If a source sound of frequency 500 Hz produces waves of wavelength 0.1 m. Then the waves travel a distance of 300 m in the time in the time interval will be

Options

A. 0.6 s
B. 6 s
C. 1.67 s
D. 50 s

Explanation

To solve the problem, we need to find the time it takes for sound waves to travel a distance of 300 meters, given the frequency of the sound and its wavelength. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Frequency (f) = 500 Hz
- Wavelength (λ) = 0.1 m
- Distance (s) = 300 m

### Step 2: Calculate the velocity of the sound wave
We can use the formula that relates velocity (v), frequency (f), and wavelength (λ):
\[ v = f \cdot \lambda \]
Substituting the given values:
\[ v = 500 \, \text{Hz} \cdot 0.1 \, \text{m} \]
\[ v = 50 \, \text{m/s} \]

### Step 3: Use the velocity to find the time taken to travel the distance
We can use the formula that relates distance (s), velocity (v), and time (t):
\[ s = v \cdot t \]
Rearranging the formula to solve for time (t):
\[ t = \frac{s}{v} \]
Substituting the values we have:
\[ t = \frac{300 \, \text{m}}{50 \, \text{m/s}} \]
\[ t = 6 \, \text{s} \]

### Final Answer
The time taken for the sound waves to travel 300 meters is **6 seconds**.

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