Simple waves, finding difference in phase.

OxicGaming

New member
Currently doing networking at University and its pretty maths heavy. Last time I did maths was about 5-6 years ago at GCSE which isn't helping. I've been asked to find the difference in phase between:
1. f(x) = sin x and g(x) = cos x
2. f(x) = sin x and g(x) = -sin x
3. f(x) = sin x and g(x) = sin 2x

How would I go about doing this? I'm at a complete loss. What do cos and sin mean in this context? Most YouTube videos don't go into the depth required. If anyone could help I'd greatly appreciate it.

Last edited:

Subhotosh Khan

Super Moderator
Staff member
Currently doing networking at University and its pretty maths heavy. Last time I did maths was about 5-6 years ago at GCSE which isn't helping. I've been asked to find the difference in phase between:
1. f(x) = sin x and g(x) = cos x
2. f(x) = sin x and g(x) = -sin x
3. f(x) = sin x and g(x) = sin 2x

How would I go about doing this? I'm at a complete loss. What do cos and sin mean in this context? Most YouTube videos don't go into the depth required. If anyone could help I'd greatly appreciate it.
Can you plot y = cos(x) and plot cos( x + pi/2) on the same graph (for x = -4*pi to x = 4*pi ) Now plot y = sin(x). Tell us about your observation.

blamocur

Full Member
When you have functions [imath]f(x)[/imath] and [imath]g(x) = f(x+\phi)[/imath] then it is said that the difference in phase between [imath]f[/imath] and [imath]g[/imath] is [imath]\phi[/imath].

In you case you want to represent the right hand sides in 1. and 2. as [imath]\sin (x+\phi)[/imath], where the value of [imath]\phi[/imath] has to be computed individually for each of the two cases.

I don't understand how they expect you to compute phase differences for functions with different frequencies/periods, i.e. the third line.

Dr.Peterson

Elite Member
Currently doing networking at University and its pretty maths heavy. Last time I did maths was about 5-6 years ago at GCSE which isn't helping. I've been asked to find the difference in phase between:
1. f(x) = sin x and g(x) = cos x
2. f(x) = sin x and g(x) = -sin x
3. f(x) = sin x and g(x) = sin 2x

How would I go about doing this? I'm at a complete loss. What do cos and sin mean in this context? Most YouTube videos don't go into the depth required. If anyone could help I'd greatly appreciate it.
If you are saying that you don't know what sine and cosine are, then you really need to review all the basics of trigonometry.

I have seen phase difference defined in different ways, namely as the actual difference in time between corresponding points of two waves (a time delay), or as the difference in angle represented by those points (in either degrees or radians). I think the latter is the proper meaning; the former is sometimes used in introductory trig books, so you should be careful in your review.

For the first two examples, the two definitions are the same, because x is the angle! All you need to do is to either graph the functions, or use some basic identities to write the two functions as sin(x) and sin(x + phi); the phase difference is phi.

The whole concept of phase is meaningless when comparing sinusoids with different periods, as in example 3; the phase difference is constantly varying, rather than constant.

Can you show us the context of your assignment, such as the definition given for phase difference, or an examples in which phase is used?

OxicGaming

New member
Unfortunatley that is the only context. It's a bit of a confusing one which I can't find much information on, not even in lecture slides or presentations.

I did miss out that they either want the answers in radians or degrees.

Thanks for everyones replies so far, I really appreciate it.

OxicGaming

New member
Can you plot y = cos(x) and plot cos( x + pi/2) on the same graph (for x = -4*pi to x = 4*pi ) Now plot y = sin(x). Tell us about your observation.
It seems cos(x + pi/2) has a positive phase shift for cos(x) and sin(x) has a negative phase shift from cos(x)