Speaker
Description
Students: determine the end correction using a set of nine cylindrical Helmholtz resonators. Resonators differ only by the diameter of a single hole at the top. Diameters $D$ were 4/8 to 13/8 inch in 1/8 inch increments. A homemade (analog) sweep spectrum analyzer (0-1000Hz) is essential. The essence of the frequency analyzer is a watch crystal oscillator ($f_o$=32.768kHz), a 4-element ladder crystal filter (1Hz bandwidth at 32.768kHz), VCO (voltage-controlled oscillator) operating between 32.786kHz < $f$ < 33.768kHz, multipliers and op amp low and high pass filters. Measure resonance by driving a loudspeaker placed above the orifice with a 0-1000Hz signal generated by $f_o$ multiplied by $f$ and lowpass filtered. A microphone in the resonator generates the response signal $f_r$ multiplied by $f$ , filtered at 32.768kHz. The VCO ramp voltage vs. time and mean squared filter response determine the resonant frequency for each $D$. Use $L_{eff}=L+εD$ for end correction analysis.
