Give some examples of everyday vibrating objects. Which exhibit SH ej7smc.*t.(husp5 b01vk xcpM, at least approxima xem.p(vh.s*k0 c7sb1 pt5ucjtely?

Is the acceleration of a simple harmonic oscilln zjdcbyhik/-:n4f c 4x-c3w *ator ever zero? If so, where?

Explain why the motion of a piston in an automobile en t 7*(eun8 q7dtjlij: 6rkjt6ggine is approximately simp(7dlutn7 ji:q686 *etgkjj trle harmonic.

Real springs have mass. Will the true period and frequency be larger or small+dg3 ym w, 2yg5qgq4jf w:t3ocer than given by the equations for a mass oscillating on thj dw24y :g5gqw3mc qo,g+ yf3te end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscih14 w pue-5eufllator (SHO)?

A 5.0-kg trout is attached to thej 5; jbpz(mhb. hook of a vertical spring scale, and then is released. Describe the scale reading as a function of mzjj ph5(.; bbtime.

If a pendulum clock gt16- ez9 tbxyt6 w;wmis accurate at sea level, will it gain or lose time when taken to high altitude? Whyzt-;6byt e xwm w6t1g9?

A tire swing hanging from a branch r cq1pw:; +fvekeaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using op 1qv c+;wfe:knly a stopwatch?

Why can you make water slosh back and forth in a pahk:x2fbxtc 9w v:5ke,n only if you shake the pan at a certb5v:t2 e ch kfxw,x9k:ain frequency?

Give several everyday examples 8+ as/4k4 2bcx::n8ht .hzybrta esbpof resonance.

Is a rattle in a car ever a resonance phenomenon? Expi9r4 zqsh;,)k w lj+ o5qrv+lplain.

Is the frequency of a simple periodic wave equal to the frequency 3+g, wa6embynof its source? Why or why n+ nwg 6b3,yemaot?

Explain the difference between the speed of a transverse wave trave wse-rq6w9ie ;q- q6mmling down a cord and the speed of a ti6mwr e-qqsi;w q-9me 6ny piece of the cord.

Why do the strings used :h 6pcox nz)eulz,n-0for the lowest-frequency notes on a piano normally have wire wrp0 lze,6: cn)xh znuo-apped around them?

What kind of waves dorc g glf8(5vw0 you think will travel down a horizontal metal rod if you st0r(cflvg8 5 gwrike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in t5nszw+-k*ma s emperature, but the bulk modulus B is nearly independent of temperats*m5+zsnk -awure, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they tr3 (u+xx;s8vvdjd.a io*ko l4favel away from the sourc(83 v+*fsi4;o. adjkxxvul ode.

Two linear waves have the same amplitude and speed, and 6.*qipql)j w,8 edospotherwise are identical, except one has half the wavelen) *i ,lqodjw8qp6 s.epgth of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between tws m6yjfih12:c:* vcyfbc93d lo sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength ayfymf3divcbh9 6l :2j*c1s c:nd velocity do change). Explain why.

If a string is vibrating in three segm fke/dqy91 e:lents, are there any places you could touch it with a knife blade without dis ql/efk:1ey9 dturbing the motion?

When a standing wave exi/qxem sx+8f-h 1qum+nsts on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy w xs+hfnuem8/m+1 xq-qas destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mig..6 d*)z xtibhxfy ,luh ),hl.x xuifybd* .6ztt we determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance i /q/6 wcz mej/lz(xc5d- qyez)t travels in one p-xwdl//j/emq ceyz zz)56(cq eriod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 87o 46cwkev2-n e:)pm swi xi-j5 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cordk-w4 smx6ejc7iepi)o2v -w:n ?    N/m

  The springs of a 1500-kg car compress 5.0 cib)v;c g- /mbmm when its 68-kg driver gets into the driver’s seat. If the c -bmb civ/gc);ar 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 6mbb 1bm,:k-ikf,tvzgo8 c5yit. (a) What is thvb6b1o,m5m zk8:b y cfgi,tk-e spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates wi 5eaxdfa-mv4 8th a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is itsevm5ad 48x af- frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating uj buwq;,6,2skf.d/ hqq+he cthe position x of the mass in Fig. 11–2 at times t = 0,t =,wq bf u2;+ q/.khe6chujds,q $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 i(0kdzzm i0 7xb x.xzj x+m64xspider’s web. The web vibrates predominately wix7 +0(6ibxxzxmjdk xzz4m0 .i th 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 gbly jdumym42 9.1gv0.*fq cpfrequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. Wvy*jdgg.qulpb20m4 cm9 f y1.hat is the value of m?    kg

  A 0.60-kg mass at the end of 0/jep bp/8p zmfuv,q//+vhsq a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determszp pq 8qvmjp//bhv/,uf0+/ eine
(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 of a SHO half the maximum valhchgb9. w o9ly.og2g2a 91 l8wamb(peu 8eg2 9opg ogc9bw1a9l.wlay2bm h.(he?$\approx$    A

A mass attached to the end of a spring is stretched a dezfx:-gghw3 uq0-y,9wh kw9kistance $x_0$ 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 fp -v,9/;sbhofa h8. isgsp:rvertical spring 0.315 m. If the spring is stretched an additiona p8vsi hsr;-.fa pgbho9s /f:,l 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 k0 e*lrvk .hb5nl2w o i66;hstncz4dw+ g is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from iv6o24 i;6b.nwwh rdkcn+e * 5zllh0stts equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 5rf.b0 )y(vq)oictnk m to “load” a 0.180-kg ball. With what speed will cvnof.b)05yi tk(r) qthe ball leave the gun?    m/s

  A mass sitting on a horizontal, 6zn,fcu2u86 e8yg pkr frictionless surface is attached to one end of a sf ynzuk8u,6 cg p268erpring; 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 to the equation x = 0.45cos6.4t where x is ppa h4 s1r4 3xqfa c:nf,e1c 1),wevwoin meters and t is in seconds. Determine)pwqev 31eof, x4h arccf ,wpsn11:4a
(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 i 6z i mg8ynnepvsqhr2mc +3-;6/q.ldks the energy of a SHO half KE and half PE? ny gs6rn6m ezqm8dc2/l+pkv-h . q i3;±    A

  If one vibration has 7.0 times the en/v -av9w+f +xjezn;yaergy of a second, but their frequencies and massew9/v-jx+fen+y av za;s are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring onl me* qg0e-ti:0:vb fcce every 0.65 s.: l*- tfebvqcgm00:ie
(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 tw* .k : 4gj0wrfutfy4jfo identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibratkwyffu .r4j:j4*f 0t gion?

  A 300-g mass vibrates accoi rck;(u2d f*+m(l ylarding to the equation x = 0.38sin6.5t where x is in metersmalr;+yl 2( i(kcuf*d 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, lapbj9 zrgn 9* .-tczeq8beled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = vuke:0y1 p5awj 2e41pima6lh 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determmpihe6awlekv1 520:ju p4 ya1ine
(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 305nmerd pa0+ +0ipvrk i67afb6 1 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point0ni e7fp+ kbma6r+6i1da v0rp (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 sp2cgkrhk7 wv))t 8y0lp ring 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 horh q-*p6wdph: c xobz9uc4y7o-izontal spring whose spring stiffnesbq-o 6-zup*o 4cxhpwyd7h9 c: s constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching h ijig;u 6 *tucsf3hv-jeq(:2kis 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 constantvst fu(32jke -;6hiqiugcj:* 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 jfjfq u:3pr 5pk dw98ba0d-d5vibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it isfaecmwpa:d+a8bze:81 gcmg xz31 2 3t to make exactly one swing per second? (T g 3xm:eza8c1f2gea d8c3zb p:+1mtwahat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, whe,ju5 j4qf9m)xvf**fc; dbo f rre the acceleration of gravity is about 0.37 that on Earvf q5mb9cr fjud;4fo*j* x),fth?    s

  What is the period of a simple pendulum 80 coq- tneju9)yq.*j a7 lm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 e0v: b pm k31sd0(,zfj bvgxdk-;.xfvm, the pendulum bob has a mass of 365 grams, and it isxf,:z00ps mk ;jxek .d-bv vdvbf(1 3g 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 0t sn0v8vb;ttiw 4rd9/.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shobvd4t/9n; sw0 tirvt8rtened by    mm.

Derive a formula for the mai;cm7f3 h jsm3qur-.ahg 8qyv7m w1;sximum 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 axr2oijhm +, p1t a frequency of 2.5 Hz. At it is released from rest starting at an aih1+jm rpo ,x2ngle 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 pajqcxb4;rr0 . kvn0r8mss the bow of his anchored boat every 3.0 s. He measures the distance be; xbnmv.0r0 rjk 48rqctween two 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 travels with a speed ksv*d8ssw5rtw 2 b-d :vkb4 3cy 0rh/vof 343 m/s How far apart are the wave crebk2sw bd3k*scr-85d4t:yr /v wv v0shsts (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (k+ 8jbq7 r*muahilohertz) and travelr 7u+aq*j mhb8 with a speed 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 9kdu,ully (9+fo jx9)eqpn3v waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as uevb)(* q, i9zt ayx/vthe other. In which roduy)/ v9,ez avb (qxt*i will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is vfyl4t (q9c0rstretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a p(c fyq9l0 r4vtulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hi pnh9tdmdtd7g8g kp ;pa.),75t( yb acll 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 it took 16 s for the puls9ct bdptg kph77(n,.tad y d8mp)5;g ae 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 of6u ..zh, fszgw 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 deep is the ocean at this poizsw. fz,gh u.6nt?    m

  P and S waves from an earthqopspeu3i;xlv.ab4y 8 *; 0g sjuake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (g3xib;eu.*p8s;0l o ya4 jpvswhere 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 )o.asiub8 .,p dxi sa7by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acce.a,bi)uas p d.8x io7sleration a>g]    m

  What is the ratio of (a) the intensities, and (b) t8 uzlk9iusk4 ;he amplitudes, of an earthquake P wave passing through thsu8 i49zk kul;e Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthqd7hsl 0lq + s1zq-7xp(olc(jpuake wave passing through the Earth is measured to be 1 clzpspljdxhloq7+ -0s((q 7$ 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 travpl 778oy+9 xj1xkncfkel through the same portion of the Earth, but one is carryingj7kyc lxopx 9k8+ n1f7 twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, butygcd 3mhs1a 5 q+,c:mr one transports three times the power of dsgc ,+q51mmhy 3acr:the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of/ko ,x.,l)okm,0cm sd nis) 6qy0q mfy a pond is observed to move up and down a total vertical distanid. oqfm,0 )/km,s6)ksxco nl ,q yy0mce of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in ul:4e2y 6 v adpqi jv0t-9m,poFig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moop4,29v0- pquj iv ya t:6edmlment 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 moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, wha2lckj;pl m7 e;ow7;dkt are the e ;wlk;cmp7kl7dj o2 ;frequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At whxkv uk i1f2k0 /gg+0aqgcx13hat frequency will it vibrate if gx x011 gu3i 2kk+a/0cvg fqkhit is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loopst. fyk ua2k4,( my(url at a frequency of 280 Hz. Name at least three other frequencies at which iur .k( 2yk(fa utym4,lt 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 frequency of sty9zgp.sz9c6f :thqu+ ,eotv+anding waves is 475 Hz, how far apart are twoey,u +6 g:z+. vfo9tzspht9q c adjacent nodes?   m

  If two successive overtoncc5xrhnd2) / lt:czl;es of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamentalc5/z; )nc:lr tdhxcl2?    Hz

  A guitar string is 9lsql 4i;:y (f3dww6 ,c dlzosj:uzg5p- xm3r20 cm long and has a mass of 3.6 g. The distance from the bridge to the support pluyc lm szdop3igql3(:2-4 6s j;5wfwdr:,xzost is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suj819c0qx g wyypposed to vibrate at 200 Hz, but it is measured to vibrate at 2cjy19 qg80xw y05 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 vibrataj e r6t/kmh2/hj0egl j,1g.te at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension ijhgk r 0tat.e/2/j,h16 elgmjn the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached paa8 n.t r2 k*mnm68sito a small-amplitude mechanical 60-Hz vibrator.nmsat. kr 868*a2mpn i 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 length of t*8t9/qq1bxs 4ndi a vvhe string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, hownqa *1qvtsv4 9idb/8x 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 b (jkzi j,,so-tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed kjzjs,,o(b i-of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earth 33 8fud*x /lp dyna9pibetween two kinds of material. If it approaches the boundary at an incident angle8dp yl3p*3 nu9f/iadx 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 underw;y 0 bch6:vrjhmr1ay 9ater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incidc b1rja hvrmy;h9 :0y6ent wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveluaqavll n25 lx;s:f(o9u 1vw0uxa -pvvf-/) qing in warm air when it hits a layer of cold, dense air. If the sounnfu(ou- 0aa9v1)lx : aq;xvvvlq /lpwu5 f2s-d 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 stri3 ug+p8dx25yz cv fuipr h08fo.2bx4bkes a boundary between two types of rock at a 38h8vpzbxbg0xior22 c8+ 3u5 fy.fdpu4 $^{\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 d)+zd v7xbd5buv .hf 5giameter. According to the user’s manual, the dish has tof) 5dvbdg+xzh v7.5ub be pointed in the 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 250 km and velocity 750 km/h travels acroz bv8f d/48 d0f34 iqptp9xtjuss the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and qf4d xp08tjz9vtfp4i 83db/u 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 stiu )jiqwh4(qhf x.1ls2ffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with1 2u(4lfxjwi.qh )s qh mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a wi3ny ev9y-dlh x, v6: k;ug2afindow to a fire net 18 m below, which stretches the netvyf;-vg h2 6nuidl3x:a yk 9,e 1.1 m. Assume 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: q8hpro,xu , dcnlk19nppo 27 hanging spring. The mass then falls 33 cm before it stops and beg pun lp9 h2:1xpr od7q,8,ckonins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge springrhrmsw xe67q 5x+8k m; at a speed of 22 m/s (Fig. 11–54), compressing thw qxr7smkh6r ;+ex58me spring 5.0 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) at juc(p u )v:scel ;6qdh*q 6p:jhihx403l;cs bmwst the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig.h)qxscbv 6cd 0he:(p:34lj;wqcm6* ;sh upil 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 r7u0 nm;. aybkphonograph record have a wavelength of 1.70 mm. What will be th;.ra y7 knu0bme frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t .iyaz3 7zb,y hen.7a jg; ;nzpwhere x is in p;;3.ne7zh7zi agn.ay yz bj,meters and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum osc(fno,prar1fd8 .y dk6illates with frequency f. What is its frequency if it accelerates at 0.50g (a) upwardfkfdrd 1n8pya.ro,6 (,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands t+) gpyc/gqi+on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whtp )c+g/yg i+qile.
(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 bdn z5pu0p7r ,w-r93z5 m evbuHz (nuppu - 9,br35 wr0ezmb75vdzA).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave trav:websci3 7i o+eling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelengtie + :sbic37owh greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each ttx. s 9* pk9tap4(juva 8(iigprong moves 1.8 mm p9(8ust*x vp gak9it. i(ta4jto either 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 simpl-/z0 hr:id wcfvth4)fgc jq 7+e harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a fh 0r/7ct4g:qhc zvd-iw+) fj pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached )fj9d gq.)lqmt90b-gi/e p d2ql)aqgto a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other freaq eq qqgl gfp mj .btld92)/)9g-i0)de.

  A “seconds” pendulum has a period of eep-j- 34sc6a(uzh s6onz( n8s *ivby zxactly 2.000 s — each one-way swing takes 1.000 ssz3 cs6u4 (-(s6oyn-hivj*z e8azbnp.
(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 oscvvf0gx qd+bvjy6 t.1gy0bz2 dsz8 8a9 bjd z69illate 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 ver.t02b gdxdyyv j86fvg0z9jqz9z1v +bds8ba 6tical 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 f( bij g6yn8+5pek66i 6sqheo phv/1iN. A pulse is generated at one end, and 20.0 ms later a second pulse i6 qsvpk/8p 6h1i+e 6nh e6(i5joif ygbs generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended eng+fbp u9;1+b i5kdzfrom a ceiling by a spring with spring stiffness constant k. A pen9z; 1bbgk++i5fpnudeny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The stei g:diyj9 e vn**u1g.z3(ulhtn 3*rolel crane cable is 22 m long and haslg9 rjuyn ivd3oug .*3 :lz(eh 1*tn*i a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown ixi(c myg691mlv*h nkoy4j,2fn 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 vibr64,( *fmhm ygloy nv12ikc9x jating 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