Question

A standing wave has X nodes in a string Y m long The wavelength of this wave is ___ m rounded to the first decimal place.

Answer 1

Given:

The standing wave has X nodes.

The length of the string is Y.

To find:

The wavelength

Explanation:

For a string fixed at both the ends,

for 2 nodes, the wavelength is,

$\lambda=2Y$

for 3 nodes, the wavelength,

$\lambda=Y$

For 5 nodes,

$\lambda=\frac{Y}{2}$

We can generalize for X number (odd) of nodes as,

$\lambda=\frac{2Y}{X-1};\text{ X}\ne1$

Hence, the wavelength is,

$\lambda=\frac{2Y}{X-1};\text{ X}\ne1\text{ and X is always odd}$