A string clamped at both its ends is stretched out, it is then made to vibrate in its fundamental mode at a frequency of 45 Hz. The linear mass density of the string is \( 4.0 × 10^{-2}kg/m\) and its mass is \( 2 × 10^{ -2} kg\). Calculate:

**(i)** the velocity of a transverse wave on the string,

**(ii)** the tension in the string.

Asked by Pragya Singh | 1 year ago | 107

Given,

Mass of the string, m = 2 x 10^{-2} kg

Linear density of the string = 4 x 10^{-2} kg

Frequency, v_{F} = 45 Hz

We know, length of the wire = m/µ

= \( \dfrac{(2 \times 10^{-2})}{(4 \times10^{-2})}\) = 0.5 m

We know, λ = \( \dfrac{2I}{n}\)

Where, n = number of nodes in the wire.

For fundamental node, n =1

=> λ = 2l

= 2 x 0.5 = 1m

**(i)** Therefore, speed of the transverse wave, v = λ v_{F}

= 1 x 45 = 45 m/s

**(ii)** Tension in the string = µ v^{2}

= 4 x10^{-2} x 45 = 81 N

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