The transverse standing wave on a string fixed at both ends is vibrating at its fundamental frequency of 250 Hz. What would be the fundamental frequency on a piece of the same string that is twice as long and has four times the tension

Explanation:

fundamental frequency, f = 250 Hz

Let T be the tension in the string and length of the string is l ans m be the mass of the string initially.

the formula for the frequency is given by

   .... (1)

Now the length is doubled ans the tension is four times but the mass remains same.

let the frequency is f'

   .... (2)

Divide equation (2) by equation (1)

f' = √2 x f

f' = 1.414 x 250

f' = 353.5 Hz

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it is called kinetic energy