The magnetic field in a plane electromagnetic wave is given by `B_(y)=(2xx10^(-7)) T sin (0.5xx10^(3)x+1.5xx10^(11)t)`.
What is the wavelength and frequency of the wave?

Explanation

For a given plane electromagnetic wave propagating along X - axis, as per the statement,
`B_(y)=2xx10^(-7)sin {(0.5xx10^(3))x + (1.5xx10^(11))t}` tesla ….(1)
Comparing above equation with
`B_(y)=B_(0)sin (kx + omega t)`, we get
`B_(0)=2xx10^(-7)T " "` ...(2)
`k=0.5xx10^(3)("rad")/("m") " "` ....(3)
`omega =1.5xx10^(11)("rad")/(s) " "` ...(4)
From equation (3),
`(2pi)/(lambda)=0.5xx10^(3)(because k=(2pi)/(lambda))`
`therefore lambda =(2xx3.14)/(0.5xx10^(3))=1.256xx10^(-2)m` (Ans 1)
From equation (4),
`2pi v=1.5xx10^(11)(because omega = 2pi v)`
`therefore v=(1.5xx10^(11))/(2xx3.14)=2.388xx10^(10)` Hz (Ans 2)
Note : wavelength and frequency values are asked but not in specific units and so you may simply find them in SI units. If `lambda` is asked in cm and v is asked in GHz then.
`lambda = 1.256xx10^(-2)m=1.256 cm`
`v=2.388xx10^(10)Hz=23.88xx10^(9)Hz`
`=23.88` GHz