Question

The sound of a starting pistol can be heard easily from a distance of 800.0 m but the smoke can be seen much sooner than the sound is perceived. Why is the smoke seen before the sound is heard? What is the speed of sound if the air temperature is 15 °C?

Answer 1

Part A.

smoke is seen before the sound is heard, because light travels very fast in comparison to sound.

Speed of light = c = 3*10^8 m/s

Speed of sound at room temperature 20 C = 343 m/s

So time taken by light to seen at 'd' distance will be, t1 = distance/speed of light = d/c

And time taken by Sound to heard at 'd' distance will be, t2 = distance/speed of sound = d/v

So for same distance time is inversely proportional to the speed, and since speed of light is much faster than speed of sound, So

t1 <<<< t2

Which means smoke is seen before sound is heard.

For numerical values: t1 = 800.0/(3.0*10^8) = 2.67*10^-6 sec

t2 = 800.0/343 = 2.33 sec

Part B.

Now relation between temperature and speed of sound is given by:

V = 331 + 0.6*T

Where T = temperature in C = 15 C

So,

V = 331 + 0.6*15

V = 340 m/s

Let me know if you've any query.