Question

A string of length 2 m is vibrating with 2 loops. The distance between its node and adjacent antinode is ______.

Options

• 0.5 m

• 1.0 m

• 1.5 m

• 2.0 m

Answer 1

A string of length 2 m is vibrating with 2 loops. The distance between its node and adjacent antinode is 0.5 m.

Explanation:

Given Data:

• Length of the string, L = 2 m
• Number of loops (antinodes) = 2

The formula for the length of a vibrating string in terms of wavelength and number of loops is:

`L = n λ/2`

`2 = 2 xx λ/2`

λ = 2 m

The distance between a node and an adjacent antinode in a standing wave is one-fourth of the wavelength:

`λ/4`

= `2/4`

= 0.5 m