Two identical waves each of frequency 10Hz, are travelling in opposite directions in a medium with a speed of 20 cm/s . Then the distance between adjacent nodes is

Options

A. 1cm
B. 1.2 cm
C. 1.5 cm
D. 2.0 cm

Explanation

To solve the problem of finding the distance between adjacent nodes for two identical waves traveling in opposite directions, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Frequency (f) = 10 Hz
- Speed of waves (v) = 20 cm/s

2. **Use the Wave Equation**:
The relationship between speed (v), frequency (f), and wavelength (λ) is given by the equation:
\[ v = f \cdot \lambda \]

3. **Rearrange to Find Wavelength**:
We can rearrange the equation to solve for the wavelength (λ):
\[ \lambda = \frac{v}{f} \]

4. **Substitute the Values**:
Now, substitute the given values into the equation:
\[ \lambda = \frac{20 \, \text{cm/s}}{10 \, \text{Hz}} = 2 \, \text{cm} \]

5. **Determine the Distance Between Adjacent Nodes**:
In a stationary wave, the distance between adjacent nodes is half the wavelength:
\[ \text{Distance between nodes} = \frac{\lambda}{2} \]
Substituting the value of λ:
\[ \text{Distance between nodes} = \frac{2 \, \text{cm}}{2} = 1 \, \text{cm} \]

### Final Answer:
The distance between adjacent nodes is **1 cm**.

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