The Question is from neet-physics , and it was created by the author Mr. ANIL KUMAR.G

Question

The equation of a progressive wave is given by $y = A \sin(\omega t - kx)$. What does $k$ represent?

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
 **Primary Concept**: Wave equation and its parameters
 **Related Topics**:  Progressive waves, wave number, wavelength
 **Prerequisites**: Understanding of trigonometric functions and wave phenomena.
## SOLUTION PATHWAY
**Given Information**:
  Equation of a progressive wave: $y = A \sin(\omega t - kx)$
**Method & Steps**:
 1. Identify the general equation of a progressive wave.
  Reasoning: The general equation for a progressive wave traveling in the positive x-direction is given by $y = A \sin(\omega t - kx)$, where:
  * $A$ is the amplitude
  * $\omega$ is the angular frequency ($\omega = 2\pi f$, where $f$ is the frequency)
  * $t$ is the time
  * $k$ is the angular wave number
  * $x$ is the position
  Formula/Rule: $y = A \sin(\omega t - kx)$
 2. Analyze the given equation and identify the parameter $k$.
  Working: Comparing the given equation with the general equation, we can see that $k$ is the angular wave number.
  Key Point: The angular wave number is related to the wavelength ($\lambda$) by the equation $k = \frac{2\pi}{\lambda}$.
 3. Determine the meaning of $k$.
  Result: $k$ represents the angular wave number.
  Verification: The units of $k$ are radians per meter (rad/m), which is consistent with the definition of angular wave number.
 ## OPTION ANALYSIS
A :x: Angular frequency ($\omega$) is represented by $\omega$ in the equation, not $k$.
B ✓: Angular wave number ($k$) is correctly identified as the representation of $k$ in the given equation.
C :x: Wavelength ($\lambda$) is related to $k$ but is not directly represented by $k$ in the equation. ($\lambda = \frac{2\pi}{k}$)
D :x: Time period ($T$) is related to angular frequency ($\omega$) ($T = \frac{2\pi}{\omega}$), not $k$.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing angular frequency ($\omega$) with angular wave number ($k$): Remember that $\omega$ relates to time, while $k$ relates to spatial position.
  2.Misinterpreting the relationship between $k$ and $\lambda$:  Remember that $k = \frac{2\pi}{\lambda}$, not $k = \lambda$.
 **Quick Tips**:
  1.Remember the units: $\omega$ is in rad/s, $k$ is in rad/m.
  2.Relate the parameters to the physical quantities they represent: $\omega$ to frequency, $k$ to wavelength.

Mr. ANIL KUMAR.G · Answer

Angular frequency

Mr. ANIL KUMAR.G · Answer

The correct Option is "Angular wave number"

Mr. ANIL KUMAR.G · Answer

Wavelength

Mr. ANIL KUMAR.G · Answer

Time period

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