Two interferring waves have the same wavelength, frequency and amplitude. They are travelling in the same direction but `90^(@)` out of phase compared to individual waves. The resultant wave will have the same.

Options

A. amplitude and velocity but different wavelength
B. frequency and velocity but different wavelength
C. wavelength and velocity but different amplitude
D. amplitude and frequency but different wavelength

Explanation

To solve the question, we need to analyze the properties of the two interfering waves and how they interact with each other. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the properties of the waves
We have two waves that have:
- Same wavelength (λ)
- Same frequency (f)
- Same amplitude (A)
- They are traveling in the same direction but are 90 degrees out of phase.

### Step 2: Analyze the phase difference
Since the two waves are 90 degrees out of phase, this means that when one wave is at its maximum (crest), the other wave is at its equilibrium position (zero displacement). This phase difference will affect how the waves combine.

### Step 3: Determine the resultant wave
When two waves interfere, the resultant wave's amplitude can be calculated using the principle of superposition. For two waves that are 90 degrees out of phase:
- The resultant amplitude (R) can be calculated using the formula:
\[ R = \sqrt{A^2 + A^2} = \sqrt{2A^2} = A\sqrt{2} \]
This shows that the amplitude of the resultant wave will be greater than the amplitude of the individual waves.

### Step 4: Consider the velocity and wavelength
The velocity (v) and wavelength (λ) of the waves depend on the medium through which they are traveling. Since both waves are traveling in the same medium:
- The velocity of the resultant wave will be the same as the individual waves.
- The wavelength of the resultant wave will also remain the same as the individual waves.

### Conclusion
Thus, the resultant wave will have the same wavelength and velocity as the individual waves, but the amplitude will change.

### Final Answer
The resultant wave will have the same wavelength and velocity, but a different amplitude.

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