Question

Two waves, travelling in the same direction through the same region, have equal frequencies, wavelengths and amplitudes. If the amplitudes of each wave is $4mm$ and the phase difference between the waves is $90°$, what is the resultant amplitude?

Answer 1

Step 1: Given

Amplitude of the wave: $A=4mm$

Phase difference: $\varphi =90°$

Step 2: Formula Used

For 2 waves with same frequencies, wavelengths and amplitudes, the resultant amplitude is given as

$R=2A\cos \frac{\varphi }{2}$

Step 3: Calculate the resultant amplitude using the formula

$$\begin{gathered} R=2\times 4\times \cos \left(\frac{90°}{2}\right) \\ =8\times \cos 45° \\ =8\times \frac{1}{\sqrt{2}} \\ =4\sqrt{2}mm \end{gathered}$$

Hence, the resultant amplitude is $4\sqrt{2}mm$.