resonance

[rickrun]

Hello!

I am confused about resonant frequency. I know that a driving force with a frequency equal to a natural frequency of a string will increase the amplitude, but can the driving force have a frequency equal to any of the harmonics or just a single, natural frequency?

The question that confused me says this.....

A force driving a string causes the string to oscillate at its resonant frequency. If the frequency of the driving force increases, then the amplitude of the resulting vibration would:

a) decrease, b) increase, c) remain the same, d) cannot be determined

...According to the answer, the amplitude will decrease, because the frequency no longer matches the natural frequency. However, I thought it would be that it can't be determined because the new frequency might possibly still be equal to another harmonic, which would cause the amplitude to increase as well. Am I wrong?????

Thanks!!

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[milski]

You are somewhat correct but you need to keep in mind that the resonance amplitudes when the driving force has a harmonic frequency instead of the natural one will be smaller than the resonance amplitude when at the natural frequency.

As you move to higher orders of harmonics, the resonance amplitudes will be getting smaller and smaller.

 

[Singhp03]

Hello!

I am confused about resonant frequency. I know that a driving force with a frequency equal to a natural frequency of a string will increase the amplitude, but can the driving force have a frequency equal to any of the harmonics or just a single, natural frequency?

The question that confused me says this.....

A force driving a string causes the string to oscillate at its resonant frequency. If the frequency of the driving force increases, then the amplitude of the resulting vibration would:

a) decrease, b) increase, c) remain the same, d) cannot be determined

...According to the answer, the amplitude will decrease, because the frequency no longer matches the natural frequency. However, I thought it would be that it can't be determined because the new frequency might possibly still be equal to another harmonic, which would cause the amplitude to increase as well. Am I wrong?????

Thanks!!

my physics teacher told me to think of resonant frequency as a person on a swing, and yourself(or a second person) as the driving force. In order for you(or that second person) to keep the person swinging at a certain frequency, you need to apply force exactly at the swinger's resonant frequency(as am sure you have experienced at a play ground) if you push to early, or to late, it actually causes them to "slow-down" bc you are not matching their natural rhythm. once your frequencies match, you can even put more energy(increase amplitude) into the wave caused at that frequency, and eventually throw the swinger off the swing. This is also how an opera singer can, supposedly, break a wine glass with his/her voice. Note, during this phenomena frequencies must correlate, resonant frequency and others.

edit: the question is also worded in a way that they expect to you to reason there is only one resonant frequency, guessing it was safe to ignore the other "might be" present harmonics

hope this helped

 

[milski]

edit: the question is also worded in a way that they expect to you to reason there is only one resonant frequency, guessing it was safe to ignore the other "might be" present harmonics

hope this helped

Even if the other resonant frequencies are included, they will have smaller amplitudes than the natural one. (Provided the amplitudes are finite).

 

[rickrun]

Awesome, thanks! I think the take-home message from that question was that a driving force that matches the natural frequency will increase the amplitude, and removing that force will decrease it. And yea, it makes sense that the amplitudes will continue to decrease even at higher harmonics.

Thanks again