phyiscs help needed!!

I don't understand how to solve this or questions like this. COuld you help me!

Trying...

the answer is C, but idk how.
With the formula of 2pi times path difference divided by wavelength gives 3pi

I see..was the path difference 0?

Mark scheme says- π radians is the phase difference between the two waves at A – the path difference between the two waves is (8cm – 5cm) = 3cm = 1.5λ. This results in the waves arriving in antiphase (π radians out of phase) which also occurs when the path difference is 1cm.

Wait...(8cm-5cm?) how did that happen tho thought it was 6.5-6.5...

4 4=8
and 2.5 2.5=5

Mark scheme says- π radians is the phase difference between the two waves at A – the path difference between the two waves is (8cm – 5cm) = 3cm = 1.5λ. This results in the waves arriving in antiphase (π radians out of phase) which also occurs when the path difference is 1cm.

@BobbJo
Do you think the phase difference is π?
for yer time!

Yes. We ignore any phase change during reflection [if interested on this : https://physics.stackexchange.com/questions/150661/does-light-change-phase-on-refraction, ]https://physics.stackexchange.com/questions/32122/phase-shift-of-180-degrees-of-transversal-wave-on-reflection-from-denser-medium]

The path difference is (4+4)-(2.5+2.5) = 8 - 5 = 3 cm

3 cm is equal to 1.5 wavelengths
The path difference is 1.5 wavelengths. We have destructive interference and the phase difference is pi.
[1.5 wavelengths corresponds to a phase difference of 3 pi which is equivalent to a phase difference of pi]

for extra links and yer patience
And also how do I plug in values into this equation?
Φ = (2π/λ) * x ?
I thought this was to be done...
(2π/λ) * 1.5λ but it results in 3 π

I got it till the destructive interference part....

Is it a rule of thumb that all destructive interferences should have a phase difference of π?

[Note: the reflection can be ignored because both will undergo reflection and hence both will have the pi phase change, hence it cancels out]

For the equation, plug in values of λ and x
Φ = (2π/λ) * x
in this question, λ = 2 cm
hence Φ = (2π/2) x 3 = 3π
or convert x = 3 cm to x = 3/2 λ and replace, thus
Φ = (2π/λ) * 3/2 λ = 3π


Yes, all destructive interferences occur when the phase difference is π.
In fact, the path difference must be half a wavelength, or (n+1/2)λ where n is an integer.
This corresponds to a phase difference of Φ = (2π/λ) * x = (2n+1)π for integer n.
Destructive interference therefore occurs for a phase difference: π, 3π, 5π, 7π
But all of these are equivalent to a phase difference of π


The displacement of a point on a wave varies sinusoidally:
x = x₀sin(ωt+Φ), Φ denotes the phase angle
Look at the following:
https://www.desmos.com/calculator/epjylr2j7v
Notice that the curves are identical for Φ = π, 3π, 5π, ...
This is due to the periodicity of the sine curve. Hence phase difference of 3 pi and 5 pi are equivalent to a phase difference of pi