Superposition And Interference

When two coherent waves overlap, the type of interference is decided by the path difference relative to the wavelength. Constructive interference, giving maximum loudness, requires a path difference of a whole number of wavelengths, while destructive interference, giving minimum loudness, requires an odd number of half-wavelengths. Here the path difference is $0.75\text{ m}$ and the wavelength is $0.5\text{ m}$, so the path difference equals $0.75/0.5=1.5$ wavelengths, which is three half-wavelengths, an odd multiple of $\lambda /2$. This is exactly the condition for fully destructive interference, where the two coherent in-phase signals arrive perfectly out of step. The option of constructive interference is wrong because $1.5\lambda$ is not a whole number of wavelengths. The option claiming no interference is incorrect, since identical in-phase coherent sources interfere strongly. The option of a beat pattern is wrong because beats arise from different frequencies, not from a fixed path difference at one frequency. This applies the NCERT superposition principle for coherent sources. As a plausibility check, an odd number of half-wavelengths places one wave's crest on the other's trough, cancelling the sound, consistent with the minimum loudness conclusion.