Question

An open organ pipe of length L vibrates in a second harmonic mode. The pressure vibration is maximum
(A). At the two ends
(B). At a distance L/4 from either and inside the tube
(C). At the midpoint of the tube
(D). None of these

Answer 1

- Hint: In these types of questions remember the basic concepts of harmonic mode and also the formula of the length of an organ pipe .i.e.$L={\displaystyle \frac{n\lambda }{2}}$to find the modes of vibrations putt n = 1, 2, 3 ……..then find the correct option.

Complete step-by-step solution -

We know that for an open organ pipe, the length L is given as $L={\displaystyle \frac{n\lambda }{2}}$
Where $\lambda$ is the wavelength of the wave and n is an integer and by putting n = 1, 2, 3 ….... we get the modes of vibration.

Let substituting n=1 gives for first harmonics and let n=2 gives second harmonics and so on.
Here, an open organ pipe of length L vibrates in second harmonic mode,
Hence the length of the pipe is
$L=\lambda$$L={\displaystyle \frac{2\lambda }{2}}$
Therefore, the length of the pipe at both open ends is equal to the distance between two adjacent antinodes. The nodes are at distance ${\displaystyle \frac{\lambda }{4}}$ ​from the antinodes.
Because there is no particle displacement at nodes, there is maximal pressure vibration.
Hence, in an open organ pipe, the pressure vibration is maximum at a distance ${\displaystyle \frac{L}{4}}$​(since, L=λ) from either end inside the tube.

Note: In the above question a term harmonic frequency is used which can be explained as; every natural frequency produced by an object or instrument has its characteristic vibrational mode or standing wave pattern. Such patterns are produced only at different vibrational frequencies within the object or instrument; such frequencies are known as harmonic frequencies, or merely harmonics. The resulting disturbance to the medium is unpredictable and non-repetitive at any frequency other than a harmonic frequency.