Physics · Principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, beats
Two waves represented by \) and \) are superimposed at any point at a particular
Two waves represented by \( y_{1}= \) \( 10 \sin (2000 \pi t) \) and \( y_{2}= \) \( 10 \sin (2000 \pi t+\pi / 2) \) are superimposed at any point at a particular instant. The resultant amplitude is?
- A. 10 units
- B. 20 units
- C. 14.1 units
- D. zero
Step-by-step solution
The given waves have equal amplitude (10 units) and a phase difference of π/2. The resultant amplitude is given by A = √(A1² + A2² + 2A1A2 cos φ) = √(10² + 10² + 2×10×10×cos(π/2)) = √(200) = 10√2 ≈ 14.1 units.