Question:
The equation of a simple harmonic progressive wave is given by y = 0.05 (100 t - 0.4 x), where x and y are in meters and t is in seconds. The wave velocity is:
The equation of a simple harmonic progressive wave is given by y = 0.05 (100 t - 0.4 x), where x and y are in meters and t is in seconds. The wave velocity is:
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For any wave equation given in the standard sinusoidal format, you can find the wave velocity instantly without full conversion steps using this simple ratio rule:
Here, Velocity = 1000.4 = 250 ms^-1.
Updated On: Jun 10, 2026
- 250 ms^-1
- 100 ms^-1
- 50 ms^-1
- 25 ms^-1
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The Correct Option is A
Solution and Explanation
Concept:
A simple harmonic progressive wave travelling along the positive x-axis can be mathematically described by the standard wave equation:
where:
• A is the amplitude of the wave.
• is the angular frequency of oscillation ( = 2 f).
• k is the angular wave number or propagation constant (k = 2).
• t is the time, and x is the spatial position along the propagation axis.
The linear speed at which the wave profile moves through the medium—known as the Wave Velocity (v)—is related to its frequency and wavelength by v = f. In terms of the wave coefficients and k, this relation simplifies directly to:
Step 1: Extracting Wave Parameters by Comparison
We are given the specific wave equation: Let us match this given function directly, term-by-term, with our standard baseline formula y = A ( t - kx):
• The coefficient of the time variable t gives the angular frequency: = 100 rad^-1
• The coefficient of the spatial position variable x gives the wave number: k = 0.4 rad^-1
Step 2: Calculating Wave Velocity (v)
Using the wave velocity formula v = k, substitute the extracted constants: The phase factor cancels out from both the numerator and denominator: To evaluate easily, multiply the top and bottom by 10: Therefore, the propagation velocity of the progressive wave is 250 ms^-1, which matches Option (A).
• A is the amplitude of the wave.
• is the angular frequency of oscillation ( = 2 f).
• k is the angular wave number or propagation constant (k = 2).
• t is the time, and x is the spatial position along the propagation axis.
The linear speed at which the wave profile moves through the medium—known as the Wave Velocity (v)—is related to its frequency and wavelength by v = f. In terms of the wave coefficients and k, this relation simplifies directly to:
Step 1: Extracting Wave Parameters by Comparison
We are given the specific wave equation: Let us match this given function directly, term-by-term, with our standard baseline formula y = A ( t - kx):
• The coefficient of the time variable t gives the angular frequency: = 100 rad^-1
• The coefficient of the spatial position variable x gives the wave number: k = 0.4 rad^-1
Step 2: Calculating Wave Velocity (v)
Using the wave velocity formula v = k, substitute the extracted constants: The phase factor cancels out from both the numerator and denominator: To evaluate easily, multiply the top and bottom by 10: Therefore, the propagation velocity of the progressive wave is 250 ms^-1, which matches Option (A).
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