What is the wave number of a wave whose displacement, y is defined by the equation y = 25 cos (280t – 75x) in metres?*1 point28/m25/m75/m84/m

1. Break Down the Problem

To find the wave number $k$ from the given wave equation, we need to identify the coefficients related to $x$ in the equation of the wave.

2. Relevant Concepts

The general form of a wave equation is given by:

$y = A \cos(\omega t - kx)$

where:

• $A$ is the amplitude,
• $\omega$ is the angular frequency,
• $k$ is the wave number,
• $x$ is the position,
• $t$ is time.

In this case, we have the equation:

$y = 25 \cos(280t - 75x)$

3. Analysis and Detail

From the equation, we can identify that the term associated with $x$ is $-75x$. This means that the wave number $k$ is represented by the coefficient of $x$:

$k = 75 \, \text{m}^{-1}$

4. Verify and Summarize

Thus, the wave number $k$ is $75 \, \text{m}^{-1}$. This matches the expected format for wave number in wave equations.

Final Answer

The wave number of the wave is $75 \, \text{m}^{-1}$.