Question

The equation of a standing wave is given by y = 0.02 cos (πx) sin (100 πt) m. Find the amplitude of either wave interfering, wavelength, time period, frequency and wave speed of interfering waves.

Answer 1

Data : y = 0.02 cos (πx) sin (100 πt) m Comparing this equation with 

y = 2A cos \((\frac{2\pi x}\lambda)\) sin (2πnt)

we get for either interfering waves,

1. the amplitude, | A | = \(\frac{0.02}2\) = 0.01 m

2. the wavelength, λ = 2 m

3. the time period, T = \(\frac 1n\) = \(\frac 1{50}s\) = 0.02 s

4. the frequency, n = 50 Hz 

5. the wave speed = nλ = 50 × 2 = 100 m/s