Question

Derive expression for displacement of a plane progressive wave in a different forms

Answer 1

Answer:

A progressive wave is a term given to a wave that travels from a specific point A in the medium to another point B. In simple terms, a wave that continuously travels in a medium in the same direction minus the changes is known as a traveling wave or progressive wave. Furthermore, a progressive wave is of two types; namely, transverse wave and longitudinal wave.

Transverse Waves: These are waves in which the particle displacement in the medium is measured perpendicular to the wave direction or direction of wave travel.

Longitudinal Waves: With Longitudinal Waves, the particle displacement remains in the same direction to the wave travel.

Answer 2

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We know that y =A sinWt

$ᴀᴛ \: \: \: ᴘ \: \: y = ᴀ\sinᴡ(t - \frac{x}{ᴠ} ) \\ y = ᴀ\sin(ᴡt - \frac{ᴡ}{ᴠ} x) \\ y = ᴀ\sin(ᴡt - ᴋx) \\ ⟹ᴋ = \frac{2\pi}{λ}$

Different forms of progressive wave

$1)y = ᴀ\sinᴡ(t - \frac{x}{ᴠ} ) \\ 2)y = ᴀ \sin(ᴋx + or - \:ᴡ t) \\ 3)y = ᴀ\sin2\pi( \frac{t}{ᴛ} - \frac{x}{λ} )$

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