Question

In an open end organ pipe of length $l$, if the velocity of sound is $v$ then the fundamental frequency will be :

• A. $\frac{v}{2l}$ and all harmonics are present
• B. $\frac{v}{4l}$ and all harmonics are present
• C. $\frac{v}{2l}$ and all harmonics are absent
• D. $\frac{v}{4l}$ and all harmonics are absent

Answer 1

The correct option is A $\frac{v}{2l}$ and all harmonics are present

For first mode of vibration in an open organ pipe of length $l$ ,

$\lambda /2=l$ ,

or $\lambda =2l$ ,

therefore , frequency in this first mode ,

$n_1=v/\lambda =v/2l$ ,

this is called fundamental frequency of open organ pipe or first harmonic .

Now , for second mode of vibration in an open organ pipe,

$\lambda =l$ ,

therefore , frequency in this second mode ,

$n_2=v/\lambda =v/l=2n_1$ ,

this is called second harmonic , as its frequency is twice of the fundamental frequency ,

for third mode of vibration in an open organ pipe,

$3\lambda /2=l$ ,

or $\lambda =2l/3$

therefore , frequency in this third mode ,

$n_3=v/\lambda =v/\left(2l/3\right)=3n_1$ ,

this is called third harmonic , as its frequency is thrice of the fundamental frequency .

Therefore all harmonics (odd and even) are present in an open pipe .