Question

Show that the frequencies of first three harmonics of an open organ pipe are in the ratio 1 : 2 : 3

Answer 1

First Harmonic or Fundamental Frequency :
First Harmonic should  at least have an antinode at each end with node included between them.
Vibrating length , l=λ/2
⇒λ=21
n1=V/λ where V is the velocity of sound in air.
                 ∴  n₁=V/2l --------------(1)

Second harmonic : 
Second harmonic should have atleast one node and antinode between than the fundamental frequency .
Vibrating length, l=λ
Then n2=V/λ=V/l=2V/2l
                    ∴n2=2n1----------(2)

Third harmonic : 
Third Harmonic should will have three nodes and fore antinodes
Vibrating lenth, l=3λ/2
⇒λ=2l/3
then
n3=3V/2l
                   ∴n3=3n1----------(1)
By comparing equation 1, 2 and 3 we say that....
 frequencies of first three harmonics of an open organ pipe are
 in the ratio 1 : 2 : 3

Answer 2

it is true write the first second and third harmonic s of open pipe and it will come like f1= v/2l____1

f2=2f1______2

f3=3f1_______3.

so hope this is helpful...