The requirement for the wavelength and frequency of waves to be equal for interference is based on the fundamental principle of wave behavior. Let's break it down:
Wavelength (λ): It represents the spatial distance between successive crests (or troughs) of a wave. It is measured in meters (m) or other units of length.
Frequency (f): It represents the number of complete wave cycles passing a fixed point per unit of time. It is measured in hertz (Hz), which corresponds to cycles per second.
Now, the key concept is that the wavelength and frequency of a wave are inversely proportional to each other. This relationship is expressed by the formula:
v = λ * f
where: v is the wave velocity (speed) in meters per second (m/s).
The formula shows that for a given wave, if the wavelength increases, the frequency decreases, and vice versa, while keeping the wave velocity constant. This inverse relationship ensures that the product of wavelength and frequency remains constant.
Now, when it comes to interference, constructive or destructive interference occurs when two or more waves meet at the same point in space. For constructive interference to happen, the peaks of one wave must align with the peaks of the other wave, while for destructive interference, the peaks of one wave must align with the troughs of the other wave.
For this alignment to occur consistently over time, the waves must have the same wavelength. If the wavelengths are different, the peaks and troughs will not align properly, resulting in incomplete interference or inconsistent interference patterns.
Therefore, in order to observe predictable and consistent interference patterns, the wavelength and frequency of the waves must be equal, ensuring that the peaks and troughs align properly for constructive or destructive interference to occur.