Question

The diagram below shows three different modes of vibration P, Q and R of the same string of a given length.

P	Q	R

1. Which vibration will produce a louder sound and why?
2. Which vibration will produce sound of maximum shrillness (or pitch) and why?
3. What is the ratio of wavelength of vibrations P and R?

Answer 1

(a) R will produce maximum sound because it has maximum amplitude.

(b) P will produce maximum shrillness because it has a maximum frequency.

(c) Let's suppose the string has length l

Then wavelength of P = ${\displaystyle \frac{\text{2 l}}{3}}$

Wavelength of R = 2 l

∴ ${\displaystyle \frac{{\lambda }_{\text{P}}}{{\lambda }_{\text{R}}}=\frac{\frac{\text{2 l}}{3}}{\text{2 l}}=\frac{1}{3}}$

∴ λ_p : λ_R = 1 : 3