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 the man, we can follow these steps:

### Step 1: Understand the problem
The man claps his hands and hears echoes at regular intervals of 1 second. The speed of sound is given as 340 m/s. We need to find the distance between the two hills.

### Step 2: Determine the distance sound travels for each echo
When the man claps, the sound travels to the first hill and back, which we can denote as \(2x_1\) for the first echo. For the second echo, the sound travels to the second hill and back, denoted as \(2x_2\).

### Step 3: Set up the time equation
Since the man hears successive echoes at intervals of 1 second, we can set up the following equations based on the time taken for the sound to travel to the hills and back:

1. For the first echo:
\[ \frac{2x_1}{v} = 1 \quad \text{(where \(v\) is the speed of sound)} \]
Substituting \(v = 340 \, \text{m/s}\):
\[ 2x_1 = 340 \times 1 \implies x_1 = 170 \, \text{m} \]

2. For the second echo:
\[ \frac{2x_2}{v} = 2 \]
Substituting \(v = 340 \, \text{m/s}\):
\[ 2x_2 = 340 \times 2 \implies x_2 = 340 \, \text{m} \]

### Step 4: Calculate the total distance between the hills
The total distance between the two hills is the distance to the first hill plus the distance to the second hill:
\[ \text{Total distance} = x_1 + x_2 = 170 \, \text{m} + 340 \, \text{m} = 510 \, \text{m} \]

### Step 5: Conclusion
Thus, the distance between the two hills is:
\[ \text{Distance between the hills} = 510 \, \text{m} \]

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