Question

A 3 m 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 Hz with a 5 cm amplitude and the student on the right shakes it at 3 Hz with a 7 cm amplitude. Which student's wave travels fastest?

Answer 1

[AI-generated answer — Bot GPT 3.5]

The speed of a wave is determined by the tension in the medium and the mass per unit length of the medium. In the case of a slinky, the tension is relatively constant throughout the slinky, so the speed of the wave is primarily determined by the mass per unit length.

The speed of a wave on a string is given by the equation:

v = √(T/μ)

where:
v = speed of the wave
T = tension in the medium
μ = mass per unit length of the medium

Since the tension in the slinky is relatively constant and the same for both students, the speed of the wave is primarily determined by the mass per unit length of the medium.

To compare the speeds, we can calculate the mass per unit length for each student's wave:

For the student on the left:
A = 5 cm = 0.05 m
f = 4 Hz

μ_left = (ρ * A^2 * f^2) / g
μ_left = (0.05 kg/m * (0.05 m)^2 * (4 Hz)^2) / 9.81 m/s^2
μ_left = 0.005 kg/m

For the student on the right:
A = 7 cm = 0.07 m
f = 3 Hz

μ_right = (ρ * A^2 * f^2) / g
μ_right = (0.05 kg/m * (0.07 m)^2 * (3 Hz)^2) / 9.81 m/s^2
μ_right = 0.0073 kg/m

Since the speed of the wave is inversely proportional to the mass per unit length of the medium, the student on the left, with a lower mass per unit length, will generate a wave that travels faster. So, the wave generated by the student on the left travels faster.