Two waves are approaching each other with a velocity of `20m//s` and frequency `n`. The distance between two consecutive nodes is

Options

A. `20/n`
B. `10 / n`
C. `5/n`
D. `n/10`

Answer

To find the distance between two consecutive nodes for the given waves, we can follow these steps:

### Step 1: Understand the concept of nodes and antinodes
Nodes are points where the two waves cancel each other out, resulting in minimum amplitude. The distance between two consecutive nodes is half the wavelength (λ/2) of the waves.

### Step 2: Use the wave velocity formula
The velocity (V) of a wave is related to its frequency (f) and wavelength (λ) by the formula:
\[ V = f \cdot \lambda \]

### Step 3: Substitute the known values
In this problem, the velocity (V) is given as 20 m/s, and the frequency (f) is given as \( n \). We can substitute these values into the formula:
\[ 20 = n \cdot \lambda \]

### Step 4: Solve for wavelength (λ)
Rearranging the equation to solve for λ gives:
\[ \lambda = \frac{20}{n} \]

### Step 5: Find the distance between consecutive nodes
Since the distance between two consecutive nodes is half the wavelength, we can express this as:
\[ \text{Distance between nodes} = \frac{\lambda}{2} \]

Substituting the value of λ we found:
\[ \text{Distance between nodes} = \frac{20/n}{2} = \frac{10}{n} \]

### Final Answer
Thus, the distance between two consecutive nodes is:
\[ \frac{10}{n} \]