Consider the commonly used relation connecting the speed of a mechanical wave with…

PHYSICS · Multi-part · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

Consider the commonly used relation connecting the speed

v

of a mechanical wave with its wavelength

\lambda

and frequency

\nu

. (i) Write the dimensional formulae of

v

\lambda

and

\nu

. (ii) Using dimensional analysis, verify whether the relation

v=\lambda\nu

is dimensionally consistent. (iii) Re-express the same relation in terms of angular frequency

\omega

and wave number

k

, and again confirm its dimensional correctness.