Finding Tbeat for 2 waves of periods T1 and T2 using oscilloscope

[-EquinoX-]

Homework Statement

I am asked to measure T1, T2, Tbeat, and Tbar using oscilloscope.

Can anyone tell me what these means?

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

Measuring music?
http://en.wikipedia.org/wiki/Time_signature

 

[-EquinoX-]

nope.. it has nothing to do with music... but yea.. I am given two frequencies that I need to set in the oscilloscope...

 

[LowlyPion]

So like acoustic beats:
http://en.wikipedia.org/wiki/Beat_(acoustics )

 

[-EquinoX-]

it has to do with electricity and nothing with music... it has to do with T-networks

 

[Redbelly98]

Just taking an educated guess, that:

• T1 and T2 are the periods of two separate waveforms
• Tbeat is the period of the beats, when the two waveforms are combined.
• Tbar is the "period" of the sine-wave-like waveform, when the two waveforms are combined.

 

[-EquinoX-]

I guess you're right redbelly98... I still however don't understand how to get Tbeat in an oscilosscope

 

[Redbelly98]

Tbeat would be the time interval of each beat. For example, 20 to 21 ms in this waveform:

http://www.picotech.com/experiments/sound_interference/graphics/frequency_image.gif

 

[-EquinoX-]

ermmm.. the picture didn't show up

 

[George Jones]

ermmm.. the picture didn't show up

Here is the image of the sum of two equal amplitude sinusoidal waves whose frequencies differ by 10%.

Do you see how to measure T_bar and T_beat?

 

[Redbelly98]

ermmm.. the picture didn't show up

Sorry!

George has posted an equally good picture. But just to prove to everybody that I'm not a completely stark raving lunatic , here is the image I meant to include:

http://www.picotech.com/experiments/sound_interference/graphics/frequency_image.gif

 

[-EquinoX-]

>>Do you see how to measure T_bar and T_beat?

No I don't, can you please explain?

 

[-EquinoX-]

Sorry!

George has posted an equally good picture. But just to prove to everybody that I'm not a completely stark raving lunatic , here is the image I meant to include:

http://www.picotech.com/experiments/sound_interference/graphics/frequency_image.gif

And it's still not there

 

[Redbelly98]

My image is still not displaying! Shoot, just click here:

http://www.picotech.com/experiments/sound_interference/graphics/frequency_image.gif

 

[-EquinoX-]

and so how do you calculate the T bar and T beat from that image

 

[Redbelly98]

Just measure them off of the graph ... but first you have to know what they mean . What were you told is the definition of Tbar and Tbeat?

EDIT: I ask this because beating should have been discussed either in a class lecture, or in your textbook.

 

[-EquinoX-]

What were you told is the definition of Tbar and Tbeat?

that's why I asked it here, but someone defined it for me above

 

[Redbelly98]

2 questions for you:
Have you used an oscilloscope before? Also, has there been any discussion of beating in your class lectures?

If the answer is "no" to either of these questions, it is very difficult to give you a good explanation and I would recommend that you ask your lab instructor about it. Wikipedia has a pretty decent explanation of beating:
http://en.wikipedia.org/wiki/Beat_(acoustics)#Mathematics_and_physics_of_beat_tones

And if you have already used an oscilloscope, and have learned about beating in your lectures:

Tbeat is the time interval between beats. Once you have the waveform displayed on the oscilloscope, measure that time interval.

I think Tbar is the period of the fast-oscillating part of the waveform. Again, it's just measured on the oscilloscope.

 

[-EquinoX-]

well.. yes there has been a discussion about beating in the class, but it wasn't that clear..

 

[-EquinoX-]

Ok I just realized that T_bar is just the average of T1 and T2, is there a specific way to know this in an osciloscope? Or do I just simply measure T1 and T2 and do the math on paper?

 

[George Jones]

Ok I just realized that T_bar is just the average of T1 and T2, is there a specific way to know this in an osciloscope? Or do I just simply measure T1 and T2 and do the math on paper?

Feed a sinusoidal signal with period T1 into channel 1 of the scope and a sinusoidal signal with period T2 into channel 2 of the scope. If you use function generators that have digital frequency readout, then the periods can be calculated from the frequecies. If your generators don't have digital readouts, then maybe you should use the scope to determine periods T1 and T2.

Do you know how to do this?

I think part of the point of this is to determine Tbar from both tbar = (T1 + T2)/2, and from the scope, and to compare the two values. In other words, compare theory and experiment.

Set the scope to sum channels 1 and 2. If the amplitudes of your two signals are almost equal, you should see a pattern like Redbelly98 posted. Measure the period the "short" wiggles. This should be Tbar.

 

[-EquinoX-]

yes I know exactly how to measure T1 and T2, so I guess to get T_bar I should just add them and divide by 2? no way to see it on the scope? and yes that is true, the purpose is just to compare T_average that I got from the scope and computation, however how do I get T_average from the scope?

as of the T_beat all I need to do is just add T1 and T2 and from the produced sinusoidal signal I measure the T, and this T will be T_beat, am I right?

 

[George Jones]

no way to see it on the scope?

Read the last two paragraphs of my previous post.

 

[-EquinoX-]

okay sorry for not reading well, how about to measure T_beat then? Isn't that the same way to measure T_beat as well.. set the scope to sum/add both channels?... or do I invert one of the signals first and then add them to get the T_beat?

 

[George Jones]

I think I can be more clear by using the image

http://en.wikipedia.org/wiki/File:Beating_Frequency.svg,

which should be similar to what you see on the scope when you sum channels 1 and 2.

There are two characteristic time periods in this image, the time between consecutive black peaks, and the time between consecutive orange peaks. Measure both these periods with the scope. Which is which?

 

[-EquinoX-]

I think I can be more clear by using the image

http://en.wikipedia.org/wiki/File:Beating_Frequency.svg,

which should be similar to what you see on the scope when you sum channels 1 and 2.

There are two characteristic time periods in this image, the time between consecutive black peaks, and the time between consecutive orange peaks. Measure both these periods with the scope. Which is which?

you mean one is T_beat and one is T_bar?

 

[George Jones]

you mean one is T_beat and one is T_bar?

Yes!

 

[-EquinoX-]

in that case the black one is T_beat and orange is T_bar, is this correct?

 

[George Jones]

in that case the black one is T_beat and orange is T_bar, is this correct?

Oops.

I know you're not applying this to sound, but I want to use sound as example. Two musical instruments that are not quite in tune play the "same" note. What do you hear?

Pitch is determined by frequency, and you hear the average of the two frequencies, i.e., the black. But you hear the loudness of the tone vary with time - loud, soft, loud, soft, ... This is the phenomenon of beats.

Loudness is determined determined by the orange "envelope", so this gives the period of the beats.

 

[-EquinoX-]

oh I see, so I got it reversed then.. orange is T_beat and the black one is the T_average... thank you so much for explaining this, I appreciate it