Ncert Exercises & Solutions

At what temperatures (in $° C$ ) will the speed of sound in the air be 3 times its value at $0 ° C$ ?

Hint: Use the formula of the velocity of sound.

Step 1 : Find the relation between v and T .

We know that speed of sound in air v \propto \sqrt{T} .

∴ \frac{v_{T}}{v_{0}} = \sqrt{\frac{T}{T_{0}}} = \sqrt{\frac{T}{273}} [where T is in kelvin]

Step 2 : Find the final temperature .

But, \frac{v_{T}}{v_{0}} = \frac{3}{1} [∵ speed becomes three times]

∴ \frac{3}{1} = \sqrt{\frac{T}{T_{0}}} \Rightarrow \frac{T}{273} = 9

∴ T = 273 \times 9 = 2457 K = 2457 - 273 = 2184 ° C