<p class="Abstract">Thermoacoustic prime movers work by using thermal energy to produce acoustic energy in the form of sound wave through thermoacoustic effect which occurs in a porous medium called stack. This paper describes an experimental study on the relation between the order of resonance frequencies generated by a thermoacoustic prime mover and the length of the resonator and the viscous penetration depth. Extending the resonator length will decreasing the resonance frequency which result in the increasing in the viscous penetration depth. Generally, the generated sound consists of only one frequency, that is the first-order one. However, under certain conditions, the sound has only the second-order frequency or comprises two frequencies of the first-order and second-order resonance frequencies. This phenomenon can be explained by considering the comparison between the effective hydraulic radius of stack () and the viscous penetration depth (). It is found that the first-order frequency appears when , while when   (with  calculated by using the first-order frequency) then the second order frequency is produced so that  is back to a smaller value and therefore the condition of  is recovered. In addition, when of  the thermoacoustic prime mover will<em> </em>generate the first and second order frequencies together.</p>

<p class="Abstract">Thermoacoustic prime mover is a device which converts thermal energy into acoustic work. The device mainly consists of a resonator pipe, a stack (a porous medium), and two heat exchangers. Four stacks were made of a pile of stainless wire-mesh screens with various mesh numbers of #12, #14, #16, and #18, providing the effective hydraulic radius of 0.32 mm, 0.28 mm, 0.25 mm, 0.23 mm, respectively. Each stack has 4 cm length. By using the wire-mesh screens, it is easier to vary the hydraulic radius of stack than any other material. The stack is sandwiched between a hot heat exchanger and an ambient heat exchanger. The resonator is made of a stainless-steel pipe with one end open and the other closed. The stack and heat exchangers are placed inside a resonator pipe near the closed end. The thermal energy were provided by using an electric heater which is installed at the hot heat exchanger. Ambient water was flowing through the ambient heat exchanger. Sound is produced by the stack when the temperature difference between the both ends of stack reachs an onset point. This experiments were performed by recording the temperatures at both ends of stack and the pressure amplitudes of the sound at several points along the resonator for various hydraulic radius of stack. It is found that the effective hydraulic radius of 0.28 mm gives the lowest onset temperature, the shortest time to reach onset condition, and the highest pressure amplitude which are 314°C, 299 s, and 2.89 kPa, respectively. The frequency of sound is not altered by the change of hydraulic radius of stack.</p>