Question

The pressure of air increases by 100 mm of Hg and the temperature decreases by $1^{o}C$. The change in the speed of sound in air at STP is

• A. 61 ms${}^{-1}$
• B. 61 mms${}^{-1}$
• C. 61 cms${}^{-1}$
• D. 0.61 cms${}^{-1}$

Answer 1

Answer: (C)

61 cms${}^{-1}$

Both Pressure and density contribute equally to speed of sound in air. Any change in Pressure would cause a change in density as well which in turn negates the effect caused by pressure leaving speed of sound dependent on temperature alone.

Since $V\propto \sqrt{T}$.

Therefore, $\frac{V_1}{V_2}$ = $\sqrt{\frac{T_1}{T_2}}$.

Now, let $V_1$ be speed of sound in air at temperature $T_1$ and $V_2$ be the speed at temperature $T_1+1$.

Now calculating $V_2$ in terms of $V_1$:

We get, $V_1$= $V_2\times$$\sqrt{\frac{T_1}{T_1+1}}$.

Now, $T_1=273K$

$V_1=330m/s$.

To calculate the change in velocity, calculate $V_2-V_1$ which we get as $61cm/s$.