Govt. Exams
From y = 0.02sin(50πt - 4πx), comparing with y = Asin(ωt - kx): ω = 50π rad/s, k = 4π rad/m. Wavelength λ = 2π/k = 2π/(4π) = 0.5 m. Wave velocity v = ω/k = 50π/(4π) = 12.5 m/s.
When a wave reflects from a fixed (denser) end, it undergoes a phase change of π radians or 180°
Beat frequency = |f₁ - f₂| = |250 - 254| = 4 Hz
In the second harmonic (n=2), f₂ = 2f₁. Therefore, f₁ = f₂/2 = 200/2 = 100 Hz
For constructive interference, A_resultant = A₁ + A₂ = 3 + 4 = 7 cm
Intensity is proportional to the square of amplitude (I ∝ A²). When A becomes 2A, I becomes 4I
In the nth harmonic, the number of antinodes equals n. For the third harmonic (n=3), there are 3 antinodes
The fundamental wave equation is v = fλ, where v is velocity, f is frequency, and λ is wavelength
Using v = fλ, f = v/λ = 340/0.85 = 400 Hz
Doppler effect occurs due to relative motion between source and observer, causing apparent frequency change
