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A simple pendulum consists of a ball of mass M hanging from a uniform string of...

A simple pendulum consists of a ball of mass M hanging from a uniform string of mass m and length L, with m << M. (a) If the period of oscillations for the pendulum is T, derive an expression for the speed of a transverse wave in the string when the pendulum hangs at rest in terms of m, M, T and g (the acceleration due to gravity). Your expression should not include L. (b) If the string is made to vibrate at a frequency f, what is an expression for the wavelength of the wave in the string in terms of f, m, M, T and g?

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