Beat Frequency of 2 Waves in Free Space

[nmsurobert]

Homework Statement

Two waves of different wavelengths λ₁= 1.5μm, λ₂ = 1.63μm, are combined in free space E_t = 1.5cos(k₁x - ω₁t) + 2cos(k₂x -ω₂t)
Find the beat frequency

Homework Equations

(ω₁- ω₂) = 2ω_m=beat frequency

E₀² = 4E₀₁²cos²(k_mx - ω_mt)

The Attempt at a Solution

I am quite stuck on this problem. Can I get a numerical solution for question with what I've been given?

 

[drvrm]

I am quite stuck on this problem. Can I get a numerical solution for question with what I've been given?

first you must superpose the two waves and see the waxing and waning of sound intensities and count its frequency per second.
that can be simply done on a plot of amplitude with time graph.
your amplitudes are different -so the destructive interference will not necessarily produce a zero intensity but the envelope of intensity and its maximum and minimum values will give you beat frequency.
so proceed ahead.

 

[ehild]

Homework Statement

Two waves of different wavelengths λ₁= 1.5μm, λ₂ = 1.63μm, are combined in free space E_t = 1.5cos(k₁x - ω₁t) + 2cos(k₂x -ω₂t)
Find the beat frequency

Homework Equations

(ω₁- ω₂) = 2ω_m=beat frequency

Yes, you need to determine the beat frequency which is half the difference of frequencies of the constituent waves. You are given the wavelengths. What are the frequencies?
What kind of waves they are?

 

[nmsurobert]

Yes, you need to determine the beat frequency which is half the difference of frequencies of the constituent waves. You are given the wavelengths. What are the frequencies?
What kind of waves they are?

I don't know what kind of waves they are. I wrote the question as it is on the paper. I've been trying to figure out a way to find the frequency but I feel like I'm missing something.

 

[nmsurobert]

first you must superpose the two waves and see the waxing and waning of sound intensities and count its frequency per second.
that can be simply done on a plot of amplitude with time graph.
your amplitudes are different -so the destructive interference will not necessarily produce a zero intensity but the envelope of intensity and its maximum and minimum values will give you beat frequency.
so proceed ahead.

Asking me to plot something isn't going to help haha he's been asking us to plot stuff all semester and I haven't been able to figure out how to plot any of this stuff.

 

[ehild]

I don't know what kind of waves they are. I wrote the question as it is on the paper. I've been trying to figure out a way to find the frequency but I feel like I'm missing something.

How do you get the frequency from the wavelength of the wave?

 

[nmsurobert]

How do you get the frequency from the wavelength of the wave?

The only way I've found how to do this is v = fλ. However, I don't know what the velocity of the way is unless I assume the velocity is c.

 

[ehild]

The only way I've found how to do this is v = fλ. However, I don't know what the velocity of the way is unless I assume the velocity is c.

Yes, the speed of the wave is crucial. it is said, the wave travels in free space. What do you think free space means? Was the original text English?

 

[nmsurobert]

It was in English. I'll just assume that then. Sometimes the assignments are either vague or misleading for the class so I try not too assume too much. Thank you though! That makes the problem much easier lol