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

Correct Answer: 1

Explanation:
Given:
The wave on a string is described by
$u(x,t)=0.005\sin (6.28x-314t)$...(i)
Displacement of a general plane progressive wave is given as
$y(x,t)=A\sin (\omega t-kx)$....(ii)
where,
$k=\frac{2\pi }{\lambda },$ wave number and $\omega =\frac{2\pi }{T},$ angular frequency
Substituting the values in eq. (ii), we get
$y(x,t)=A\sin (\frac{2\pi }{T}t-\frac{2\pi }{\lambda }x)$...(iii)
Comparing eqs. (i), (ii) and (iii), we get
$A=0.005$
$k=6.28=\frac{2\pi }{\lambda }$
$\Rightarrow \lambda =\frac{2\pi }{6.28}$
$=\frac{2\times 3.14}{6.28}=\frac{6.28}{6.28}=1\mathrm{m}$
Hence, the correct answer is 1.