A splash is heard 3.12 seconds after a stone is dropped into a well 45m deep. The speed of sound in air is. (g=10m/s^2)

Question

1)330m/s

2)375m/s

3)340m/s

4)346m/s

Answer 1

v = speed of sound

 

T = time it took for stone to fall

 

h = depth = 45 m

 

h = gT²/2 ⇒

 

T = √(2h/g)

 

t = travel time of sound

 

t = h/v = 3.12 - T (seconds)

 

Put this all together and get

 

v = h/t = h/(3.12 - T) = h / [3.12 - √(2h/g)] = 45 / {3.12 - √[2(45)/10]} m/s

 

v = 375 m/s