Question

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Answer 1

The equation for the resultant wave, assuming wave interference in the negative x-direction, can be expressed as:

`\[ F(x, t) = A_1 \cos(k_1x - \omega_1t) + A_2 \cos(k_2x - \omega_2t) \]`

Step-by-step explanation:

In the given scenario, where two waves travel along the x-axis in the negative x-direction, the resultant wave equation is a superposition of the individual waves. The general form for this is
`\( F(x, t) = A_1 \cos(k_1x - \omega_1t) + A_2 \cos(k_2x - \omega_2t) \)`,

where A₁ and A₂ are the amplitudes, k₁ and k₂ are the wave numbers, and ω₁ and ω₂ are the angular frequencies of the two waves, respectively.

The cosine terms represent the oscillatory nature of the waves, with k indicating the spatial variation and ω representing the temporal variation. The negative sign in the argument of the cosine function denotes the waves propagating in the negative x-direction. The coefficients A₁ and A₂ determine the amplitudes of the individual waves, influencing the overall shape of the resultant wave.

To predict the specific behavior of the resultant wave, additional information about the individual waves, such as their amplitudes and frequencies, would be required. Adjusting these parameters would lead to variations in the shape, amplitude, and frequency of the resultant wave, providing a comprehensive understanding of the wave interference in the negative x-direction.