Question

Calculate the temperature at which the sound travels in hydrogen with the same speed as in helium at N.T.P. The density of helium is twice that of hydrogen.

Answer 1

Let θ°C be the required temperature at which the speed of the sound in hydrogen is same as that in helium at NTP (i.e., 0°C).

Let v_θ and v₀ be the speeds of sound in hydrogen at 0°C and 0°C respectively.

If v₀' be the speed of sound in helium at 0°C, then,

v₀' = v_θ   ....(i)

From equation (i) and (ii), we have

where ρ_H and ρ_He and densities of hydrogen and helium gas respectively.

If ρ_H = P

then ρ_He = 2P

Then

From equations (iii) and (iv), we have,