Two coherent sources excite waves of wavelength λ = 0.5 m. At some point P the path difference of the waves is Δ = 1.25 m. Is there reinforcement or attenuation of the oscillations at this point?
λ = 0.5 m
Δ = 1.25 m
Divide the path difference by the wavelength — you get the number of half-wavelengths.
An odd number of half-wavelengths gives a minimum, an even number gives a maximum.
1. Find how many wavelengths fit into the path difference:
$$\frac{\Delta}{\lambda} = \frac{1.25}{0.5} = 2.5$$2. Condition for reinforcement (maximum): Δ = kλ — a multiple of the wavelength. Condition for attenuation (minimum): Δ = (2k + 1) * λ/2 — a multiple of the half-wavelength.
$$2.5 = \frac{5}{2} = (2 \cdot 2 + 1) \cdot \frac{1}{2}$$The path difference equals 2.5 wavelengths, i.e. an odd number of half-wavelengths (k = 2).
Attenuation is observed at point P — a dark (minimum) fringe will appear there.