You are using a tuning fork of frequency 320 Hz. For one particular water level, you hear a loud sound when the fork is struck and positioned just above the open end of the tube. When the water level is lowered by 535 mm, you again hear a loud sound. What is the wavelength of the 320 Hz sound waves in the column of air

The wavelength of the 320 Hz sound waves in the column of air is 1070 mm.

Explanation:

To solve the question, we note that the tube acts as a pipe with one end closed and that a stationary wave is formed in the tube from the top, to the bottom of the tube and back.

The simplest and the first wave form in the tube has length L = Lambda/4

That is, a node at the closed end and an antinode at the open end

The second stationary wave is given by

l + 535 mm = 3/4*lambda

However v = f*lambda

f = v/lambda = v / (4l)

Therefore

Lambda/4 + 535 mm = 3/4lambda

Or 535 mm = 3/4lambda - Lambda/4 = lambda/2

Therefore, lambda = 2*535 mm = 1070 mm

The wavelength = 1070 mm

Ln = 1/4 * (2n + 1) λ

where,

n = 0, 1, 2, 3, 4, ...,

Ln = the length which is defined to be the distance measured from the open end of the tube to the water surface.

Ln = 1/4 * (2n + 1) λ

at n = 0,

L0 = 1/4 * λ

at n = 1,

L1 = 3/4 * λ

L1 - L0 = 1/2 * λ

535 * 2 = λ

λ = 1.07 m