Question

A column of soldiers, marching at 132 steps per minute, keep in step with the beat of a drummer at the head of the column. It is observed that the soldiers in the rear end of the column are striding forward with the left foot when the drummer is advancing with the right. What is the approximate length of the column? (Take the speed of sound to be 343 m/s.)

Answer 1

The approximate length of the column of soldiers is 754.6 meters.

Step-by-step explanation:

In order to answer this question, we need to consider the difference in speed between the sound wave (drummer's beat) and the soldiers' steps. The sound wave travels at a speed of 343 m/s, and we are given that the soldiers are marching at 132 steps per minute, which can be converted to steps per second by dividing by 60. Therefore, the soldiers take approximately 2.2 steps per second (132/60).

Now, we need to determine the time it takes for the sound wave to move from the drummer to the soldier in the rear of the column. We can use the formula t = d/v, where t is the time, d is the distance, and v is the speed of sound. Rearranging the formula to solve for d, we have d = t * v. Substituting the known values, d = 2.2 * 343. This gives us an approximate length of the column of 754.6 meters.

Answer 2

132 steps / min ≈ 2 steps / s

They are one step out of sync

1 step ⇒ ≈0.5 s

sound reaches rear with 0.5s delay

sound travels in 0.5 seconds = 343 m/s * 0.5s = 171.5m