Understanding Sinusoidal Waves: Exploring Phase, Wavelength, and Amplitude

In summary, the conversation discusses two sinusoidal waves traveling in the same direction along a string. The waves are identical except for their phase, with one having a phase difference of 0.390 radians. The equation for the net wave is y(x,t)=(5.5 mm)sin(12.0x -2.0 s-1 * t+0.390 rad), where x is in meters and t is in seconds. The wavelength of the two waves is calculated to be 0.524 meters, where the 12.0 coefficient in the equation was used. The amplitude of the waves, ym, is not mentioned. The discussion also touches on the general equation for a traveling wave, writing a second equation with
  • #1
Mr Krabs
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Member advised to use the homework template for posts in the homework sections of PF.
Two sinusoidal waves, identical except for phase, travel in the same direction along a string, producing the net wave

y(x,t)=(5.5 mm)sin(12.0x -2.0 s-1 * t+0.390 rad),

A. with x in meters and t in seconds. What is the wavelength λ of the two waves?
B. What is the phase difference between them?
C. What is their amplitude ym?

I know A is .524 m but I am not too sure why. Other than that, I don't really know what I am doing. My general issue here is that I do not fully understand the form of the equation. Any information on what the different terms in the equation do would be helpful.

I got the answer for A from (2pi)/12 btw. The 12 was the coefficient of the first term, but again I don't really understand what is happening here.
 
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  • #2
Mr Krabs said:
I know A is .524 m but I am not too sure why.
The wavelength is the smallest nonzero change in x which completes a cycle, i.e. changes the argument to the sine function by 2π.
Mr Krabs said:
I do not fully understand the form of the equation.
Write a general equation for a traveling wave. Write a second one which only differs in phase. Write the sum of the two.
What trig formulae do you know that can put the sum of two sine functions in a different form? (These should be listed in the Relevant Equations section of the template. Oh, you didn't keep the template. Tut tut.)
 

1. What is the principle behind the addition of two waves?

The addition of two waves is based on the principle of superposition, which states that when two or more waves meet at a point in space, the resulting displacement at that point is the algebraic sum of the individual displacements caused by each wave.

2. How do you determine the amplitude of the resulting wave when two waves are added together?

The amplitude of the resulting wave can be determined by adding the amplitudes of the individual waves. If the waves have the same amplitude and are in phase, the resulting amplitude will be twice the amplitude of each individual wave. However, if the waves have different amplitudes, the resulting amplitude will be somewhere between the two individual amplitudes.

3. What happens when two waves with the same frequency and amplitude are added together?

If two waves with the same frequency and amplitude are added together, the resulting wave will have the same frequency and amplitude. This is known as constructive interference, where the individual waves reinforce each other.

4. Can two waves with different wavelengths be added together?

Yes, two waves with different wavelengths can be added together. However, the resulting wave will have a different wavelength than the individual waves. This is known as interference, where the waves can either reinforce or cancel each other out depending on their relative phase difference.

5. How does the phase difference between two waves affect the resulting wave when they are added together?

The phase difference between two waves can greatly affect the resulting wave when they are added together. If the phase difference is 0 or a multiple of 2π, the waves will be in phase and the resulting wave will have a higher amplitude. However, if the phase difference is π or a multiple of π, the waves will be out of phase and the resulting wave will have a lower amplitude.

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