My Math Forum A double beam oscilloscope

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 July 5th, 2011, 09:00 AM #1 Senior Member   Joined: Oct 2009 Posts: 895 Thanks: 1 A double beam oscilloscope Hi all A double beam oscilloscope displays 2 sinusoidal waveforms A and B . The time/cm switch is on 100 µs/cm and volt/cm switch on 2V/cm. The width of each complete cycle is 5 cm for both the waveforms. The height of waveforms A and B are 2 cm and 2.5 cm respectively. Determine the phase difference ? please help me , How I can solve like this Q ....
 July 5th, 2011, 09:25 AM #2 Senior Member   Joined: Sep 2010 Posts: 101 Thanks: 0 Re: A double beam oscilloscpe Hello there r-soy, To determine phase difference (or phase shift) between two sine waves A and B we will need some more info than what is posted. Width and height for each signal only gives us amplitude and frequency. Is there some picture for that question which actually shows oscilloscope's output? It could look like this one:
 July 6th, 2011, 03:14 AM #3 Senior Member   Joined: Oct 2009 Posts: 895 Thanks: 1 Re: A double beam oscilloscpe My teacher told me the answer would be 36 degrees Unfortunately, I can't get that same answer !!!!
 July 6th, 2011, 09:05 AM #4 Senior Member   Joined: Sep 2010 Posts: 101 Thanks: 0 Re: A double beam oscilloscpe I think i might have found solution. Both sine waves have same amplitude so maximum for both is 2.5 cm. We have two sine waves A and B. They have same period / frequency and in given moment t height of sine wave A is 2.5 cm (or it's maximum) and height of sine wave B is 2 cm(not maximum yet). Let's represent values of sine waves in given moment t with following eqations(U_max=2,5cm): sine wave A: u(t)=U_max * sinA sine wave B: u(t)=U_max * sinB We know that in moment t sine wave A reaches its maximum therefore u(t)=U_max*sinA => 2,5=2,5*sinA=> sinA=2,5/2,5=1 => A = 90 degrees For sine wave B: u(t) = 2cm, U_max= 2,5cm: 2cm = 2,5cm * sin B => sin B = 2/2,5 = 0,8 => B = 54 degrees (approximately) Now that we know angles A and B in one moment t and it is stated that waves have same frequency we can find phase difference(P): P=angle A - angle B = 90degrees - 54degrees = 36 degrees Now the important thing here was that you wrote: "The height of waveforms A and B in moment t are 2 cm and 2.5 cm".I was confused at first because i thought those were the maximums for sine waves but now i understand that those were heights in certain moment.
 July 6th, 2011, 10:26 AM #5 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs Re: A double beam oscilloscpe We could also use (assuming the same amplitude and frequency): $A\sin\theta+A\sin\varphi=A+\frac{2}{2.5}A=1.8A$ Divide through by A: $\sin\theta+\sin\varphi=1.8$ For simplicity, we can let: $\theta=\frac{\pi}{2}$ $\varphi=\frac{\pi}{2}+P$ Now we have: $\sin$$\frac{\pi}{2}$$+\sin$$\frac{\pi}{2}+P$$=1.8$ $\sin$$\frac{\pi}{2}+P$$=0.8$ $\cos(P)=0.8$ $P=\cos^{-1}$$0.8$$\approx0.643501\approx36.87^{\circ}$
 July 6th, 2011, 11:11 AM #6 Senior Member   Joined: Sep 2010 Posts: 101 Thanks: 0 Re: A double beam oscilloscpe Nice! I also got 36,87 degrees because angle B is actually 53.13 deg and then P=90-53.13=36.87 degrees, but I rounded it to match r-soy's solution. Good job
 July 6th, 2011, 11:21 AM #7 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs Re: A double beam oscilloscpe Well, once you figured out that both waves have the same amplitude A, and that A = 2.5 cm, the only real difference between what you did and what I did boiled down to using: $\cos^{-1}(P)=\frac{\pi}{2}-\sin^{-1}(P)$
 July 7th, 2011, 03:39 AM #8 Senior Member   Joined: Sep 2010 Posts: 101 Thanks: 0 Re: A double beam oscilloscope Yes the same amplitude was key. Maybe this problem should be more precise so we didn't have to assume this stuff?
 July 7th, 2011, 08:44 AM #9 Senior Member   Joined: Oct 2009 Posts: 895 Thanks: 1 Re: A double beam oscilloscope Thank you .. I am happy now because I understand the solution .... MarkFL , How are you ? You are absent from the scene?
 July 7th, 2011, 08:50 AM #10 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs Re: A double beam oscilloscope I'm fine, how are you? The part of physics I remember least about is electricity...so I haven't been able to answer many of your questions lately.

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