Last Activity: 10 Years ago
Sol. f = 100 Hz, λ = 2 cm = 2 * 10 base 2 mrn∴ wave speed, v = f λ = 2 m/srna in 0.015 sec 1^ST wave has travelledrnx = 0.015 * 2 = 0.03 m = path diffnrn∴ corresponding phase difference, ∅ = 2π*/λ = 2π/ 2 * 10^2 * 0.03 = 3π.rnb Path different x = 4 cm = 0.04 mrn⇒ ∅ = π/λx = 2π/2 * 10^2 * 0.04 = 4 π.rnC The waves have same frequency, same wavelength and same amplitudernLet, Y base 1 = r sin wt y base 2 = r sin wt + ∅rn⇒ Y = Y base 1 + y base 2 = [r sin wt + wt + ∅rn= 2r sin wt + ∅/2 cos ∅/2rn∴ resultant amplitude = 2r cos ∅/2rnSo when ∅ = 3π, r = 2 * 10^ 3 m rnrnR base res = 2 * 2 * 10^3 cos 3π/2 = 0rnAgain, when ∅/2π, R base res = 2 * 2 * 10^3 cos 4π/2 = 4mm.
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