Question

Solve the following problem.

A girl stands 170 m away from a high wall and claps her hands at a steady rate so that each clap coincides with the echo of the one before.

1. If she makes 60 claps in 1 minute, what value should be the speed of sound in air?
2. Now, she moves to another location and finds that she should now make 45 claps in 1 minute to coincide with successive echoes. Calculate her distance for the new position from the wall.

Answer 1

Given: distance (s) = 170 m

To find:

1. velocity of sound (v)
2. distance (s)

Formula: Speed = `"distance"/"time"`

Calculation:

1. Girl produces 60 claps in 1 minute i.e., 1 clap in second From formula,
   v = `(2("s"))/"t"`             .....(for an echo)
   ∴ v = `(2 xx 170)/1` = 340 m/s
2. Girl produces 45 claps per minute i.e., 1 clap in `4/3` s
   From formula,
   v = `(2("s"))/"t"`            ....(for an echo)
   ∴ 2s = v × t
   ∴ s = `(340 xx 4)/(2 xx 3) = (340 xx 2)/3`= 226.67 m

1. When the girl makes 60 claps in 1 minute, the value of speed of is 340 m/s.
2. The girl is at a distance of 226.67 m from the wall when she produces 45 claps per minute.