The figure displays two wave pulses on a string at t = 0 , travelling in opposite directions with an identical wave speed of 50 cm s ⁻¹ . Among the times t = 4 ms , 6 ms , 8 ms , and 12 ms , at which instant will the string have zero displacement everywhere?

Step-by-step solution

The initial position of the first wave pulse (positive displacement) is from x = 2 mm to x = 6 mm . It is travelling in the positive x-direction. The initial position of the second wave pulse (negative displacement) is from x = 10 mm to x = 14 mm . It is travelling in the negative x-direction. The wave speed is given as v = 50 cm s ⁻¹ = 500 mm s ⁻¹ . At any time t , the position of the first pulse is [2 + vt, 6 + vt] and the position of the second pulse is [10 - vt, 14 - vt] . For the string to have zero displaceme