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

$$\begin{gathered} \frac{V_2}{V_1}={\left(\frac{273+31}{273+27}\right)}^{1/2}={\left(\frac{304}{300}\right)}^{1/2}={\left(\frac{152}{150}\right)}^{1/2} \\ We know, frequency is proportional to speed of sound \\ \begin{array}{l}\therefore \frac{n_2}{n_1}=\frac{V_2}{V_1}={\left(1+\frac{2}{150}\right)}^{1/2}\simeq \left(1+\frac{1}{150}\right)usebinomialapprox\\ \Rightarrow n_2=300\times \left(1+\frac{1}{150}\right)=300+2=302Hz\\ \therefore beat frequency =302-300=2Hz\end{array} \end{gathered}$$