- #1

ngn

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- TL;DR Summary
- If I have two sine waves (pure tones) that differ in frequency but each have the same amplitude, then they would be equal in power. So, the two sounds would be equivalent in their intensities and sound pressures? But what about displacement and particle velocity?

Hello,

I have a problem wrapping my head around the relationship between frequency, power/pressure, and displacement. Let's say I have two sine waves that I generated in my computer: A 50 Hz tone and a 100 Hz tone. Let's say they both have an amplitude of 1. Therefore, they will both have the same RMS value of 0.707. That means that when I play these tones out of a loudspeaker (assuming a perfect loudspeaker with perfect performance and frequency response), both sounds will have the same intensity. Both sounds will also have the same pressure, since Intensity = pressure^2 / impedance.

Now here is where I'm having trouble understanding this. I am assuming that both tones when played out of the loudspeaker will produce the same particle displacement, because their amplitudes are the same. That is, if we could plot a waveform with particle displacement on the y axis, then we would find that both tones have equal amplitude.

But here is the issue. If the particle displacement is the same, then wouldn't the particle velocity be twice as high for the high frequency tone, because the particles need to cover the same distance in half the time. If that is true, then shouldn't power and pressure be higher for the high frequency tone?

If that is not true, then that would mean that displacement for the higher tone is half the lower tone. And if that is true, then wouldn't pressure be half and the sound should be less intense?

I believe I am missing some connection between what is meant by amplitude of a sine wave and how it maps onto particle displacement/velocity and how that translates into pressure.

I've been thinking about a pendulum and how the distance it swings translates into amplitude and the frequency it swings into frequency. It seems that for the same amount of power, a 100 Hz pendulum would have to swing half as far as a 50 Hz pendulum. But that would mean that the two sine waves would have different amplitudes, and hence different powers. So, I can't figure it out. If there's a way to explain it with a simple model like a pendulum, that would be helpful I think.

Thank you!

I have a problem wrapping my head around the relationship between frequency, power/pressure, and displacement. Let's say I have two sine waves that I generated in my computer: A 50 Hz tone and a 100 Hz tone. Let's say they both have an amplitude of 1. Therefore, they will both have the same RMS value of 0.707. That means that when I play these tones out of a loudspeaker (assuming a perfect loudspeaker with perfect performance and frequency response), both sounds will have the same intensity. Both sounds will also have the same pressure, since Intensity = pressure^2 / impedance.

Now here is where I'm having trouble understanding this. I am assuming that both tones when played out of the loudspeaker will produce the same particle displacement, because their amplitudes are the same. That is, if we could plot a waveform with particle displacement on the y axis, then we would find that both tones have equal amplitude.

But here is the issue. If the particle displacement is the same, then wouldn't the particle velocity be twice as high for the high frequency tone, because the particles need to cover the same distance in half the time. If that is true, then shouldn't power and pressure be higher for the high frequency tone?

If that is not true, then that would mean that displacement for the higher tone is half the lower tone. And if that is true, then wouldn't pressure be half and the sound should be less intense?

I believe I am missing some connection between what is meant by amplitude of a sine wave and how it maps onto particle displacement/velocity and how that translates into pressure.

I've been thinking about a pendulum and how the distance it swings translates into amplitude and the frequency it swings into frequency. It seems that for the same amount of power, a 100 Hz pendulum would have to swing half as far as a 50 Hz pendulum. But that would mean that the two sine waves would have different amplitudes, and hence different powers. So, I can't figure it out. If there's a way to explain it with a simple model like a pendulum, that would be helpful I think.

Thank you!