Q. A wave in a string has an amplitude of 2 cm. The wave travels in the + ve direction of x axis with a speed of 128 m/sec. and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is:
A) y = (0.02) m sin (15.7x - 2010t)
B) y = (0.02) m sin (15.7x + 2010t)
C) y = (0.02) m sin (7.85x - 1005t)
D) y = (0.02) m sin (7.85x + 1005t)
Explanation
[Solution from source] λ = 4/5 = 0.8 m, so k = 2π/0.8 ≈ 7.85 m⁻¹ and ω = kv = 7.85 × 128 ≈ 1005 s⁻¹. A wave moving towards +x has the form sin(kx − ωt), so y = 0.02 sin(7.85x − 1005t); the '+' form travels towards −x and 15.7 uses λ = 0.4 m. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.