SATHEE: Wave Motion 2 Question 29

Wave Motion 2 Question 29

29. One end of a taut string of length $3 m$ along the $X$ -axis is fixed at $x = 0$ . The speed of the waves in the string is $100 m s^{- 1}$ . The other end of the string is vibrating in the $y$ -direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary wave is (are)

(2014 Adv.)

(a) $y (t) = A \sin \frac{π x}{6} \cos \frac{50 π t}{3}$

(b) $y (t) = A \sin \frac{π x}{3} \cos \frac{100 π t}{3}$

(d) $y (t) = A \sin \frac{5 π x}{2} \cos 250 π t$

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Answer:

Correct Answer: 29. (a, c, d)

Solution:

There should be a node at $x = 0$ and antinode at $x = 3 m$ .

$\begin{array}{ll} Also, & v = \frac{ω}{k} = 100 m / s . \\ ∴ & y = 0 at x = 0 \\ and & y = \pm A at x = 3 m . \end{array}$

Only (a), (c) and (d) satisfy the condition.

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Wave Motion 2 Question 29

29. One end of a taut string of length 3m along the X-axis is fixed at x=0. The speed of the waves in the string is 100ms−1. The other end of the string is vibrating in the y-direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary wave is (are)

Answer:

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