Question

A sonometer wire of length 30cm vibrates in the second overtone

1. Represent it pictorially

2. What is the distance between two points in the string which has a phase difference of n

3. A violin string resonates in its fundamental frequency of 196hz. Where along the string must you place your finger so that the fundamental frequency becomes 440Hz, If the length of violin string is 40cm.

Answer 1

1.

2. 0.30 = \(\frac{3}{2}\)λ

λ = \(\frac{2×0.3}{3}\) = 0.2

We know 2π = λ

ie. π radian = \(\frac{λ}{2}\) wave length

= \(\frac{0.2}{2}\) = 0.1m

∴ The distance between two points is 0.1 m (for a a phase difference of π radian).

3. For fundamental mode of vibration.

The finger must be placed 37.5 from one end.