Resonance and Non-Resonance - 384 Hz

A 384 Hz tuning fork is touched to three resonance boxes that are tuned to 512 Hz, 440 Hz, and 384 Hz. The box with the same frequency as the fork resonates more loudly than the others.

Discussion

Resonance boxes are rectangular boxes made of wood that are open at one end, with a mount to hold a tuning fork; they are designed to resonate most strongly at a single sound frequency. As we have seen in previous sections, for resonance to occur, it must be possible to establish a standing wave. A standing sound wave is a longitudinal standing wave in which nodes correspond to regions where there is minimal displacement of gas molecules and antinodes to regions where there is maximal displacement. The longest wavelength standing wave in a resonance box is one for which a quarter wavelength is equal to the depth of the resonance box. A quarter-wavelength standing wave in a resonance box has a single node at the closed end, where there is zero displacement of gas molecules, and a single antinode at the open end, where there is maximum displacement of gas molecules.

With the relationship between the speed of sound and the wavelength and frequency of a sound wave, v = ƒλ ≈ 340 m/s, you can calculate the inside length of a resonance box (for example, the depth of a 384 Hz resonance box is 0.22 m).

In this and the two movies that follow, a vibrating tuning fork transmits sound energy efficiently only to the resonance box that is designed to support a standing sound wave of the same, or resonant frequency. You can hear when a tuning fork is resonant with a box: the sound level is greatest when a vibrating tuning fork is touched to a resonance box tuned to the same frequency.