Question

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms^-1. The third resonance is observed when the air column has a length of ______ cm.

Options

• 101

• 102

• 100

• 104

Answer 1

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms^-1. The third resonance is observed when the air column has a length of 104 cm.

Explanation:

When the first resonance occurs,

`l_1 + e = lambda/4` ............(1)

where, l₁ = length of air column and e = end correction.

`lambda = v/ν = 336/400 = 0.84 m`

= 84 cm

Hence, `l_1 + e = 84/4` (By using equation (1))

`l_1 + e = 21`

`e = 21 - l_1`

e = 21 – 20

e = 1 cm

Third resonance will occur, when,

`l_2 + e = (5lambda)/4`

`l_2 + 1 = 5 xx 21`

l₂ = 105 – 1

l₂ = 104 cm