New wave after superposition (interference)

[Helly123]

Homework Statement

1. Homework Statement [/B]
The displacement y of standing wave that is obtained by a superposition of waves :
Y1 = 3 sin (2$\pi$(0.5t - 0 25 x))
Y2 = 3 sin (2$\pi$(0.5t + 0 25 x))

Homework Equations

Formula for standing waves
Y = 2Asinkx coswt

The Attempt at a Solution

Y1 going to right
Y2 going to left
Both have different direction.

How to decide it is constructive or destructive interference?
Are they longitudinal or transverse waves? Does it matter?

How to know in the new equation, which belong to sin x or t variable, which belong to cos?

 

[kuruman]

You might wish to look up a trig identity for sinθ + sinφ here
https://en.wikipedia.org/wiki/List_of_trigonometric_identities
It's a good starting point.

 

[Helly123]

You might wish to look up a trig identity for sinθ + sinφ here
https://en.wikipedia.org/wiki/List_of_trigonometric_identities
It's a good starting point.

Ok. what is the relation?

 

[kuruman]

You should be able to find these on your own. Look under Sum-to-product.

 

[Helly123]

You should be able to find these on your own. Look under Sum-to-product.

Oh. So superposition is y1 + y2 ?
Why superposition not happen to be y1 - y2?
How to know if both waves get destructive or constructive interference?