Physics - Sound Wave Question with Solution | TestHub

$T_1=273+20=293\mathrm{K}$ $$T_2=273+40=313\mathrm{K}$$ The velocity of sound wave in gases or air is given by $$v=\sqrt{\frac{\gamma R{T}_1}{M}}$$ where, $\gamma =$ Ratio of $C_p/C_V$ $$\begin{array}{l}R=\text{ gas constant }\\ \begin{array}{l}{v}_1=\sqrt{\frac{\gamma R{T}_1}{M}}\\ v_2=\sqrt{\frac{\gamma R{T}_2}{M}}\end{array}\\ \frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}}=\sqrt{\frac{293}{313}}\end{array}$$ $\begin{array}{rl}\text{ Given, }{v}_1=344.2\mathrm{m}/\mathrm{s}& \\ \begin{array}{rl}\therefore v_2& =v_1\sqrt{\frac{313}{293}}\\ & =344.2\times \sqrt{1068}\\ & =344.2\times 103\mathrm{m}/\mathrm{s}\\ & =35575\mathrm{m}/\mathrm{s}\\ & =356\mathrm{m}/\mathrm{s}\end{array}& \end{array}$