Question

The velocity of sound is v at 273 K. The temperature at which it is 2v is

• A. 2 $\times$ 273 K
• B. 4 $\times$ 273 K
• C. 8 $\times$ 273 K
• D. 16 $\times$ 273 K

Answer 1

Answer: (B)

4 $\times$ 273 K

Answer 2

Velocity of sound is given by
\hspace40mm v = \sqrt{\frac{3RT}{M}} = v ? T
Given, t = 273 K, $v_1 = v, v_2 = 2 v.$
\therefore \hspace30mm \frac{v_1}{v_2} = \sqrt{\frac{T_1}{T_2}} \Rightarrow \, \, v_2 = \sqrt{\frac{T_2}{T_1}}v_1
\hspace40mm 2v = \sqrt{\frac{T_2}{273}v}
\Rightarrow \hspace30mm T_2 = 273 \times 4 \, K