The distance of a reflecting surface from a source is 513 m, and speed of sound is `342 m s^(-1)`. Find the time in which the echo return.

Explanation

To solve the problem of finding the time in which the echo returns, we will follow these steps:

### Step 1: Understand the Problem
We have a source of sound that is 513 meters away from a reflecting surface. The speed of sound is given as 342 m/s. We need to find the total time taken for the sound to travel to the reflecting surface and back (echo).

### Step 2: Calculate the Time for One-Way Journey
We can use the formula for time, which is derived from the equation of motion:
\[ \text{Time} (T) = \frac{\text{Distance} (S)}{\text{Speed} (V)} \]
Here, the distance to the reflecting surface is 513 meters, and the speed of sound is 342 m/s.

### Step 3: Substitute the Values
Substituting the known values into the formula:
\[ T = \frac{513 \, \text{m}}{342 \, \text{m/s}} \]

### Step 4: Perform the Calculation
Now, we perform the division:
\[ T = 1.5 \, \text{seconds} \]
This is the time taken for the sound to reach the reflecting surface.

### Step 5: Calculate the Total Time for Echo
Since the echo has to return back to the source, we need to double the time calculated in the previous step:
\[ \text{Total Time} = 2 \times T = 2 \times 1.5 \, \text{seconds} = 3 \, \text{seconds} \]

### Final Answer
The total time in which the echo returns is **3 seconds**.

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