Resonance and Energy Transfer - Matched and Unmatched Resonance Boxes

The relative efficiency of energy transfer between matched (resonant) and unmatched (non-resonant) sound boxes is demonstrated.

Discussion

Two 440 Hz resonance boxes and tuning forks are placed close to each other, with open ends facing. One of the forks is struck and then damped. The sound continues because it is being generated by the other box and fork. This sequence is repeated. When both boxes have the same resonant frequency, energy transfer is efficient.

Next, a small clamp is placed on the second tuning fork. The increased mass causes the frequency to be lowered slightly. The two forks are then compared by striking each of them, and different frequencies can be heard. The initial experiment is now repeated with the "untuned" forks and resonance does not occur, because energy transfer is inefficient when the two boxes have different resonant frequencies.

Finally, both forks are struck and "beats" can be heard. When sound waves of slightly different frequencies interact, what one hears sounds quite complex, but is actually rather simple. There is an oscillation of sound intensity – loud, soft, loud, soft – at a frequency that is equal to the difference between the frequencies of the two tuning forks. The greater this difference, the more rapid the oscillations in sound intensity become. The frequency of the sound whose intensity is fluctuating is simply the average of the two tuning fork frequencies. This effect is often used by musicians to tune their instruments. For example, guitarists use a tuning fork that vibrates at the proper pitch of one string of their guitar. When the tuning fork and guitar string are not vibrating with the same frequency, there is beating between the two. As the guitar pitch comes closer to that of the tuning fork, the beat frequency decreases, vanishing when the string is properly tuned. In a bootstrap operation of sorts, this tuned string is then used in place of the tuning fork to tune a second string, which is then used as the tuning fork for a third string, etc., until all of the strings are tuned.