What is phase difference between two particles , separated by 6.4 cm when a wave motion of wavelength 2 cm is propagated ??
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The wave at any instant can be represented as shown.
wave_phase
The phase difference between two particles A and B depend on the fraction of wavelength by which they are separated in the wave. If the separation between Particles A and B is Δx, then the phase difference between them during oscillation is given by $Φ\:=\"\frac{2\pi}{\lambda}Δx$.
Comparing the given wave $y\:=\:1.0\:sin(628.0\:t\:-\:6.28\:x)$ with the standard equation for a travelling wave $y\:=\:A\:sin(\omega\:t\:-\:k\:x)$ we get $\omega\:=\:628.0$ , $k\:=\:6.28$.
The propagation constant k is related to wavelngth as $k\:=\:\frac{2\pi}{\lambda}$ .
From this $\lambda\:=\:\frac{2\pi}{k}\:=\:\frac{2\pi}{6.28}\:=\:1.00\:m$
Phase difference
Using the equation for phase difference, $Φ\:=\"\frac{2\pi}{\lambda}Δx$ we get the phase difference for a separation of 25 cm or 0.25 m as , $Φ\:=\"\frac{2\pi}{1.00}0.25\:=\:0.5\pi\:radian\:=\:\frac{\pi}{2}$.
So the two particles separated by a distance 25 cm will have a phase difference of 90°.
wave_phase 1
In the wave shown particle at A is in the maximum position whereas the particle B at a distance of 25 cm is in the mean position which has phase difference of 90°.
wave_phase
The phase difference between two particles A and B depend on the fraction of wavelength by which they are separated in the wave. If the separation between Particles A and B is Δx, then the phase difference between them during oscillation is given by $Φ\:=\"\frac{2\pi}{\lambda}Δx$.
Comparing the given wave $y\:=\:1.0\:sin(628.0\:t\:-\:6.28\:x)$ with the standard equation for a travelling wave $y\:=\:A\:sin(\omega\:t\:-\:k\:x)$ we get $\omega\:=\:628.0$ , $k\:=\:6.28$.
The propagation constant k is related to wavelngth as $k\:=\:\frac{2\pi}{\lambda}$ .
From this $\lambda\:=\:\frac{2\pi}{k}\:=\:\frac{2\pi}{6.28}\:=\:1.00\:m$
Phase difference
Using the equation for phase difference, $Φ\:=\"\frac{2\pi}{\lambda}Δx$ we get the phase difference for a separation of 25 cm or 0.25 m as , $Φ\:=\"\frac{2\pi}{1.00}0.25\:=\:0.5\pi\:radian\:=\:\frac{\pi}{2}$.
So the two particles separated by a distance 25 cm will have a phase difference of 90°.
wave_phase 1
In the wave shown particle at A is in the maximum position whereas the particle B at a distance of 25 cm is in the mean position which has phase difference of 90°.
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The phase difference between a node and its nearest antinode is π2π2 or 90 degrees. This can be seen by thinking of the wave as a simple sine function. There is a node at 0, then again at ππ, before the whole thing begins to repeat at 2π2π. The antinodes are half way between each pair of adjacent nodes, at π2π2, 3π23π2, etc.
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