Question

On a dry day, sound travels a certain distance in 10 seconds. What is the time required for sound to travel the same distance on a humid day. The densities of dry air and humid air are in the ratio 3:2 :

• A. 8.165 sec
• B. 7.165 sec
• C. 5.165 sec
• D. 4.165 sec

Answer 1

The correct option is A 8.165 sec

Time taken for sound to travel a certain distance on a dry day$=10second$

Densities of dry air and humid air are in the ratio $3:2$

Let time taken for sound to travel the same distance on the humid day be $t_n$

$\frac{v_d}{v_h}=\sqrt{\frac{{\rho }_h}{{\rho }_d}}=\sqrt{\frac{2}{3}}$

$v_h=\sqrt{3/2}{v}_d=1.224v$

$\frac{v_h}{v_d}=\frac{t_d}{t_h}$

or, $t_h=t_d\frac{v_d}{v_h}=10v_d/\left(1.224v_d\right)=8.165sec.$