Calculating Phase Difference and Zero Point of Two Sinusoidal Waves

In summary, two sinusoidal waves in a string are defined by the functions y1 = (2.00 cm) sin(20.0x – 32.0t) and y2 = (2.00 cm) sin(25.0x – 40.0t) where y and x are in centimeters and t is in seconds. The phase difference between these two waves at the point x = 5.00 cm at t = 2.00 s is 0.72 radians. The positive x value closest to the origin for which the two phases differ by pi at t = 2.00 s is approximately 0.25 cm.
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Homework Statement



Two sinusoidal waves in a string are defined by the functions
y1 = (2.00 cm) sin(20.0x – 32.0t) and
y2 = (2.00 cm) sin(25.0x – 40.0t) where y and x are in centimeters and t is in seconds.
(a) What is the phase difference between these two waves at the point x = 5.00 cm at t = 2.00 s?
(b) What is the positive x value closest to the origin for which the two phases differ by at t = 2.00 s? (This is where the two waves add to zero.)


Homework Equations





The Attempt at a Solution

 
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What do you call the phase of a sinusoidal wave?

ehild
 

1. What is the formula for calculating phase difference between two sinusoidal waves?

The formula for calculating phase difference is given as Φ = (Δt/T)*360°, where Φ is the phase difference, Δt is the time difference between the two waves, and T is the period of the waves.

2. How do you find the zero point of two sinusoidal waves?

The zero point is the point where the two waves intersect and have the same amplitude. To find this point, you can set the equations of the two waves equal to each other and solve for the value of x. This will give you the x-coordinate of the zero point.

3. Can phase difference and zero point be negative?

Yes, phase difference and zero point can both be negative. This can happen when the two waves are out of phase or when the zero point is located in the negative y-axis.

4. Is it possible for two sinusoidal waves to have a phase difference of 180 degrees?

Yes, it is possible for two sinusoidal waves to have a phase difference of 180 degrees. This means that the two waves are completely out of phase and have opposite amplitudes.

5. How does changing the frequency affect the phase difference and zero point of two sinusoidal waves?

Changing the frequency does not affect the phase difference and zero point of two sinusoidal waves. These values are determined by the time difference between the waves and the period of the waves, which are not affected by changes in frequency.

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