? Explain.

If we knew that energy was being transmitted from one place to another x ;;u9u7q,kzykko tj+, how might+kjqku,yx97;ku to; z we determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitudwg4k7(6md ii r pk9fjdi5nii/ wu(2h 9b+v*v le 0.18 m, what is the total distance it trair/gmkwii74ki 2n(ih*w(9v pfvb6u dd9+j l5vels in one period?    m

  An elastic cord is 65 cm long when a weight of 91zo/w1 nrne ud2ddt3g6 pk-e 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of thkgt/d3rd ouz9 2e61nn1 ew -pdis elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver geteyox75 er9 )sps into the driver’s seat. If the car goes over a bump, what woxr 5ep9)ys7eill be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.koo 4jlsat yk0;d4 qv a0 0yf7yr8p:6u7-kg fish hangs from it. (a) What is the spring stiffny y:6y4aa8vr00o;tdlkpuj ko0q4 fs 7 ess 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 i4/(ap ur;rb6b 9 epwuwith a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its i4pp w9u; a(bbrer/6u frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the pyap,9e6b x:cv b4-7eqdz(yvkw/g k. tosition x of the mass in Fig. 11–2 at times t = 0,t = - gkwpe kdcve(,qvbtxz 6:a 79yb./y4$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 1 ;b. ekvefykp+:vq:qin a spider’s web. The web vibrates predominately witfe.kby1 q: pqv+v;e:k h 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 frequencg;bxkeap3n*cq1 :( cwy of 0.88 Hz. When an additional 680-g mass is added to m, a;3xp q cw1ng bcke:(*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 3.0 times per skwk .nq,3 :goz,y -sbjecond with an amplitude of 0.13 m. De:kk ,byqo jn.s3g w,z-termine
(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 cq4du ,+7ix-cbn 3mndfrom equilibrium is the speed of a SHO half the maximum value?cc4qm3d+b dn,i n7u -x$\approx$    A

A mass attached to the end of a spring is sq 3xu)o(p. oy(4sgzxug3pcbe6b tl /6 tretched 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 is st6p zxyw0x)-bh sk2g+ pretched an additional 0.130 m and released, how long doesw6-g0 2+bh)xsk p zxyp it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is a tz :p ok,inlh,axp:dw 3e.*8dttached to a spring with spring stiffness constand d,:tp.l8 ,i npoh az3e*k:xwt k = 280 N/m and is executing simple 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 80to x1 p(esx6n )2ng(sr*zrm:m .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 bmsrrxo2 ten(: x6(s*n1zgp )m all leave the gun?    m/s

  A mass sitting on a horg.q:bq (8yu ikizontal, frictionless surface is attached to one end of a spring; the other e.(kbq8q yi :ugnd 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 to the rf xzz3vjb7 bgy/: i*) odjj1+)i(zgpequation x = 0.45cos6.4t where x is in meters and t is in:girjzpjv7o* xy)d )z g 1z/+b fi3jb( 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 equilibriu; v;uqz c-fww ne+zm;-m is the energy of a SHO half KE and half PE+ ;fczq-we;wuz-v n;m ? ±    A

  If one vibration has 7.0 times the enev;g g6w g)ms(/o;ofex/e e9 ddrgy of a second, but their frequencies and masses are the same, what ise/oe96egsgdo (gm/dfv; xw) ; the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lightr3u ,8o 4 ).gmdrjsuwg spring once every 0.os,8ugr d4 m)gu3r.jw 65 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,xzw9f 2i; mx6 quxpor1v b;m: identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What wi 6 p;m9 ;zxxo fmi21qb:rvuwx,ll be the frequency of vibration?

  A 300-g mass vibrates according to the equation.txe9wqkatgk,* 0n f 0kb ,:cm x = 0.38sin6.5t where x is in meters and t is ketcq. x9k0a b m, t0fg,kwn*: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, whsalr8zv bio7p1ev5r*r;jdy 4 g l36- jat 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 = 1*bu6 p7my1t:luyhy r2z ay-5b24 N/m) is struck by a hammer, which gives the mass an initial speed of 2*h:2zt-yyry 67yupbabu1 l5m .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 constanh/m r0asc3a aaout* 9fl384rlt 305 N/m vibrates with an amplitude of 28.0 cm whesfr8 o330laaa a9/*l c mtr4uhn 0.260 kg 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 two springs, with spring stiffness constan r4bpiry.8mr87 ek)pvts $k_1$ 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 striktpfuchji9 6 7do+f-1uxx/yy (es a 0.600-kg block attached to a fixed horizontal spring whose spring stiffness c9f6otu+xy/xu1 -ycfpdh 7 j i(onstant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reachingg0q +/qbauby+p 2 8.xw4udkj p 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. Calculqq++0g2pya.8/bp4dj u x wukbate 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 i ef3udwr/( af/n exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing1ec yq74qj so5 per second? (That is, one complete vibration takes exactly 2.0 s 57qje4qo sy1c.)    m

  A pendulum has a period of 0.80 s on Earth. What itob9f(i*2dre hw x53xgtq )t 4s its period on Mars, where the acceleration of gravity is about 0.3x*5bi oq)xt(wrt3e 9gf h t42d7 that on Earth?    s

  What is the period of a simple pendu+camsyqeov t q5)-va*ula)87q;qzvg lg ;*b9 lum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendd gn a7sqi3*a)k 4h ; dx,lw/5lv9;fkbf5iwthulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is rel4l9x)d* i v qk/;k7nif w,swt5f;ldbh3h gaa5 eased 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 lecnu5w7gb11g sa+ ue,ugb1 va* ngth of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened ugvcu+1w a15egu b,1*7nb gsaby    mm.

Derive a formula for the maximum spk2p 82bz;z. gebzgad*eed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillate:+zmqx qrv+dgoe7u6 bg5x7g)s at a frequency of 2.5 Hz. At it is released from rest start6xrg + )bv57oqq+guzdgm 7 xe:ing 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 evei+jal *gn0eei scqu1w7okxgz *:l wg-(a( c), ry 3.0 s. He measures the distance between two crests to be 6.5 m qsliligcnk ) :c( oe07z ,(*wwugxa1gja+-e* . How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and1yl -qhvjrdede,naw/1)nvo/ a (g66y travels with a speed of 343 m/s How far apart are the wave crwdvnv/g,16e y lq6e1/o)(dyah ajn -rests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (k dv5y8n hitz::ilohertz) and travel with a speed :yvhidt5z:8n of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in5(1zsci) xldy)d2rl 8 twr6qp
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the bfm3h,z l,u-nsame elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, a bmu,nz,-fl3hnd by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m aparbsor3l5y xx90+l o ur;nf8otm.2 ev j.t. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the other? t jof39rvb 8euo l0o.+yls5;2mnx r.x   s

  A ski gondola is connected to the to2av4t voj8br.p 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 into the terminal and sends a wave pulse along the cable. It is observed that o 24aj.8vv btrit 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 sid, /32api v(l)flh upwv x 0j+60mkmgmce of his ship just below the surface of the sea. He hears the echo of the wave refl /halcvji xl+m,fmpg v06) 2ukpmw(0 3ected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthqua zo.rxealhr(x;0 iw, 8ke travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took place)l xier;8ozahr.(0 xw,.
(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 zuft )-x)ydgj)lg4r 7by 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 co dj7y 4)ltgx )fugz)r-ntact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the ampluyf1ajslbls. 3i//q)itudes, of an earthquake P wave passing thrlyb i1suq /sj3 ./a)flough the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured tos 9mfe5ug3lnt)n6lt/7 v; tt o be 6gun9) tmt ;te/s o l7t5lfvn3$ 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 t74u1c zr( o4 uu,4*p4zo foymtqbw+q qhrough the same portion of the Earth, but one is carry4+7o4oqcp 1b uzo, wqq 4(tzr4*yuf uming twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling alodg u d*ioh6(+fi-uk +rng a stretched string have the same frequency, but one transports three times the power of the other. What is the ratio of thk(- or*idufud+6g+ ih e amplitudes of the two waves?   

  A bug on the surface of a pond is observed tokr yj2kya2;k * 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 rip2 k*a; jrkyk2yples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each otvtvnv 1 )m,up-her. (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 straight. What has happened to the energy at this momenvv-pnm utv1,) t?

  If a violin string vibrates at 440 Hz as its fundamental frequency,k f)t9+zs4z-4o nbkra what are the frequencies of the first four harm9ftz4 k ko)+-ba4s nrzonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will i4e ddjrl/,y (bt vibrate if it is fingered one-third of the way down from the end? (That id4ldjre(b/,y s, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates etpg75-zv 3nxp5pf )uy ij*+win four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonpxf+ u nwgv7) -e5i5tpy3*p jzate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the freq ;p6r(- k,res(lutenyuency of standing waves is 475 Hz, how far apart are two adjacy -r,lren;ut se((6k pent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 i.qm8 7ui ozb2Hz, what is the frequ.uq2i m bz8o7iency of the fundamental?    Hz

  A guitar string is 90 cm long 4 3 4 dpwb7mrahfohdw5+tg(s;and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520gswom;dd 7 w5hbr 34+h4fa(pt N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibnvw5oz26drg :a o3v:a3 i s7hkrate at 200 Hz, but it is measured to vibra v6i ::ds73wk2z3rgvna ooh 5ate 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 is measure5l*y)i -mmlms d to vibrate at 205 Hz. By what percent should the tension in the string b)ll*i-m ymsm5e changed to correct the frequency? decreased by    %

  One end of a horizontal string icgp e:*a v3s tjjb4j3.s attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit le3jj sgtvbcjae3p*.4 :ngth 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 le ly,+ pu1,wc:kum5mromm u2*kngth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L betw w ,2k+mm5pm*uuu1kcy:l mor,een 10 cm and 1.5 m?   

  When you slosh the water back adk opw9dk q(lo4 1+jx/nd forth in a tub at just the right frequency, the water alternately rises and falls at eac9j/+wd4pkookl q1 d( xh 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 travelib.9+zpwrun*/4 nttbbng at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approachezn ub9/t*np.+t bwr4bs the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocityu.fzz97gr )tig ytry6l . 4.ln changes from 2.8 m/s to 2.1 m/s If the incident wave crests maknlg9tyu6t4 ).igzz f7ylrr . .e 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 ao,l am0id5y7*pmu n) q layer of cold, dense air. If the sound wp7* ldqi uam5mo)0,nyave 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 typejn kk0 pn7)nukj38bsw nvj*i6 3:xe /ws of rock at as*u8 p/7kxkjn3) jwk iv6 b3n0:njwne 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 to the user’s manuaae+y0r;f6zo:nhuo3 vc +)e pbl, the dish has to be pointed in tpe : e u;+rzoyhofn30 6av)bc+he direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 25vv k3rf,t 1wweat.a3*+iv 9k c0 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unus k rf v+9act3tew1w*., ikav3vual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have 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/xaz) ooap)w4 8- 6orm5 .ckokbd4xymvja:+r /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 (appao 5m+6oax)c:pk 4j x/wo.ya km)rvz4b od-r8roximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a windoz)sjim cq-e,7:uoo2rw to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, and ,os7 zr-qm: c eiuo2j)
(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 h vzu9 k-uhpaavr9 9e31anging spring. The mass then falls 33 cm before it stops and1vukua-3 r9p9z9 heav begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), ch*inef-8))a to9r tsjompressing the spring 5.0 m. (a) What is the spring stiffness constant of the spring?i9aefs h n-j*o)t8)rt    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just thesx-jl j 63ex mpokwni5(6u8nt.tq 8u1 right pace of about 1 step per second8n 3x5u iequkp. (jnlm1txjw6s t86 o-, 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 ycoi958i k ;l p 1zfwil5z-by.groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted? -z98ik cilb1l;zwfp.o5 yy5i    Hz

  A 2.00-kg mass vibrates according to the equa84m3 lp2mvm ontion x=0.650cos7.40t where x is in meters and t in so mmlv83n42mp econds. 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 oscillatez60-gnp0x hfs+ p*niyocu57rs with frequency f. What is its frequency if it accelerates at 0.50p fn0i7pr*+56-oc0 sy nzhxgu g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the ghr5y w +qd4e5 244v+owlwggoraft, it sinks 4.0 cm deeper into the water. When he steps ofqe gvo5w+dlow+442 hy r5w4g gf, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 gb1 0hims9 ,qtHz (m9g ,itbh10qs A).
(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 stretchynv+6 dek26ji4 h jourq3hm09ed 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 the wavelength greater in the heavq4vh6oj+nr0 deh36i yj 29k umier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tilod +:as7b)ezmu2*lb uu1adx 55t pa,q x9f*wp of each prong moves 1.8 mm to either side of center. Calmu* pt7a xlu,deq12 fab*5ws:9zua x5 )ld ob+culate
(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.kp4h0em;:4qz;k +h+y.ii 4 gcyyui f d5 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 fck.pekih+y y +4q0 m4zu;y;h gdi:4iwith the board during the oscillation?

A string can have a “free” end if that end6ye6;xiw qtq2. m8h :kghs*ios i8k3e is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonan2688q*ih x iw;3kyst.ei :6s hqke omgt vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing tamt4 /+ hvjlb1vj1bwp1 kes 1.000 j1p+/t1vhl 41 wbmjb vs.
(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 xlmbo so.*32z/+oo imfms.+o spring can oscillate 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, and by what amount? [Hint: Lofm+m/s+loi*xz bo oos3m.2. et $l_0$ 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 strek;wela,sia(wyti e5 t iqw( q .s;3-2htched 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 oppositaw s,tq25w- ki(3y . ;e(tliesiahq ;we end. Where will the two pulses first meet?    m

A block of mass M is suspendedi+a(ez )qtezi 9y fy 2-(fb:*9rrgumb from a ceiling by a spring with spring stiffness constant k. A penny of *(im ) ybfe2 9bzfe9gu-r+i:tra( zqy 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? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyarl8byapbl07 jbi06o0u d. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. Whatjbp68yla0li07 0uob b 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. 1 v k;0jft:th2k1–58 (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 shear modulus (;f: h0t t2kkjvSection 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz