How many divisions will the traces differ in this oscilloscope calculation?

[eehelp150]

Homework Statement

V1 = 10cos(10^4t)
V2 = 5cos(10^4t + pi/3)
Time Base setting = 0.1msec/div

By how many divisions will these two traces differ?

Homework Equations

W = 2pi/T[/B]

The Attempt at a Solution

W = 2pi/T
T = 2pi/W
W = 10^4
T = 0.628 milliseconds
0.628milliseconds/(0.1msec/div) = 6.28 divisions
Would the difference between 10cos and 5cos add a factor of 2 or 1/2 to the # of divisions?

 

[CWatters]

Would the difference between 10cos and 5cos add a factor of 2 or 1/2 to the # of divisions?

No. The 10 and 5 give you the amplitude. For example at a peak, when cos(...) =1, one waveform has the value 10 and the other 5.

Hints:

a) Both waveforms have a common 10⁴t term. What does that mean?
b) One also has another term pi/3. What does that represent?

 

[NascentOxygen]

Would the difference between 10cos and 5cos add a factor of 2 or 1/2 to the # of divisions?

You are making this difficult for yourself if you are attempting to answer this question without first sketching how the oscilloscope is displaying these two signals.

If you think you don't need to sketch this, then I say you most certainly do need to‼‼ [emoji678]

 

[eehelp150]

No. The 10 and 5 give you the amplitude. For example at a peak, when cos(...) =1, one waveform has the value 10 and the other 5.

Hints:

a) Both waveforms have a common 10⁴t term. What does that mean?
b) One also has another term pi/3. What does that represent?

a. Same frequency
b. Phase shift

 

[CWatters]

Correct.

Which of a and b shifts the trace left to right along the time axis relative to the other?

 

[eehelp150]

Correct.

Which of a and b shifts the trace left to right along the time axis relative to the other?

B would shift the graph over to the right by pi/3?

 

[CWatters]

Correct.

Although I think V2 would be shifted left relative to V1.

 

[eehelp150]

Correct.

Although I think V2 would be shifted left relative to V1.

So how many divisions will these two traces differ?

Pi/3 divisions?

 

[gneill]

You have calculated the period of the signals (the time for one cycle). How much of one period does the phase angle represent? What is it in milliseconds?

 

[eehelp150]

You have calculated the period of the signals (the time for one cycle). How much of one period does the phase angle represent? What is it in milliseconds?

1/3 of the period?
0.209 ms?

 

[gneill]

1/3 of the period?
0.209 ms?

Can you show how you determined the 1/3 value? Is pi/3 really 1/3 of a full circle?

 

[eehelp150]

Can you show how you determined the 1/3 value? Is pi/3 really 1/3 of a full circle?

Pi/3 is 1/6 of the total period, so would it be 0.105ms or 1.05 divisions?

 

[gneill]

Pi/3 is 1/6 of the total period, so would it be 0.105ms or 1.05 divisions?

That looks better!