Question

The speed of sound in a container of gas at 20.0°C is v. If the temperature of the gas is increased to 80.0°C, the new speed will be?

Answer 1

Answer : The new speed will be, 1.098v

Explanation :

The formula used for speed of sound in a container of gas is:

$c=\sqrt{\frac{\gamma RT}{M}}$

where,

c = speed of sound

R = gas constant

$\gamma$ = adiabatic constant

T = absolute temperature

M = molecular mass of gas

As, $c\propto \sqrt{T}$

or, we can say that

$\frac{c_1}{c_2}=\sqrt{\frac{T_1}{T_2}}$            .............(1)

Given:

$T_1$ = $20.0^oC=273+20.0=293K$

$T_1$ = $80.0^oC=273+80.0=353K$

$c_1$ = v

Now put all the given values in the above formula 1, we get:

$\frac{v}{c_2}=\sqrt{\frac{293}{353}}$

$c_2=1.098v$

Thus, the new speed will be, 1.098v