Question

Imagine that you create a second harmonic in a short and long rope (both of the same mass density and with the same mass suspended at the end). which of the three quantities: λ, f (frequency), and v (velocity), would be larger, smaller or the same for both rope?

Answer 1

The velocity and frequency would be different for the short and long rope, while the wavelength would be the same.

Step-by-step explanation:

When creating a second harmonic in a short and long rope with the same mass density and a mass suspended at the end, the velocity (v) and frequency (f) would be different for both ropes, while the wavelength (λ) would be the same. This is because the velocity of a wave on a string depends on the tension and linear mass density of the string. Since the rope lengths are different, the tensions would be different, resulting in different velocities. The frequency is determined by the velocity and wavelength, so it would also be different for the two ropes.