Question

Two identical flutes produce fundamental notes of frequency 300 Hz at ${27}^0$C. If the temperature of air in one flute is increased to ${31}^0$C, the number of the beats heard per second will be

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B

2

Velocity of sound increases if the temperature increases, So with $v=n\lambda$, if v increases n will increaseat ${27}^{\circ }C,v_1=n\lambda$, at ${31}^{\circ }C,v_2=(n+x)\lambda$

Now using $v\propto \sqrt{T}⟮\because v=\sqrt{\frac{\gamma RT}{M}}⟯$

$\frac{v_2}{v_1}=\sqrt{\frac{T_2}{T_1}}=\frac{n+x}{n}$

$\Rightarrow \frac{300+x}{300}=\sqrt{\frac{(273+31)}{(273+27)}}=\sqrt{\frac{304}{300}}=\sqrt{\frac{300+4}{300}}$

$\Rightarrow 1+\frac{x}{300}={⟮1+\frac{4}{300}⟯}^{1/2}=⟮1+\frac{1}{2}\times \frac{4}{300}⟯\Rightarrow x=2$. $[\because (1+x{)}^n=1+nx]$