17.2. Derivation of the One-Dimensional Wave Equation

Try these first

1. 1.

   What does transverse displacement refer to?

   Hint

   Think about how strings move when plucked.

2. 2.

   Write the wave equation derived from the force analysis.

   Hint

   Recall the relation between acceleration and displacement.

3. 3.

   What is the equation for the wave speed (c)?

   • c = √(T/ρ)
   • c = T/√(ρ)
   • c = ρ/T

   Hint

   Think about the properties of both tension and mass per unit length.

4. 4.

   The wave equation is a differential equation of which order?

   • True
   • False

   Hint

   Consider the number of derivatives with respect to time and space.

5. 5.

   Consider a string with mass density ρ = 0.01 kg/m and tension T = 10 N. Calculate the wave speed c and discuss its significance.

   Hint

   Be sure to plug the values into the wave speed formula correctly.

6. 6.

   If the tension in the string is doubled while keeping the mass density constant, how does the wave speed change?

   Hint

   Think about the relationship expressed in the wave speed formula.