Q.Define the relation between velocity, wavelength and frequency of wave.

[!TLDR] Wave velocity equals frequency times wavelength -- the distance covered in one period is exac …

During one period T, a wave advances a distance equal to exactly one wavelength λ (by the very definition of wavelength as the spatial repeat-distance of the wave pattern). Since velocity is distance covered per unit time, $v=\dfrac{\lambda}{T}$. Using the definition of frequency as the reciprocal of the period, $n=\dfrac{1}{T}$, this becomes the single most important relation in wave motion: $v=n\lambda$. This relation shows that for waves travelling through a FIXED medium (fixed v), frequency and wavelength are inversely related -- raising one lowers the other -- and that when a wave crosses into a new medium …

Derive $v=n\lambda$ directly from the definitions of wavelength (distance covered in one peri …

Writing the relation with wavelength and period confused (e.g. $v=\lambda/n$ instead of $v=\lambda T$ being nonsensical, or forgetting $n=1 …