Search any question & find its solution
Question:
Answered & Verified by Expert
The speed of sound in air at temperature $T$ and pressure $p$ is $v$. When the temperature is increased to $2 T$ and the pressure is reduced to $\frac{p}{2}$, then the speed is changed to
Options:
Solution:
1342 Upvotes
Verified Answer
The correct answer is:
$\sqrt{2} v$
Speed of sound in air does not depend on pressure, but directly proportional to the root of temperature, i.e.
$$
v \propto \sqrt{T} \Rightarrow \frac{v_2}{v_1}=\sqrt{\frac{T_2}{T_1}}
$$
Given, $T_1=T$ and $T_2=2 T$,
$$
\begin{aligned}
& v_1=v_1 v_2=? \\
& \frac{v_2}{v}=\sqrt{\frac{2 T}{T}} \Rightarrow v_2=\sqrt{2} v
\end{aligned}
$$
$$
v \propto \sqrt{T} \Rightarrow \frac{v_2}{v_1}=\sqrt{\frac{T_2}{T_1}}
$$
Given, $T_1=T$ and $T_2=2 T$,
$$
\begin{aligned}
& v_1=v_1 v_2=? \\
& \frac{v_2}{v}=\sqrt{\frac{2 T}{T}} \Rightarrow v_2=\sqrt{2} v
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.