Question

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

Answer 1

Step-by-step explanation:

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

Answer 2

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

Step-by-step 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