Displacement of a wave is expressed as x(t)=5 cos (628 t+π/2) m. The wavelength of the wave when its velocity is 300 m / s is :
(π=3.14)

Solution

Physics sir · 3 steps

The 628 is angular frequency, not frequency. Divide by 2π first, then use v = fλ.

1. Read off ω. Compare with x = A cos(ω t + φ). The coefficient of t is the angular frequency, so ω = 628 rad s⁻¹. The amplitude 5 m and the phase π/2 do not affect the wavelength.
2. Find frequency. f = ω/2π = 628/(2 × 3.14) = 628/6.28 = 100 Hz.

   λ = v/f = (300 m s⁻¹)/(100 Hz) = 3 m

3. So. The wavelength is 3 m, which is option (c).

The idea to keep. In any wave equation, the number multiplying t is ω. Always convert it with f = ω/2π before using v = fλ.

Answer from the NTA final answer key. Solution by PrepWiser.