What is the standard equation for a traveling sinusoidal wave?

Conditions

• Applies to a traveling sinusoidal wave in physics.
• $y$ depends on two variables, $x$ and $t$.
• $A$, $k$, $\omega$, and $\phi$ are treated as problem-specific constants for a particular wave.

Reasoning, step by step

1. Identify the dependent variable $y(x,t)$ as the vertical position of the wave.
2. Identify the independent variables $x$ as the horizontal position and $t$ as the time variable.
3. Recognize the coefficient $A$ as the amplitude.
4. Recognize the term $k$ as the angular wave number.
5. Recognize the term $\omega$ as the angular frequency.
6. Recognize the term $\phi$ as the phase.

Example

The video displays the equation $y(x,t)=A\sin(kx-\omega t+\phi)$ and sequentially labels each component: $y$ as vertical position, $x$ as horizontal position variable, $t$ as time variable, $A$ as amplitude, $\phi$ as phase, $\omega$ as angular frequency, and $k$ as angular wave number.

Common misconceptions

• Assuming $y$ represents the horizontal position of the wave.
• Thinking that $k$ in this context refers to the spring constant from mechanics.
• Believing that $\omega$ is the Latin letter W rather than the Greek letter omega.

Watch the explanation

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