General Physics General Physics Help Forum Jan 25th 2018, 06:43 PM #1 Junior Member   Join Date: Jan 2018 Posts: 1 The adding of 3 waves. I have been stuck on this problem for hours and i cant seem to find any information or anything online that makes since to me. There are 3 waves traveling in the +x direction, what is the amplitude, phase and speed of the resulting wave? y=3cos(14x-2600t) y=4cos(14x-2600t+1) y=5cos(14x-2600t-pi/2) Not to seem ignorant, but i am not sure what it is i am even suppose to do. My initial though was to add the first two together, so my amplitude would be 7, but i am not sure what to do with the phase shift. I thought maybe 7cos1 as new amplitude but nothing online seems to give me any information, everything is in sin and we are being "taught' everything in cos, so i assume things just switch a bit? would the new phase be (1-pi/2) and would the rsulting speed be (2pi/14)(2600/2pi)? much help is appreciated.      Jan 26th 2018, 04:29 AM #2 Senior Member   Join Date: Oct 2017 Location: Glasgow Posts: 395 There is an identity: $\displaystyle a \cos x + b \sin x = R \cos (x- \alpha)$ where $\displaystyle R = \sqrt{a^2 + b^2}$ $\displaystyle \alpha = arctan\left(\frac{b}{a}\right)$ I think that this identity together with $\displaystyle \cos x = \sin \left(\frac{\pi}{2} - x\right)$ should be enough to solve your problem. Basically, you will want to use the above formula to decompose your cosine waves into a mixture of sine and cosine waves where the phase difference is separated out into the sine part. Then you can add up the separate contributions.  Tags adding, waves Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post mirandaeb Kinematics and Dynamics 1 Oct 8th 2013 11:30 AM angelohastie Advanced Mechanics 3 Sep 17th 2013 03:40 PM Sml2382 General Physics 4 Nov 14th 2012 10:17 AM tonic22 Kinematics and Dynamics 1 Feb 20th 2011 03:50 PM