Find the frequencies for the first four harmonics for a string that is 2.0 m lon

Question

Find the frequencies for the first four harmonics for a string that is 2.0 m long, has linear mass density of 2.5 X10 ^-2 kg/m and is under a tension of 40 N.
For the third overtone, what are the positions of nodes and antinodes? Left end is at 0 and right end is at 2.0 m Find the frequencies for the first four harmonics for a string that is 2.0 m long, has linear mass density of 2.5 X10 ^-2 kg/m and is under a tension of 40 N.
For the third overtone, what are the positions of nodes and antinodes? Left end is at 0 and right end is at 2.0 m
For the third overtone, what are the positions of nodes and antinodes? Left end is at 0 and right end is at 2.0 m

Explanation / Answer

V = Sqrt( 40/ 2.5x10^-2)

= 40 m/s

length = 2 meters

Time period = 2/ 40 = 0.05 seconds

There are 3 loops in third overtone Nodes between 0,2 so interval is (2-0)(/3+1) = 0.5

there nodes occur at[ 0, 0.5, 1, 1.5 ,2 ]

Anti nodes occur between the nodes so,

[0.25, 0.75, 1.25 , 1.75]

Frequncy = 20 Hertz for the first harmoic

For the second harmonic , distnance = L/2, there fore

F2 = 20 Hz x 2 = 40 Hz, and similary distance = L/3 , therefore,

F3 = 20 Hz x 3 = 60 Hz

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