19.7. Normal Modes and Natural Frequencies

Try these first

1. 1.

   What do the indices (n,m) represent in normal modes?

   Hint

   Think about the indexes associated with vibration.

2. 2.

   What is the equation for natural frequency?

   Hint

   The form indicates it relates to the dimensions of the membrane.

3. 3.

   What is the fundamental mode represented by?

   • (0,0)
   • (1,1)
   • (2,2)

   Hint

   Think of the lowest frequency mode.

4. 4.

   Natural frequencies are associated with which concept?

   • True
   • False

   Hint

   Recall the definition of natural frequencies.

5. 5.

   A square membrane has dimensions of 2m x 2m. Calculate the natural frequency for the fundamental mode.

   Hint

   Think about the relationship between wave speed and tension.

6. 6.

   For a given rectangular membrane (4m x 2m), if 'c' is known to be 3 m/s, calculate the frequencies for modes (1,2) and (2,1).

   Hint

   Substitute into the equation carefully; ensure dimensions are consistent.