A man standing between two parallel hills, claps his hand and hears successive echoes at regular intervals of 1s. If velocity of sound is 340 m `s^(-1)`, then the distance between the hills is

Options

A. 100 m
B. 170 m
C. 510 m
D. 340 m

Explanation

To solve the problem of finding the distance between the two parallel hills based on the echoes heard by a man clapping his hands, we can follow these steps:

### Step 1: Understand the Problem
The man hears successive echoes at regular intervals of 1 second. This means that the time taken for the sound to travel to the hills and back is 1 second for the first echo and 2 seconds for the second echo.

### Step 2: Define Variables
Let:
- \( V \) = velocity of sound = 340 m/s
- \( d \) = distance between the two hills
- The time taken for the first echo (to the nearest hill and back) = 1 second
- The time taken for the second echo (to the farthest hill and back) = 2 seconds

### Step 3: Calculate the Distance for the First Echo
The distance covered by the sound for the first echo (to the nearest hill and back) can be calculated using the formula:
\[ \text{Distance} = \text{Velocity} \times \text{Time} \]
For the first echo:
\[ d_1 = V \times T_1 = 340 \, \text{m/s} \times 1 \, \text{s} = 340 \, \text{m} \]
Since this distance is to the nearest hill and back, the distance to the nearest hill is:
\[ \text{Distance to nearest hill} = \frac{d_1}{2} = \frac{340}{2} = 170 \, \text{m} \]

### Step 4: Calculate the Distance for the Second Echo
For the second echo (to the farthest hill and back):
\[ d_2 = V \times T_2 = 340 \, \text{m/s} \times 2 \, \text{s} = 680 \, \text{m} \]
Since this distance is to the farthest hill and back, the distance to the farthest hill is:
\[ \text{Distance to farthest hill} = \frac{d_2}{2} = \frac{680}{2} = 340 \, \text{m} \]

### Step 5: Calculate the Total Distance Between the Hills
The total distance between the two hills is the sum of the distances to the nearest and farthest hills:
\[ \text{Distance between hills} = \text{Distance to nearest hill} + \text{Distance to farthest hill} = 170 \, \text{m} + 340 \, \text{m} = 510 \, \text{m} \]

### Final Answer
The distance between the two hills is **510 meters**.

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