Question

The system is a Helmholtz Resonator and the energy being applied is at a frequency that is an integer multiple of the resonant frequency. If energy is decaying, the amount of energy input won't be the amount when resonance is actually occurring. The actual resonance frequency is usually around 20 times the frequency being input. That is why I am curious about how much energy has been lost by the time the resonance frequency is hit. More specifically: if the multiple changes to 23, how much more energy would it take initially to equal the same amount when the multiple is 20?

Answer 1

When the frequency of the energy being applied to a Helmholtz Resonator is a multiple of the resonant frequency, resonance occurs. The resonant frequency is usually around 20 times the frequency being input. If the multiple changes, more energy would be required initially to achieve the same amount when the multiple is 20.

Step-by-step explanation:

When the frequency of the energy being applied to a Helmholtz Resonator is an integer multiple of the resonant frequency, resonance occurs. In this case, the resonant frequency is around 20 times the frequency being input. If we change the multiple to 23, the resonant frequency will be higher. To calculate how much more energy would be required initially to achieve the same amount as when the multiple is 20, we need to consider the relationship between energy and frequency in resonance.

Resonance occurs when the driving frequency is equal to the natural frequency of the system. At resonance, the energy transfer from the driving force to the oscillator is most efficient and the amplitude of oscillations increases. The relationship between energy and frequency in resonance is non-linear. As the resonant frequency increases, more energy is required to reach the same level of amplitude. Therefore, if the multiple changes from 20 to 23, it would take more energy initially to achieve the same amount as when the multiple is 20.