The Theory of Sound, Volume 1

absolute pitch amplitude application approximately arbitrary boundary calculated circular clamped coefficients constant corresponding cosh curve denote depends determined differential equation displacement dx² effect ellipse equal equal temperament equation of motion equilibrium expressed finite forced vibration formulæ free vibrations frequency friction given gravest tone inertia initial integral internal roots interval kinetic energy length load longitudinal mass membrane modes of vibration nodal lines nodes normal co-ordinates normal functions obtained octave period phase pitch plane plate positive potential energy quadratic function quantities quarter period ratio represented result satisfied shews sinh solution sound square string suppose tension theorem theory tion tuning fork vanish velocity wave Young's modulus zero δψ κα πα ρω ψ₁ ψ₂