Following figure shows two wave pulses at t = 0 travelling on a string in opposite directions with the same wave speed 50 cm s−1. Sketch the shape of the string at t = 4 ms, 6 ms, 8 ms, and 12 ms.
Solution
Given,
Speed of the wave pulse travelling in the opposite direction, v = 50 cm s−1 = 500 mm s−1
Distances travelled by the pulses:
Using s = vt, we get:
\[In t = 4 ms = 4 \times {10}^{- 3} s, \]
\[s = \nu t = 500 \times 4 \times {10}^{- 3} = 2 mm . \]
\[In t = 6 ms = 6 \times {10}^{- 3} s, \]
\[s = 500 \times 6 \times {10}^{- 3} = 3 mm . \]
\[In t = 8 ms = 8 \times {10}^{- 3} s, \]
\[s = \nu t = 500 \times 8 \times {10}^{- 3} = 4 mm . \]
\[In t = 12 ms = 12 \times {10}^{- 3} s, \]
\[s = 500 \times 12 \times {10}^{- 3} = 6 mm .\]
The shapes of the string at different times are shown in the above.
