Stationary Waves - Effect of Frequency and Amplitude

[Peter G.]

Hi,

As part of my Physics Class, we created a spreadsheet that animates to waves moving in opposite directions to illustrate standing waves. In order to test we were told to put the same values of amplitude, wavelength and speed (frequency was calculated from wavelength and speed) for both waves.

Our assignment was to try different values for amplitude and wavelength (to change the frequency) for each wave and to describe the effect. For some reason however, excel goes crazy and it is hard to observe the effect after changing these variables.

Even though the animation is not working I wanted to submit my predictions. I am not very sure, but this is what I think would happen:

If we have different amplitudes for each wave and pick equal values for wavelength and frequency for each wave I think that, during constructive interference, the resulting amplitude would add as it did before but during destructive interference, instead of having a node at 0 displacement we would have a node at negative displacement.

For different frequencies for each wave, I don't see how it would work because, from what I understand, it only works when the two waves are coherent, correct?

Thanks,
Peter G.

 

[PeterO]

Hi,

As part of my Physics Class, we created a spreadsheet that animates to waves moving in opposite directions to illustrate standing waves. In order to test we were told to put the same values of amplitude, wavelength and speed (frequency was calculated from wavelength and speed) for both waves.

Our assignment was to try different values for amplitude and wavelength (to change the frequency) for each wave and to describe the effect. For some reason however, excel goes crazy and it is hard to observe the effect after changing these variables.

Even though the animation is not working I wanted to submit my predictions. I am not very sure, but this is what I think would happen:

If we have different amplitudes for each wave and pick equal values for wavelength and frequency for each wave I think that, during constructive interference, the resulting amplitude would add as it did before but during destructive interference, instead of having a node at 0 displacement we would have a node at negative displacement.

For different frequencies for each wave, I don't see how it would work because, from what I understand, it only works when the two waves are coherent, correct?

Thanks,
Peter G.

With different amplitudes, you will certainly not get a zero for destructive interference, though I am not sure why you said it would be negative?

With different wavelengths [frequencies if you like] you certainly won't get a simple standing wave.

 

[Peter G.]

Oh, yes, I got confused on the negative part. But it is correct to say that we would not get 0 displacement for standing waves with contrasting amplitudes?

 

[PeterO]

Oh, yes, I got confused on the negative part. But it is correct to say that we would not get 0 displacement for standing waves with contrasting amplitudes?

The more I think about it the less I like it.

If you have two waves traveling in opposite directions on a single string, they will form a, generally, complex interaction.

In one very special case, we get an interaction which is simple to analyse and observe.

If , and only if, the two waves have the same frequency [wavelength] and amplitude we get what is called a standing wave - which looks like segments of the string flopping backwards and forwards in a transverse way with no motion along the string - it is standing still.

In the absence of that one specific set of conditions, I suspect there will be no standing wave, but a complex interaction.

 

[rwisz]

Hi Peter,

Thank you for sharing your predictions for the effects of changing frequency and amplitude on stationary waves. It is always important to make predictions and hypotheses in science before conducting an experiment or simulation.

To address your first point, changing the amplitude of a wave will indeed affect the resulting amplitude during constructive and destructive interference. As you mentioned, during constructive interference, the resulting amplitude will be the sum of the individual amplitudes. This means that if the amplitudes of the two waves are different, the resulting amplitude will also be different. Similarly, during destructive interference, the resulting amplitude will be the difference between the two individual amplitudes. So, if the amplitudes of the two waves are different, the resulting amplitude will also be different and may even result in a negative displacement, as you suggested.

Regarding your second point, you are correct that stationary waves require coherence between the two waves. This means that the two waves must have the same frequency and wavelength in order to create a stationary wave. So, if the frequencies of the two waves are different, they will not create a stationary wave. However, it is still possible to observe the effects of changing frequency on a stationary wave by changing the frequency of one of the waves while keeping the other wave constant. This will result in a change in the wavelength and therefore a change in the resulting stationary wave pattern.

I hope this helps clarify the effects of changing frequency and amplitude on stationary waves. Keep up the good work in your Physics class!

Best,