A Helmholtz resonator is simply a box with a port on its front side to couple the enclosed volume of the airspace in the box to the air in the room. The depth of the enclosed airspace in the box behind the port and the width and depth of the port control the resonant frequency of the bass trap.  
Another form of helmholtz resonator is created using perforated plywood  i.e. plywood with hundreds of holes in it. You see it in hardware stores holding up tools etc. If you place a panel of this over an air cavity like in a panel resonator not only do the little holes act like bottle necks the whole panel acts as a low frequency panel resonator!  
Standing waves occur at harmonics of the fundamental frequency  that is
2, 3, and 4 times the fundamental. Thus a room with an 2.45 meter ceiling has
standing waves forming at 70 Hz (the fundamental frequency or first harmonic),
140 Hz (the second harmonic), 210 Hz (the third harmonic) and 280 Hz (the fourth
harmonic). Rooms with smaller dimensions often have standing waves or resonance build ups that are very noticeable causing coloration at around 200 Hz. 



The formula for determining the fundamental frequency of a standing wave for a particular room dimension is: fo = V / 2d where: fo = Fundamental frequency of the standing wave V = Velocity of sound (344 meter per second) d = Room dimension being considered in meter (length, width and height) 

The formula for determining f_{res}: f_{res} = c/2 * sqrt( (l/lx)^2 + (m/mx)^2 + (n/nx)^2 ), with l,m,n = 0,1,2... c = 344 m 