Answer :
Velocity of sound is given by
[tex]V= \sqrt{ \gamma\ \frac{p}{\rho} }[/tex]
[tex]initial\ density, \rho_1= \rho\\initial\ velocity, V_1= V\\ final\ density, \rho_2=3 \rho\\final\ velocity= V_2[/tex]
[tex] \frac{V_2}{V_1}= \sqrt{\frac{\gamma p}{\rho_1}/\frac{\gamma p}{\rho_2} } \\ \\ \frac{V_2}{V_1}= \sqrt{\frac{\rho_2}{\rho_1}}\\ \\ \frac{V_2}{V_1}= \sqrt{\frac{3\rho}{\rho}}\\ \\ \frac{V_2}{V_1}= \sqrt{3}\\ \\ \frac{V_1}{V_2}= \frac{1}{ \sqrt{3} } \\ \\V_1:V_2=1: \sqrt{3} [/tex]
[tex]V= \sqrt{ \gamma\ \frac{p}{\rho} }[/tex]
[tex]initial\ density, \rho_1= \rho\\initial\ velocity, V_1= V\\ final\ density, \rho_2=3 \rho\\final\ velocity= V_2[/tex]
[tex] \frac{V_2}{V_1}= \sqrt{\frac{\gamma p}{\rho_1}/\frac{\gamma p}{\rho_2} } \\ \\ \frac{V_2}{V_1}= \sqrt{\frac{\rho_2}{\rho_1}}\\ \\ \frac{V_2}{V_1}= \sqrt{\frac{3\rho}{\rho}}\\ \\ \frac{V_2}{V_1}= \sqrt{3}\\ \\ \frac{V_1}{V_2}= \frac{1}{ \sqrt{3} } \\ \\V_1:V_2=1: \sqrt{3} [/tex]
If this is a question on the velocity of sound in a gas or in air, then
v = √ (γ P/ρ ) = √ (γ R T / M) = √ (γ k_B T /m)
if the density of the gas is tripled, the pressure also triples. Hence, there is no change in the velocity. The velocity of of sound depends only on absolute temperature. in the last equation above, m = mass of a molecule, k_B and γ are constants. Hence, there is no dependence on density directly, as long as the composition of the gas or air does not change.
Density has an impact only if the gas becomes different, or its composition changes.
hence answer is 1.
v = √ (γ P/ρ ) = √ (γ R T / M) = √ (γ k_B T /m)
if the density of the gas is tripled, the pressure also triples. Hence, there is no change in the velocity. The velocity of of sound depends only on absolute temperature. in the last equation above, m = mass of a molecule, k_B and γ are constants. Hence, there is no dependence on density directly, as long as the composition of the gas or air does not change.
Density has an impact only if the gas becomes different, or its composition changes.
hence answer is 1.