Question

Two identical wires are vibrating in unison. If the tension in one of the wires is increased by 2%, five beats are produced per second by the two vibrating wires. The initial frequency of each wire is ______

`(sqrt(1 . 0.2) ≑ 1 . 0.1)`

Options

• 500 Hz

• 200 Hz

• 1000 Hz

• 400 Hz

Answer 1

Two identical wires are vibrating in unison. If the tension in one of the wires is increased by 2%, five beats are produced per second by the two vibrating wires. The initial frequency of each wire is 500 Hz.

`(sqrt(1 . 0.2) ≑ 1 . 0.1)`

Explanation:

`n ∝ 1/(2ℓ) sqrt(T/m)`

∴ n ∝ T

`n_2/n_1 = sqrt(T_2/T_1) = sqrt(1.02T_1)/T_1 = sqrt(1.02) = 1.01`

Also n₂ - n₁ = 5

∴ `1.01 n_1 - n_1 = 5`

∴ 0.01 n₁ = 5

∴ `n_1 = 5/0.01 = 500` Hz