Question

The diagram below shows three ways in which the string of an instrument can vibrate.

 

 Which has the frequency four times that of the first?

Options

• I

• II

• III

• Nothing can be decided

Answer 1

III

Explanation:

For a stretched string, frequency is proportional to the number of loops or antinodes.

• Pattern I has 1 loop → fundamental frequency \(f\)
• Pattern II has 2 loops → frequency \(2f\)
• Pattern III has 4 loops → frequency \(4f\)

Therefore, pattern III has a frequency four times that of the first.