Two coherent speakers broadcast at wavelength λ = 0.5 m. A listener is positioned so that the path difference from the two speakers to her location is 0.75 m. What does she observe?
AMaximum sound (constructive interference) — path difference 0.75 m is greater than λ/2, so waves reinforce
BSilence (destructive interference) — 0.75 m = 1.5λ, a half-integer multiple of wavelength, so crests meet troughs
CMaximum sound — any path difference less than 1 m produces constructive interference
DSilence — any path difference other than exactly zero produces destructive interference
0.75 m / 0.5 m = 1.5, which is a half-integer multiple of the wavelength (specifically 3λ/2). Destructive interference occurs at path differences of λ/2, 3λ/2, 5λ/2, ... — any (n + ½)λ for integer n. At these locations, the waves arrive exactly out of phase (crest meets trough) and cancel. Constructive interference occurs only at whole-number multiples: 0, λ, 2λ, etc. The pattern is determined entirely by the geometry of path differences.
Question 2 Multiple Choice
Two coherent light sources are 1 mm apart and project fringes onto a screen 2 m away. The source separation is then doubled to 2 mm, while wavelength and screen distance remain constant. What happens to the fringe spacing?
BThe fringe spacing decreases — the formula Δy = λL/d shows that larger d produces smaller fringe spacing
CThe fringe spacing stays the same — only wavelength affects the spacing
DThe pattern disappears — sources must be close enough for their wave fronts to overlap
The fringe spacing formula is Δy = λL/d. With d in the denominator, doubling the source separation halves the fringe spacing. This is counterintuitive: wider source separation makes the fringes *narrower*, not wider. The physical reason: farther-apart sources reach the same path-difference conditions at smaller angular separations, compressing the fringe pattern. Conversely, using a longer wavelength or placing the screen farther away widens the fringes.
Question 3 True / False
Two incoherent light sources (with randomly fluctuating phase relationship) can produce a stable two-source interference pattern on a screen if they emit the same wavelength.
TTrue
FFalse
Answer: False
Coherence — a fixed phase relationship between the two sources over time — is required for a stable pattern. Incoherent sources have a phase difference that fluctuates randomly, so the fringe positions shift continuously and wash out into uniform brightness when averaged over time. Same wavelength is necessary but not sufficient. This is why Young's original experiment used a single source illuminating two slits: both slits are driven by the same wavefront, guaranteeing coherence.
Question 4 True / False
In a two-source interference pattern, the central bright fringe at the center of the screen corresponds to a path difference of exactly one wavelength.
TTrue
FFalse
Answer: False
The central bright fringe occurs where the path difference equals zero — both sources are equidistant from the center of the screen, so the waves arrive perfectly in phase regardless of wavelength. A path difference of exactly one wavelength (1λ) gives the first-order bright fringe, displaced from the center. The condition for constructive interference is path difference = nλ for any integer n, and n=0 is the central (zeroth-order) fringe.
Question 5 Short Answer
Explain why two separate light bulbs illuminating two pinholes would NOT produce a stable interference pattern, but a single light bulb illuminating two pinholes WOULD. What property is required and why does the setup matter?
Think about your answer, then reveal below.
Model answer: Coherence — a fixed, stable phase relationship between the two sources — is required for a stable interference pattern. Two separate light bulbs emit light with independently and randomly fluctuating phases. Even if both illuminate the same pinholes, the phase difference between the two pinholes varies randomly, so the fringe positions shift constantly and average out to uniform brightness. A single bulb illuminating two pinholes guarantees coherence: both pinholes are driven by the same wavefront, so the phase difference between them is constant (zero for a point source on the axis). The fringes are stable because the interference condition is fixed in space.
This is why lasers made interference experiments easy and why Young's original 1801 experiment was so ingenious — it extracted coherence from ordinary (incoherent) sunlight by using a single pinhole as the source and two downstream pinholes as the coherent pair. The spatial coherence of the single source is transferred to the pair. Modern interference experiments typically use laser light directly, since laser emission is highly coherent by design.