A travelling wave has an amplitude of 0.15 m, a frequency of 550 Hz, and a wavelength of 0.01 m. What is the equation of the wave?

A travelling wave moving from left to right (positive x-direction) can be described by the equation:

where:

• $A$ is the amplitude.
• $k$ is the wave number ($k = \frac{2\pi}{\lambda}$).
• $\omega$ is the angular frequency ($\omega = 2\pi f$).
• $x$ is the position.
• $t$ is the time.

From the problem statement:

• Amplitude ($A$) = 0.15 m
• Frequency ($f$) = 550 Hz
• Wavelength ($\lambda$) = 0.01 m

Substitute the wavelength:

Substitute the frequency:

We can factor out $200\pi$ from the terms inside the parenthesis:

The derived equation matches option A.