Question

The harmonics which are present in a pipe, open at one end are

• A. odd harmonics
• B. even harmonics
• C. even as well as odd harmonics
• D. None of the above

Answer 1

Answer: (A)

Organ pipes are the musical instruments which are used for producing musical sound by blowing air into the pipe.
Longitudinal stationary waves are formed on account of superposition of incident and reflected longitudinal waves.
Wavelength of closed organ pipe is
$\lambda =\frac{4L}{(2n-1)}$
Putting n = 1, 2, 3 ... we find that
${\lambda }_1=4L,\frac{4L}{3},\frac{4L}{5},...$
So, frequency of vibration corresponding to modes
n = 1, 2, 3, ... is
$v_1=\frac{v}{{\lambda }_1},\frac{v}{4L}=v_1$
$v_2=\frac{v}{{\lambda }_2}=\frac{v}{4L/3}=\frac{3v}{4L}=3v_1$
$v_3=\frac{v}{{\lambda }_3}=\frac{v}{4L/5}=\frac{5v}{4L}=5v_1$
$\therefore v_3:v_2:v_1...=1:3:5:....$
So, only odd harmonics are present.