# If two waves, each of amplitude #z#, produce a resultant wave of amplitude #z#, then what is the phase difference between them? Is there a specific equation or formula I can use?

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Seems like the phase difference is **between** 0 and 180 because 0 (inphase) would imply a resultant of 2z and 180 would give a resultant of 0.....

Seems like the phase difference is **between** 0 and 180 because 0 (inphase) would imply a resultant of 2z and 180 would give a resultant of 0.....

##### 1 Answer

For the amplitude of the superposition of two waves to have the same amplitude as the original waves, their phase difference must be

#### Explanation:

Consider the superposition of two sinusoidal waves of identical amplitude

The mathematical expressions for the waves

The mathematical expression for the superposition of these two waves is :

This shows that the superposition is another sinusoidal wave of amplitude

This amplitude is the same as

**Derivation of the expression for the superposition of two waves**:

Use the trigonometric identity (**TI3**) to expand

Use trigonometric identity (**TI1**) to rewrite the **TI2**) to rewrite the

Use the trigonometric identity (**TI3**) again to simplify the terms inside the square bracket

**Useful trigonometric identities**:

**TI1**)

**TI2**)

**TI3**)