Question

As the sound TRAVELS faster in liquids than gas so why the speed of sound is higher in hydrogen (gas) than methanol (liquid)....???

Speed of sound in hydrogen- 1284m/s

Speed of sound in methanol- 1103m/s

Answer 1

    Speed of sound in any medium depends on the Bulk modulus (reciprocal of compressibility) and density.  Normally sound travels faster in liquids than in gases as they are more elastic. However, we need to take effects of both the elastic property and density together.  In some cases sound travels faster in gases like H2 than in some liquids like Methyl Alcohol. It is the ratio that matters.


Speed of sound in a medium = v
        v = $\sqrt{\frac{B}{\rho}}$

For Methanol (liquid) or Methyl Alcohol CH3 OH:
   Bulk modulus at 20°C as :  B = 823 * 10⁶ Pa
   Density = ρ = 0.792 gm/cc or  792 kg/m³
   So the speed of sound v ≈ 1, 103 m/s  (around)

For Hydrogen gas H₂   speed of sound:

$v=\sqrt{\frac{B}{\rho}}=\sqrt{\frac{\gamma \: P}{\rho}}, \: \: \: \: \gamma=1.4 \: (Diatomic)\\\\Or, \: \: v=\sqrt{\frac{R}{M}T}$

    R = Universal Gas constant = 8.314 J/K/mol
    T = Absolute Temperature
    M = Molar mass in kg/mole = 0.002 kg/mol
    B = 1.4 * 10⁵ Pa
    T = 293 °C 

 IF we use these values we get  v = around 1284 m/sec.

Answer 2

The speed of sound depends on both the density and the elasticity of the medium it's travelling through. Sounds travels in waves of compression and rarity, so it's fastest in solids because the molecules are packed together more tightly. Sound is next fastest in liquids, again for the same reason. It's slowest in a gas. And, in a gas, the temperature is particularly important--the faster the molecules are moving from heat, the more sound energy they can transfer to their neighbors.

As far as distance travelled --- again, solids and liquids win. However, there's an additional factor called 'damping' that depends on the elasticity of the medium the sounds waves are travelling through, also scattering. It ends up that lower-frequency sound waves can travel much longer distances than high frequency sounds....this is how whales can communicate over long distances in the ocean--and how elephants do the same in air. Both do their 'long distance' calling with low frequencies