Question

The velocity of sound in a gas in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12 s, will be ______.

Options

• 2.828 ms⁻¹

• 175.5 ms⁻¹

• 353.6 ms⁻¹

• 707.2 m⁻¹

Answer 1

The velocity of sound in a gas in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12 s, will be 707.2 m⁻¹.

Explanation:

Wavelength (λ₁) = 4.08 m

Wavelength (λ₁) = 4.16 m

Total beats = 40

Total time = 12 s

Beat frequency (n_b) = `"Total beats"/"Total time"`

= `40/12`

= `10/3` Hz

Using the wave formula:

v = nλ

⇒ n = `v/lambda`

The beat frequency is the difference between the two frequencies:

n_b = `v/lambda_1 - v/lambda_2`

`10/3 = v (1/4.08 - 1/4.16)`

`10/3 = v ((4.16 - 4.08)/(4.08 xx 4.16))`

`10/3 = v (0.08/16.9728)`

v = `10/3 xx 16.9728/.08`

= `169.728/0.24`

= 707.2 m/s