First slide

Speed of wave

Question

The velocities of sound in an ideal gas at temperature T₁, and T₂, K are found to be V₁, and V₂, respectively. If the root mean square speeds of the same gas at the same temperatures. T₁ and T₂, are v₁, and v₂, respectively, then

Easy

A

$v_{2} = v_{1} (V_{2} / V_{1})$
B

$v_{2} = v_{1} (V_{1} / V_{2})$
C

$V_{2} = V_{1} \sqrt{(V_{2} / V_{1})}$
D

$V_{2} = V_{1} \sqrt{(V_{1} / V_{2})}$

Solution

we know that $V = \sqrt{(\frac{γP}{ρ})} and PV = RT$
$\frac{V_{1}}{V_{2}} = \frac{{({γRT}_{1} / M)}^{1 / 2}}{{({γRT}_{2} / M)}^{1 / 2}} = {[\frac{T_{1}}{T_{2}}]}^{1 / 2} Further r \frac{v_{1}}{v_{2}} = \frac{{(3 {RT}_{1} / M)}^{1 / 2}}{{(3 {RT}_{2} / M)}^{1 / 2}} = {[\frac{T_{1}}{T_{2}}]}^{1 / 2} \frac{V_{1}}{V_{2}} = \frac{v_{1}}{v_{2}} or v_{2} = v_{1} (\frac{V_{2}}{V_{1}})$

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