Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition

14.2. Membrane wave equation in rectangular coordinates

A membrane is normally pretensioned, so we will define a force per unit length T that we can assume to be uniformly distributed throughout the membrane. As we shall see, the membrane tension is analogous to static pressure in the case of pressure waves in air as it determines the restoring force. Although pressure waves in air are longitudinal, in a membrane we have transverse waves. In other words, the displacement η at each point is normal to the direction of travel rather than back and forth in the direction of travel. Let the density of the membrane be ρ _D and its thickness be h. Referring to Fig. 14.1, we wish to find the restoring force F _x acting on the element of the membrane ...