TBR: Lowest Resonant Frequency = Highest Intensity?

[justadream]

TBR Physics Book II page 41 Passage

It says "as a general rule, the lowest resonant frequency is of the highest intensity"


Why is this? I thought higher frequency usually means higher intensity.

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[mehc012]

TBR Physics Book II page 41 Passage

It says "as a general rule, the lowest resonant frequency is of the highest intensity"


Why is this? I thought higher frequency usually means higher intensity.

Intensity has to do with amplitude. Higher amplitude = higher intensity = louder sound. A high amplitude also requires more power (aka energy).
A high frequency, while not related to amplitude/intensity/loudness, also requires more energy. Though not specifically applicable to this case (sound is not an EM wave), think E = hν. That equation is too simplified to use here because there are more variables with a sound wave, but it does help demonstrate that, all other things being held equivalent, energy and frequency are proportional for waves.

Think of it this way...if you are plucking a string, it is going to vibrate. Let's say that the odds of any given resonant frequency of that string playing are equal, and the same amount of energy ends up going into each possible waveform (this is likely untrue, but it is a useful conceptualization).
If you have a low-frequency sound and a high-frequency sound, it takes more energy to play the high-frequency one at a given volume (amplitude). If you want to have the same amount of energy in each sound, the low-frequency one will have the higher amplitude/intensity/loudness.

 

[justadream]

@mehc012

I mostly follow your second paragraph but how does that fit with "energy and frequency are proportional for waves"?

Is it that in this situation, all other things are not equivalent?

 

[mehc012]

@mehc012

I mostly follow your second paragraph but how does that fit with "energy and frequency are proportional for waves"?

Is it that in this situation, all other things are not equivalent?

No, it's that you can use energy either to generate high frequency (it takes more energy to make a high frequency wave) or amplitude. So if two waves have equal energies, the one with the lower frequency will have the higher amplitude (will be louder).

 

[justadream]

@mehc012

Oh okay, that makes sense. Is there an equation of some sort to know exactly how the energy is split up between contributing to frequency and amplitude?

Btw: where did you learn this? I've been through most of TBR and all of TPR and I never learned this.

 

[mehc012]

@mehc012

Oh okay, that makes sense. Is there an equation of some sort to know exactly how the energy is split up between contributing to frequency and amplitude?

Btw: where did you learn this? I've been through most of TBR and all of TPR and I never learned this.

No, you don't need to know how much - as I said, the energy/frequency equation we have only holds for EM waves, which we're not discussing here. This is one of those tidbits that TBR drops on you (in the sentence you pointed out)...the part you need to know is that the base frequency is typically louder than the overtones (which makes logical sense, especially if you've ever played an instrument). You asked why, so I gave you my reasoning, but you don't really need to go into this for the MCAT. I figured it out because when TBR throws those little factoids out there, I get super curious and have to figure out why and go on a great Google quest.

Anyway, they pretty much discuss energy-intensity-amplitude for sound waves and energy-Planck-frequency relations for EM waves, and very rarely vice versa.