A progressive wave is given by Y = 6 sin ( 3 t − 2 x ) m. On this wave, how far away are the two points having phase difference of 4 5 ∘ ?

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The given equation of the progressive wave is $Y = 6 sin (3 t - 2 x)$ .

Comparing this with the standard wave equation $Y = A sin (ω t - k x)$ , we get the wave number $k = 2$ .

The phase difference $Δ ϕ$ between two points separated by a distance $Δ x$ is given by $Δ ϕ = k Δ x$ .

Given $Δ ϕ = 4 5^{\circ} = \frac{π}{4}$ rad.

Substituting the values, we get:

$\frac{π}{4} = 2Δ x$

$Δ x = \frac{π}{8}$ m.

Answer: $\frac{π}{8} m$

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