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Suppose that two sinusoidal waves, Wave 1 and Wave 2, have the same frequency and wavelength, but different amplitudes. The amplitude of Wave 2, $\psi_{20}$, is greater than the amplitude of Wave 1, $\psi_{10}$, so that:

$$\psi_{20} > \psi_{10}$$

They move in the positive $\hat{x}$-direction and overlap in a certain region of space and time. The wavelength of both waves is $\lambda = 24 \text{ cm}$. Because these two waves inhabit the same region of space and time, they will interfere. Figure 1 depicts the wave resulting from the interference of these two waves at time $t = 0$, as a function of position $x$.

Figure 1. Timothy Black. Created for Albert.io. Copyright 2017. All rights reserved.

The phase difference $\phi$ between the two waves is equal to $\phi = \cfrac{\pi}{3}$.

What is the amplitude of Wave 1?

A

$\psi_{10} = \cfrac{1}{2} \text{ m}$

B

$\psi_{10} = - \cfrac{3}{4} \text{ m}$

C

$\psi_{10} = \cfrac{1}{\sqrt{3}} \text{ m}$

D

$\psi_{10} = 1.5 \text{ m}$

E

$\psi_{10} = \left(\cfrac{1}{\sqrt{3}} + 1.5\right) \text{ m}$

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