Given that: y= A sin[ (2pi)/(lambda)(vt-x)] where y and x are measured in metres. Which of the following statements is true?

Given that: y= A sin[ (2pi)/(lambda)(vt-x)] where y and x are measured

1.	Given that: y= A sin[ (2pi)/(lambda)(vt-x)] where y and x are measured in metres. Which of the following statements is true?
Answer» The unit of `lambda` is same as that of x and A The unit of `lambda` is same as that of x but not of A. The unit of v is same as that of `2PI//lambda` The unit of `(vt-x)` is same as that of `2pi//lambda` Solution :As `sintheta` is dimensionless, THEREFORE `(2pi)/(lambda) (vt - x)` is dimensionless. HENCE `(vt)/(lambda)` is also dimensionless and unit of vt is same as that of x. Therefore, unit of `lambda` is same as that of x. Also unit of y is same as that of A, which is also the unit of x.