A transverse wave on a string is described by y = 3 sin(36t+0.018x+π/4), where x and y are measured in centimetres and t in seconds. Taking π = 3.14, find the least distance between two successive crests in centimetres, to the nearest integer.
Physics · Wave Motion · general equation of wave
JEE Mains 2026 5 April Morning Shift

Question

A transverse wave on a string is described by y = 3 sin(36t+0.018x+π/4), where x and y are measured in centimetres and t in seconds. Taking π = 3.14, find the least distance between two successive crests in centimetres, to the nearest integer.

Physics · Wave Motion · general equation of wave

JEE Mains 2026 5 April Morning Shift

G1 Physics · Accepted Answer

The standard wave form is y = A sin(ωt+kx+φ), where k = 2π ÷ λ. Comparing with y = 3 sin(36t+0.018x+π ÷ 4), we get k = 0.018 cm⁻¹. Therefore, λ = 2π ÷ k = 2×3.14 ÷ 0.018 ≈ 348.89 cm. The distance between successive crests is one wavelength. To the nearest integer, λ ≈ 349 cm. Therefore the answer is 349.