Question

A simple harmonic progressive wave is given by the equation y = 0.1 sin 4π (50t – 0.1 x), in SI units. Find the amplitude, frequency, wavelength and speed of the wave.

Answer 1

Data : y = 0.1 sin 4π (50t – 0.1 x) 

= 0.1 sin 2π (100t – 0.2 x)

= 0.1 sin 2π( 100t –\(\frac x5\))

Let us compare this equation with that of a simple harmonic progressive wave.

∴ y = A sin 2π(nt – \(\frac x5\)) = 0.1 sin2π(100t – \(\frac x5\))

Comparing the quantities on both sides, we get,

1. amplitude (A) = 0.1 m 

2. frequency (n) = 100 Hz 

3. wavelength (λ) = 5 m 

4. speed (v) = nλ = 100 × 5 = 500 m/s