Compute the distance between anti-node and neighbouring node.
For nth mode, the distance between anti-node and neighbouring node is
Let f be the fundamental frequency of the string. If the string is divided into three segments l1, l2 and l3 such that the fundamental frequencies of each segments be f1, f2 and f3, respectively. Show that
For a fixed tension T and mass density µ, frequency is inversely proportional to the string length i.e.
Consider a string in a guitar whose length is 80 cm and a mass of 0.32 g with tension 80 N is plucked. Compute the first four lowest frequencies produced when it is plucked.
The velocity of the wave
The length of the string, L = 80 cm=0.8 m The mass of the string, m = 0.32 g = 0.32 × 10-3kg
Therefore, the linear mass density,
The tension in the string, T = 80 N
The wavelength corresponding to the fundamental frequency f1 is λ1 = 2L = 2 × 0.8 = 1.6 m
The fundamental frequency f1 corresponding to the wavelength λ1
Similarly, the frequency corresponding to the second harmonics, third harmonics and fourth harmonics are
f2 = 2f1 = 559 Hz
f3 = 3f1 = 838.5 Hz
f4 = 4f1 = 1118 Hz