Two transverse waves traveling on a string combine to a standing wave. The displ

Question

Two transverse waves traveling on a string combine to a standing wave. The displacements for the traveling waves are D_1(x, t) = 0.0160 sin(2.10 x - 2.30 t) and D_2(x, t) = 0.0160 sin(2.10 x + 2.30 t), respectively, where x is position along the string and t is time. a. What is the speed of the traveling waves? b. What is the amplitude of the standing wave? c. Find the location of the first antinode for the standing wave at x > 0. d. What is the earliest time (t > 0)at which all the points on the string have zero transverse velocity?

Explanation / Answer

a) speed of travelling waves is v = w/k = (2.3/2.1) = 1.09 m/sec

b) Amplitide of standing wave is A' = 2*A = 2*0.016 = 0.032 m

c) first antinode occurs at x = lamda/4

lamda is the wavelength = 2*pi/k = 2*3.142/(2.1) = 3

first antinode occurs at x = lamda/4 = 3/4 = 0.75 m

d) angular frequency is w = 2*pi/T

time period is T = 2*pi/w = 2*3.142/(2.3) = 2.73 sec

at T/4,i.e at antinode the transverse velocity will be zero

then t = T/4 = 2.73/4 = 0.6825 sec

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