When a certain string is clamped at both ends, the lowest four resonant frequencies are 50, 100, 150, and 200 Hz. When the string is also clamped at its midpoint, the lowest four resonant frequencies are .

Explanation:

Given

Lowest four resonance frequencies are given with magnitude

50,100,150 and 200 Hz

The frequency of vibrating string is given by

where n=1,2,3 or ...n

L=Length of string

T=Tension

Mass per unit length

When string is clamped at mid-point

Effecting length becomes

Thus new Frequency becomes

i.e. New frequency is double of old

so new lowest four resonant frequencies are 100,200,300 and 400 Hz      

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