Question

In a quink tube experiment, a tuning fork of frequency 300 Hz is vibrated at one end. It is observed that intensity decreases from maximum to 50% of its maximum value, as tube is moved by 6.25 cm. Velocity of sound is ______ m/s.

Options

• 100

• 150

• 200

• 250

Answer 1

In a quink tube experiment, a tuning fork of frequency 300 Hz is vibrated at one end. It is observed that intensity decreases from maximum to 50% of its maximum value, as tube is moved by 6.25 cm. Velocity of sound is 150 m/s.

Explanation:

I = I_m cos²Φ   (Φ = Phase difference, I_m = maximum intensity)

I = `"I"_"m"/2`

⇒ I = I_m cos² Φ 

Now, substituting the value of I = `"I"_"m"/2`

⇒ cos² Φ = `1/2`

⇒ cos² Φ = `1/sqrt2`

cos Φ = cos `pi/4`

We know that the general equation of wave x = a sin (ωt - k Δx)

Since, the relation between phase difference and path difference in give by

`lambda/(Deltax)=(2pi)/(Deltaphi)`

or, λ = `(2pi)/(Delta9)xxDeltax`

= `(2pi)/(pi//4)xx6.25xx10^-2`m

= 0.5 m