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

Step-by-step 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=(Y)/(2)`

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

`\lambda=(2Y)/(X-1);\text{ X}\\e1`

Hence, the wavelength is,

`\lambda=(2Y)/(X-1);\text{ X}\\e1\text{ and X is always odd}`