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A wave on a string is described by the equation y(x, t) = 0.05 sin(2Ï€(0.1x - 5t)

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Question: A wave on a string is described by the equation y(x, t) = 0.05 sin(2Ï€(0.1x - 5t)). What is the amplitude of the wave?

Options:

  1. 0.01 m
  2. 0.05 m
  3. 0.1 m
  4. 0.2 m

Correct Answer: 0.05 m

Solution: 

The amplitude of the wave is the coefficient in front of the sine function. Here, the amplitude is 0.05 m.

A wave on a string is described by the equation y(x, t) = 0.05 sin(2Ï€(0.1x - 5t)

Practice Questions

Q1
A wave on a string is described by the equation y(x, t) = 0.05 sin(2Ï€(0.1x - 5t)). What is the amplitude of the wave?
  1. 0.01 m
  2. 0.05 m
  3. 0.1 m
  4. 0.2 m

Questions & Step-by-Step Solutions

A wave on a string is described by the equation y(x, t) = 0.05 sin(2Ï€(0.1x - 5t)). What is the amplitude of the wave?
  • Step 1: Look at the wave equation given: y(x, t) = 0.05 sin(2Ï€(0.1x - 5t)).
  • Step 2: Identify the part of the equation that is multiplied by the sine function.
  • Step 3: The coefficient in front of the sine function is 0.05.
  • Step 4: This coefficient represents the amplitude of the wave.
  • Step 5: Therefore, the amplitude of the wave is 0.05 meters.
  • Wave Properties – Understanding the characteristics of waves, including amplitude, wavelength, frequency, and wave speed.
  • Mathematical Representation of Waves – Interpreting wave equations in the form of y(x, t) = A sin(kx - ωt) to extract physical properties.
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