First, we need to find the wavelength of each student's waves:
For the student on the left:
Frequency = 4 Hz
Velocity = Frequency x Wavelength
Wavelength = Velocity / Frequency
Since the speed of the waves is the same for both students, we can use the same velocity for both calculations.
Wavelength_left = Velocity / 4
For the student on the right:
Frequency = 3 Hz
Wavelength_right = Velocity / 3
Now we need to find the maximum deflection of the string, which occurs when the waves are perfectly in phase with each other. This means that the crests of one wave align with the crests of the other wave.
The difference in the phase of the two waves is given by:
Difference in phase = (Wavelength_left - Wavelength_right) / (2π)
The maximum deflection from the resting position would be when the waves are exactly out of phase, which means that the crests of one wave align with the troughs of the other wave.
This happens when the phase difference is equal to half of a wavelength:
Difference in phase = Wavelength / 2
Setting the two expressions for the phase difference equal to each other and solving for the maximum deflection, we get:
(Wavelength_left - Wavelength_right) / (2π) = Wavelength / 2
Substituting the expressions for the wavelengths and solving for the maximum deflection, we get:
(Velocity / 4 - Velocity / 3) / (2π) = Velocity / 2
(3 * Velocity - 4 * Velocity) / 12π = Velocity / 2
- Velocity / 12π = Velocity / 2
-1 / 12π = 1 / 2
Velocity = 12π cm
Therefore, the maximum deflection of the string between the students would be 12π cm.
A 3m slinky rests on a table with a student holding each end. The students laterally shake the ends of the slinky to generate transverse waves. The student on the left shakes the slinky at 4 hertz with a 5cm amplitude and the student on the right shakes it at 3 hertz with a 7cm amplitude.
The student's waves travel at the same speed. What is the maximum deflection of the string, from its resting position, between the students in cm?
1 answer