Question

A sonometer wire of length 'ℓ₁' is in resonance with a frequency of 250 Hz. If the length of the wire is increased to 'ℓ₂', then 2 beats per second are heard. The ratio of lengths `ℓ_1/ℓ_2` of wire will be ______ 

Options

• 1 : 250

• 1 : 2

• 2 : 1

• 124 : 125

Answer 1

A sonometer wire of length 'ℓ₁' is in resonance with a frequency of 250 Hz. If the length of the wire is increased to 'ℓ₂', then 2 beats per second are heard. The ratio of lengths `ℓ_1/ℓ_2` of wire will be 124 : 125.

Explanation:

`n_1ℓ_1 = n_2ℓ_2`

 `n_1 = 250  Hz, n_2 = 250 - 2 = 240 Hz`

∴ 250 ℓ1 = 248 ℓ2

∴ `ℓ_1/ℓ_2 = 248/250 = 124/125`