Question

Hydrogen gas is filled in two identical bottles, A and B at the same temperature. The mass of hydrogen in the two bottles is 12g and 48g respectively. In which bottle sound will travel faster? How many times as fast as the other?

Answer 1

Given, mass of bottle A= m = 12 g

mass of bottle B = M = 40 g

Let us suppose speed of sound in bottle A = v

And speed of sound in bottle B = V

As we know that speed of sound= 1/√d

Where d- density at constant temperature

But, density = mass/ volume

d =m/v

Where m – mass

V – volume

Speed of sound = 1/√d

Speed of sound = 1/√(m/v)

Speed of sound = √v/√m

Firstly we calculate speed of sound in bottle A= √v/√m…

But volume is constant

Sound in bottle A = 1/√m

Sound in bottle A = 1/√12

Similarly we calculate Speed of sound in bottle B= 1/√48

(Speed of sound in bottle A)/(Speed of sound in bottle B) = √48/√12

v/V= √4

= 2

v = 2V

Thus Speed of sound in bottle A is 2 times greater than speed of sound in bottle B.