Question

Scenario: A rope of length 2.00 m is fixed at both ends under 200 N of tension. We observe the 2nd harmonic of this rope occurs at 54 Hz.

Part A: What is the fundamental frequency of this rope in Hz?

Part B: What is the mass density of this rope in g/m?

Answer 1

A)
The second harmonic can be written as,
f2 = 2 * f1
Where f2 is the fundamental frequency.
f1 = f2 / 2
= 54 / 2
= 27 Hz

B)
The fundamental frequency can be written as, f1 = v / 2L
Where v is the velocity of waves and L is the length of the rope.
v = f1 * 2L
= 27 * 2 * 2
= 108 m/s

The velocity can be also written as, v = SQRT[T / ]
Where T is the tension and is the mass density.
Squaring the above equation,
v² = T/
= T / v²
= 200 / 108²
= 0.0171 kg/m
= 17.1 g/m