Govt. Exams
Constructive interference occurs when path difference = nλ. λ = v/f = 340/340 = 1 m, so path difference = 0, 1 m, 2 m, etc.
Maximum particle velocity = Aω = A(2π/T) = 5 × (2π/0.2) = 5 × 31.4 = 157 cm/s
For source moving towards stationary observer: f' = f × v/(v - v_s), so f = f'(v)/(v + v_s) when rearranged
Total internal reflection occurs when a wave travels from a denser to a less dense medium at an angle greater than the critical angle
Comparing with y = Asin(kx - ωt): k = 2π, ω = 10π. v = ω/k = 10π/2π = 5 cm/s
λ = v/f = 340/256 ≈ 1.33 m. Distance between consecutive compressions = wavelength = 1.33 m
Using Snell's law: n₁sin(θ₁) = n₂sin(θ₂), 1.5×sin(30°) = 1×sin(θ₂), sin(θ₂) = 0.75, θ₂ ≈ 48.6°
f = (1/2L)√(T/μ) where μ = 0.01/1 = 0.01 kg/m. f = (1/2)√(90/0.01) = (1/2) × 300 = 150 Hz
For a pipe closed at one end: f = v/(4L), so v = 4fL = 4 × 170 × 0.5 = 340 m/s
f' = f(v + v_observer)/(v - v_source) = 500(330 + 0)/(330 - 30) = 500 × 330/300 ≈ 545 Hz
