A soldier walks towards a high wall taking 120 steps per minute. When he is at a distance of 90 m from the wall he observes that echo of step coincides with the next step. The speed of sound must be

Options

A. 340 m/s
B. 330 m/s
C. 300 m/s
D. 360 m/s

Answer

To solve the problem, we need to find the speed of sound based on the information given about the soldier's steps and the echo he hears. Let's break it down step by step.

### Step 1: Understand the problem
The soldier takes 120 steps per minute and is 90 meters away from the wall. The echo of his step coincides with the next step, which means the time taken for the sound to travel to the wall and back is equal to the time taken for him to take one step.

### Step 2: Calculate the time for one step
The soldier takes 120 steps in one minute. To find the time for one step, we convert minutes to seconds:
\[ \text{Time for one step} = \frac{60 \text{ seconds}}{120 \text{ steps}} = \frac{1}{2} \text{ seconds} \]

### Step 3: Determine the total distance traveled by sound
When the soldier is 90 meters away from the wall, the sound travels to the wall and back, which means the total distance traveled by the sound is:
\[ \text{Total distance} = 90 \text{ m (to the wall)} + 90 \text{ m (back)} = 180 \text{ m} \]

### Step 4: Relate time and speed of sound
Since the echo coincides with the next step, the time taken for the sound to travel to the wall and back is equal to the time for one step, which we calculated as \( \frac{1}{2} \) seconds.

### Step 5: Calculate the speed of sound
Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values we have:
\[ \text{Speed of sound} = \frac{180 \text{ m}}{\frac{1}{2} \text{ s}} = 180 \text{ m} \times 2 = 360 \text{ m/s} \]

### Conclusion
The speed of sound is 360 meters per second.