Question

A wave on a string is described by u(x,t)=0.005 sin (6.28x-314t) in which all quantities are in SI units. It's wavelength is _______.

Answer 1

Explanation:
Given:
The wave on a string is described by
u(x,t)=0.005sin⁡(6.28x−314t)...(i)
Displacement of a general plane progressive wave is given as
y(x,t)=Asin⁡(ωt−kx)....(ii)
where,
k=2πλ, wave number and ω=2πT, angular frequency
Substituting the values in eq. (ii), we get
y(x,t)=Asin⁡(2πTt−2πλx)...(iii)
Comparing eqs. (i), (ii) and (iii), we get
A=0.005
k=6.28=2πλ
⇒λ=2π6.28
=2×3.146.28=6.286.28=1m
Hence, the correct answer is 1.