Q. It takes 2.0 s for a sound wave to travel between two fixed points when the day temperature is 10°C. if the temperature rises to 30°C the sound wave travels between the same fixed parts in
A) 1.9s
B) 2.0s
C) 2.1s
D) 2.2s
Explanation
(a) Velocity of sound $v \propto \sqrt{T}$
Time
$t \propto \frac{1}{\sqrt{v}}$
$\therefore t \propto \frac{1}{\sqrt{T}}$
$\frac{t_{1}}{t_{2}} = \sqrt{\frac{T_{1}}{T_{2}}}$
$\frac{2}{t_{2}} = \sqrt{\frac{273 + 30}{273 + 10}}$
$\frac{2}{t_{2}} = \sqrt{\frac{303}{283}} = 1.03$
$t_{2} = \frac{2}{1.03} = 1.9s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.