To express: The given variation as equation.
The equation of the given variation .
If the quantities and are related by the equation then for , is inversely proportional to and is called constant of proportionality.
The frequency of vibration of a violin string is inversely proportional to its length.
Thus, the equation of given variation is .
To find: The change in frequency when length of the string is doubled.
The frequency of the vibration becomes half.
The length of the string is doubled.
To calculate frequency for double the length of string, substitute for in equation (1).
Here, is the frequency of vibration when length is doubled.
Compare equation (1) and equation (2).
Thus, the frequency for double the length becomes half.
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