Consider a string of length 1m, fixed at both ends, with tension τ = 16 n and mass/length μ = 0.01 kg/m. for each of the first 4 modes, sketch the mode shape, label the nodes and antinodes and calculate the resonant frequency.

f_n= 80 Hz

Explanation:

For first four nodes there are five nodes and four antinodes and it is called a frequency of four nodes also called as frequency of fourth over tune

resonance frequency is given by

Given problem

L=1 m

τ= 16 N

μ= 0.01 kg/m = linear density of the string

for 4 nodes

n= 4

therefore,

f_n= 80 Hrz

Explanation:

For given 4 modes there 4 nodes and 4 anti-nodes

A strings with four modes are given in figure

from the data given in question we have

L = 1 m

so resonant frequency is given as

Fn = 80 Hz

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explanation: