The adjacent diagram shows three different modes of vibrations P, Q and R of the same string.

State the ratio of wavelengths of P and R.

Explanation

Let the frequency of the principal note in vibration R be f.
Then, the frequency of vibration P is 3f.
`thereforef_(R)=fandf_(P)=3f`
`rArrf_(R):f_(P)=1:3`
But `fprop1/lamda`
So, `lamda_(P)/lamda_(R)=f_(R)/(f_(P))=1/3`
`thereforelamda_(P):lamda_(R)=1:3`