A 2.00 m-long rope, having a mass of 80 g, is fixed at one end and is tied to a light string at the other end. The tension in the string is 256 N. Find the frequencies of the fundamental and the first two overtones.
10 Hz, 30 Hz, 50 Hz
Since one end is tied to a light string on the other side. At this point an antinode will be formed and a node will be formed at the fixed end.
given m = 80g = 0.08 kg
L = 2m
μ = mL = 0.082 = 0.04 kgm
tension,T = 256
v = √ = √ = 160.2 = 80 ms−1
fundamental frequency is given by v4L
f0 = 804 × 2 = 10 Hz
The first overtone is the 3rd harmonic and is given by 30 Hz.
The second overtone is the 5th harmonic and is given by 50 Hz