A transverse wave on a string has a speed of 30 m/s and a wavelength of 1.5 m. What is the time period of the wave?
**Displacement relation** encodes λ = 2π/k and f = ω/2π. Comparing given equation y = a sin(kx - ωt) with standard form yields k and ω, hence λ = 2π/k and v = ω/k, essential for identifying propagation characteristics and phase. Speed: v = v λ , v = (v/λ) = (30/1.5) = 20 Hz . Time period: T = (1/v) = (1/20) = 0.05 s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0.05 s, illustrating frequency-length-speed interdependence and quantization by boundaries.
Ref: NCERT > Physics Book > Waves > Wave Equation and Displacement Relation
