How do I find the amplitude of the combined signal?

[alexdr5398]

Homework Statement

Homework Equations

Δφ = 2π (Δr/λ)

The Attempt at a Solution

I understand how to get the phase difference, but is the equation for the combined wave (second last line) just something I should memorize?

Also, where does the sin term go in the last line? And why are the units for amplitude "μV/m"? Aren't V/m the units for electric field?

 

[gneill]

I understand how to get the phase difference, but is the equation for the combined wave (second last line) just something I should memorize?

Probably. It's that or memorize the trig identity for sin(A) + sin(B) which is used to derive it. While the latter is more useful in general, the former is more likely to be expedient in the context of your current coursework.

Also, where does the sin term go in the last line? And why are the units for amplitude "μV/m"? Aren't V/m the units for electric field?

The sin function varies between + and - 1 as t varies, so what's its magnitude?. The rest are constant terms.

The "μ" in μV stands for "micro". Thus the signal strength is being given in microvolts per meter.

 

[alexdr5398]

The sin function varies between + and - 1 as t varies, so what's its magnitude?. The rest are constant terms.

Oh I see. So the maximum y value is the amplitude, and that occurs then the sin term is 1.

The "μ" in μV stands for "micro". Thus the signal strength is being given in microvolts per meter.

I know what "μ" is, but isn't the amplitude usually measured in metres? Why is the unit "μV/m" in this case?

 

[gneill]

I know what "μ" is, but isn't the amplitude usually measured in metres? Why is the unit "μV/m" in this case?

It's the amplitude of the electric field strength that is being measured. That's the change in electric potential with distance, hence volts per meter as the basic unit. The amplitude here is not a physical distance, but a field strength.

 

[alexdr5398]

It's the amplitude of the electric field strength that is being measured. That's the change in electric potential with distance, hence volts per meter as the basic unit. The amplitude here is not a physical distance, but a field strength.

Oh, alright. thank you.