Question

a string is stretched between fixed supports separated by 75.0 cm. it is observed to have resonant frequencies of 356.0 and 445.0 hz, and no other resonant frequencies between these two. what is the lowest resonant frequency for this string?

Answer 1

This can be calculated by the simple harmonic motion, and the lowest resonant frequency for this string is 89 Hz.

Harmonic motion refers to the motion an oscillating mass experiences when the restoring force is proportional to the ​displacement, but in opposite directions. Harmonic motion is periodic and can be represented by a sine wave with constant frequency and amplitude.

Let 356Hz be the nth  harmonic of the string.

Thus nc/2l = 356 Hz

and (n+1)c/2l = 445 Hz

dividing both of them

(n+1)/n = 445/356 = 1.25

again,

n+1 = 1.25n

0.25n = 1

n = 1/0.25

n = 4

So, lowest resonant frequency = c/2l = 356/4 = 89 Hz

Hence the lowest resonant frequency for this string is 89 Hz.

To learn more about harmonic motion , visit here

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