Consider the wave equation y = 5mm sin [1cm$^{-1}$x - 60s$^{-1}$t]. The wave number is?

1. Analyze the question

You are given a standard wave equation: $y = 5\text{mm} \sin[1\text{cm}^{-1}x - 60\text{s}^{-1}t]$. You need to identify the wave number ($k$) from this equation.

2. Explain the concept

The general equation for a progressive wave traveling in the positive x-direction is given by:

Where:

• $A$ is the amplitude.
• $k$ is the wave number (or angular wave number), which is the coefficient of $x$.
• $\omega$ is the angular frequency, which is the coefficient of $t$.
• $x$ is the position.
• $t$ is the time.

By comparing the given equation to the general form, you can directly extract the value of $k$.

3. Show the solution

Given the equation:

Comparing this to the standard form $y = A \sin(kx - \omega t)$:

• The term multiplying $x$ is $k$.
• In your equation, the term multiplying $x$ is $1\text{cm}^{-1}$.

Therefore:

4. Identify the answer

Comparing our result to the provided options: A. $0.1\text{cm}^{-1}$ B. $10\text{cm}^{-1}$ C. $1.0\text{cm}^{-1}$ D. $2\text{cm}^{-1}$

The correct option is C.

5. Tip

When you see a wave equation, don't let the units (like mm, cm, or s) confuse you. Just look for the variable $x$ and the variable $t$. The number attached to $x$ is always your wave number ($k$), and the number attached to $t$ is always your angular frequency ($\omega$). Keep your eyes on the coefficients!