A 2 m-long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is 200 m s − 1 and amplitude is 0 5 cm. (A) Find the wavelength and the frequency. (B) Write the equation giving the displacement of different points as a function of time. Choose the X-axis along the string with the origin at one end and t = 0 at the instant when the point x = 50 cm has reached its maximum displacement.

A 2 m-long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is 200 m s⁻¹ and amplitude is 05 cm. (A) Find the wavelength and the frequency. (B) Write the equation giving the displacement of different points as a function of time. Choose the X-axis along the string with the origin at one end and t = 0 at the instant when the point x = 50 cm has reached its maximum displacement.

A. 2 m, 100 Hz

B. (05 cm) sin[(πm⁻¹)x] cos[(200π s⁻¹)t]

Vibrating in first overtone means, n=2

We know that, velocity,

(A)

Suppose, the stationary, wave equation is,

Computing this and putting values, we get the answer. (B)

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