Question

Two identical flutes produce fundamental notes of frequency 300 Hz at 27°C. If the temperature of air in one flute is increased to 31°C, the number of the beats heard per second will be

Options

• 1

• 2

• 3

• 4

Answer 1

2

Explanation:

The velocity of sound increases as temperature rises. So, if v = nλ, then n will increase as v increases.

At 27°C, v₁ = nλ and at 31°C, v₂ = (n + x)λ

Now using , `v  oo sqrt(T)`,  ......`(∵ v = sqrt(gammaRT)/M)`

`v_2/v_1 = sqrt(T_2/T_1)`

∴ `(n + x)/n = sqrt(T_2/T_1)`

∴ `(300 + x)/300 = sqrt(((273 + 31))/((273 + 27))) = sqrt(304/300) = sqrt(300 + 4)/300`

∴ `1 + x/300 = (1 + 4/300)^(1/2)`

= `(1 + 1/2 xx 4/300)`  .....[∵ for x << 1, (1 + x)ⁿ = 1 + nx]

∴ x = 2.