Question

Two identical flutes produce fundamental notes of frequency $300Hz$ at ${27}^{\circ }C$. If the temperature in the air in one of the flutes is increased to ${31}^{\circ }C$, the number of beats heard per second will be:

• A. $3$
• B. $2$
• C. $1$
• D. $4$

Answer 1

The correct option is B $2$

The velocity of sound increases if the temperature increases.

We know that the velocity of sound in air is given by

$v=\sqrt{\frac{\gamma RT}{M}}$

Since $f\propto v$, for constant wavelength, hence $f=k\sqrt{T}$, where $k$ is a constant.

So, $300=k\sqrt{273+27}=k\sqrt{300}$

or, $k=\sqrt{300}$

Hence, number of beats will be:

$b=f_2-f_1=k(\sqrt{273+31}-\sqrt{273+27})=\sqrt{300}(\sqrt{304}-\sqrt{300})$

or, $b=300(1+\frac{2}{300}-1)=2Hz$