11.1.1. Derivation of the One-Dimensional Wave Equation

Try these first

1. 1.

   What is the one-dimensional wave equation?

   Hint

   Think about wave propagation in a medium.

2. 2.

   Name two types of waves described by the wave equation.

   Hint

   Consider where you've encountered waves.

3. 3.

   What is the standard form of the one-dimensional wave equation?

   • ∂²u/∂t² = c²∂²u/∂x²
   • ∂u/∂t = c∂²u/∂x²
   • ∂²u/∂x² = 0

   Hint

   This equation relates how wave displacement changes over time and position.

4. 4.

   True or False: The wave equation can only model sound waves.

   • True
   • False

   Hint

   Think about different forms of wave propagation.

5. 5.

   A string with a length of 2m is under a tension of 100N and has a mass per unit length of 0.5 kg/m. What is the speed of a wave on this string?

   Hint

   Focus on finding the values for T and μ to use in the formula.

6. 6.

   Describe how to modify the wave equation for a string with varying tension and mass per unit length along its length.

   Hint

   Think about how each section of the string might behave differently due to changing properties.