A man standing at some distance from a cliff hears the echo of sound after 2s. He walks 495 m away from the cliff. He produces a sound there and receives the echo after 5s. What is the speed of sound?

Options

A. 330 m/s
B. 340 m/s
C. 390 m/s
D. 380 m/s

Answer

To solve the problem step by step, let's break it down as follows:

### Step 1: Understand the scenario
A man is initially at a distance \( x \) from a cliff. When he produces a sound, it travels to the cliff and reflects back, taking a total time of 2 seconds for the round trip.

### Step 2: Set up the equation for the first scenario
The speed of sound \( v \) can be expressed as:
\[ v = \frac{\text{Distance}}{\text{Time}} \]
In the first scenario, the distance covered by the sound is \( 2x \) (to the cliff and back), and the time taken is 2 seconds. Therefore, we have:
\[ v = \frac{2x}{2} = x \]

### Step 3: Analyze the second scenario
The man walks 495 meters away from the cliff, making his new distance from the cliff \( x + 495 \) meters. When he produces a sound at this new position, the sound travels to the cliff and back, covering a distance of \( 2(x + 495) \) meters. The total time taken for this round trip is 5 seconds.

### Step 4: Set up the equation for the second scenario
Using the same formula for speed of sound, we have:
\[ v = \frac{2(x + 495)}{5} \]

### Step 5: Substitute \( v \) from the first scenario into the second scenario
From the first scenario, we know \( v = x \). Substituting this into the second equation gives:
\[ x = \frac{2(x + 495)}{5} \]

### Step 6: Solve for \( x \)
To eliminate the fraction, multiply both sides by 5:
\[ 5x = 2(x + 495) \]
Expanding the right side:
\[ 5x = 2x + 990 \]
Now, isolate \( x \):
\[ 5x - 2x = 990 \]
\[ 3x = 990 \]
\[ x = \frac{990}{3} = 330 \text{ meters} \]

### Step 7: Find the speed of sound
Since \( v = x \), we find:
\[ v = 330 \text{ meters/second} \]

### Final Answer
The speed of sound is \( 330 \text{ m/s} \).

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