The time lag between two particles vibrating in a progressive wave seperated by a distance 20m is 0.02s. The wave velocity if the frequency of the wave is 500Hz, is

Options

A. `1000ms^(-1)`
B. `500ms^(-1)`
C. `2000ms^(-1)`
D. `250 ms^(-1)`

Answer

To solve the problem, we need to find the wave velocity given the distance between two particles and the time lag between their vibrations. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Distance (s) = 20 meters
- Time lag (t) = 0.02 seconds
- Frequency (f) = 500 Hz (though we won't need this value for calculating wave velocity directly)

### Step 2: Use the formula for wave velocity
The wave velocity (v) can be calculated using the formula:
\[ v = \frac{s}{t} \]
where:
- \( v \) is the wave velocity,
- \( s \) is the distance between the two particles,
- \( t \) is the time lag.

### Step 3: Substitute the values into the formula
Now, we substitute the given values into the formula:
\[ v = \frac{20 \, \text{m}}{0.02 \, \text{s}} \]

### Step 4: Perform the calculation
Calculating the above expression:
\[ v = \frac{20}{0.02} = 1000 \, \text{m/s} \]

### Step 5: State the final answer
Thus, the wave velocity is:
\[ v = 1000 \, \text{m/s} \]