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 (p/2), then the speed is changed to

Question

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 (p/2), then the speed is changed to (A) 2 v (B) v (C) √2 v (D) (V/√2)

Tardigrade Admin · Accepted Answer

Speed of sound in air does not depend on pressure, but directly proportional to the root of temperature, i.e.

v \propto T \Rightarrow \frac{v _{2}}{v _{1}} = \frac{T _{2}}{T _{1}}

Given,

T_{1} = T

and

T_{2} = 2 T

,

v_{1} = v, v_{2} = ?

\frac{v _{2}}{v} = \frac{2 T}{T}

\Rightarrow v_{2} = 2 v

Q. 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

$2 v$

$v$

$2 v$

$\frac{V}{2}$

Q. The speed of sound in air at temperature T and pressure p is v. When the temperature is increased to 2T and the pressure is reduced to 2p​, then the speed is changed to

2v

v

2​v

2​V​

Speed of sound in air does not depend on pressure, but directly proportional to the root of temperature, i.e. v∝T​⇒v1​v2​​=T1​T2​​​ Given, T1​=T and T2​=2T, v1​=v,v2​=? vv2​​=T2T​​ ⇒v2​=2​v

Q. 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

$2 v$

$v$

$2 v$

$\frac{V}{2}$