Govt. Exams
Entrance Exams
Let intensities be I and 4I. Amplitudes are A and 2A. Max intensity = (A + 2A)² = 9A² = 9I
v = √(T/μ) = √(200/(0.1/2)) = √4000 = 63.2 m/s. f = v/(2L) = 63.2/4 = 15.8 Hz... Recalculating: f₁ = √(T/μ)/(2L) where μ = 0.05 kg/m, so f₁ ≈ 44.7 Hz
I_max = (√I₁ + √I₂)² = (√(4I) + √I)² = (2√I + √I)² = (3√I)² = 9I
For successive resonances in a resonance tube, l₂ - l₁ = λ/2, and end correction e ≈ (l₂ - l₁)/2 = λ/4
Comparing with y = Asin(2πft - 2πx/λ), we have 2π/λ = 0.01π, so λ = 200 cm
Maximum particle velocity = ωA = 2πfA = 2πA(v/λ) = 2πAv/λ