y = (0.058 m )(sin(11 x )) cos (42 t ) A standing wave pattern on a string is de

Question

y = (0.058m)(sin(11x)) cos (42t) A standing wave pattern on a string is described by the equationbelow where x and y are in meters and tis in seconds. y = (0.058m)(sin(11pi x)) cos (42pi t) For (a) through (d), use nonnegative values for x. (Usex >= 0.) (a) Where is the node with the smallest valueof x? 1 m (b) Where is the node with the second smallest value ofx? 2 m (c) Where is the node with the third smallest value ofx? 3 m (d) What is the period of the oscillatory motion of any (nonnode)point? 4 s For (e) and (f), consider the two traveling waves that interfere toproduce this wave. (e) What is the speed of these travelingwaves? 5 m/s (f) What is the amplitude of these traveling waves? 6 m For (g) through (i), consider the times t >= 0 when allpoints on the string have zero transverse velocity. (g) For t ? 0, what is the firsttime that all points on the string have zero transversevelocity? 7 s (h) What is the second time that this occurs? 8 s (i) What is the third time that this occurs? 9 s

Explanation / Answer

Displacement y = (0.058m)(sin(11x)) cos (42t) velocity v = dy / dt                = ( 0.058) ( 42 ) sin (11x) [ -sin (42t) ] If sin ( 42 t ) = 0           42t = 0,,2,3,...... 42 t = 0 ==> t=0 42t = ==> t = 1/42                        = 0.0238 s 42t = 2 ==> t = 2 / 42                          = 0.0476 s

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.