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Suppose that two sinusoidal waves, Wave 1 and Wave 2, have the same amplitudes but different wavelengths. The wavelength of Wave 1 is $\lambda_1 = 30 \text{ cm}$ and the wavelength of Wave 2 is $\lambda_2 = 20 \text{ cm}$ . They move in the positive $\hat{x}$-direction and overlap in a certain region of space and time. Because these two waves inhabit the same region of space and time, they will interfere. Both waves are initially in phase with one another at the origin.

At time $t = 0$, what is the smallest value of $x$, greater than zero, for which the sum of the two waves is zero?

A

$x = 12 \text{ cm}$

B

$x = 30 \text{ cm}$

C

$x = 20 \text{ cm}$

D

$x = 10 \text{ cm}$

E

$x = 15 \text{ cm}$

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