Question:
A wave is represented by \( y = 0.1 \sin(200t - 10x) \). Find wave velocity.
A wave is represented by \( y = 0.1 \sin(200t - 10x) \). Find wave velocity.
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To find the wave speed from any sinusoidal wave equation instantly, simply divide the coefficient of time (\(t\)) by the coefficient of position (\(x\)):
\[ \text{Wave Velocity} = \frac{\text{Coefficient of } t}{\text{Coefficient of } x} \]
This shortcut avoids any risk of mixing up basic definitions during an exam!
Updated On: May 20, 2026
- \( 10 \text{ m/s} \)
- \( 20 \text{ m/s} \)
- \( 5 \text{ m/s} \)
- \( 2 \text{ m/s} \)
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The Correct Option is B
Solution and Explanation
Concept:
A progressive harmonic wave travelling along the positive x-direction is mathematically described by the general wave equation:
\[
y(x,t) = A \sin(\omega t - kx)
\]
where:
• \( A \) represents the amplitude of the wave.
• \( \omega \) is the angular frequency, defined as \( \omega = 2\pi f \).
• \( k \) is the angular wave number (or propagation constant), defined as \( k = \frac{2\pi}{\lambda} \). The wave velocity \( v \) (the speed at which the wave profile moves through the medium) is given by the relation: \[ v = \frac{\omega}{k} \]
Step 1: Comparing the given wave equation with the standard progressive wave form.
The given equation of the wave is: \[ y = 0.1 \sin(200t - 10x) \] By comparing this directly with the standard formula \( y = A \sin(\omega t - kx) \), we can extract the following values:
• Angular frequency, \( \omega = 200 \text{ rad/s} \)
• Wave number, \( k = 10 \text{ rad/m} \)
Step 2: Calculating the wave velocity using the extracted coefficients.
Substitute the values of \( \omega \) and \( k \) into the wave velocity formula: \[ v = \frac{\omega}{k} = \frac{200}{10} \] \[ v = 20 \text{ m/s} \] This calculated value corresponds exactly to option (B).
• \( A \) represents the amplitude of the wave.
• \( \omega \) is the angular frequency, defined as \( \omega = 2\pi f \).
• \( k \) is the angular wave number (or propagation constant), defined as \( k = \frac{2\pi}{\lambda} \). The wave velocity \( v \) (the speed at which the wave profile moves through the medium) is given by the relation: \[ v = \frac{\omega}{k} \]
Step 1: Comparing the given wave equation with the standard progressive wave form.
The given equation of the wave is: \[ y = 0.1 \sin(200t - 10x) \] By comparing this directly with the standard formula \( y = A \sin(\omega t - kx) \), we can extract the following values:
• Angular frequency, \( \omega = 200 \text{ rad/s} \)
• Wave number, \( k = 10 \text{ rad/m} \)
Step 2: Calculating the wave velocity using the extracted coefficients.
Substitute the values of \( \omega \) and \( k \) into the wave velocity formula: \[ v = \frac{\omega}{k} = \frac{200}{10} \] \[ v = 20 \text{ m/s} \] This calculated value corresponds exactly to option (B).
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