Question
Download Solution PDFThe fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The disturbance in a medium that carries energy without net movement of particles of the medium is called as wave.
There are two types of wave which are -
1. Transverse wave- It is defined as the wave in which the movement of particles of the medium is perpendicular to the direction of propagation of the wave. It travels in the form of crest and trough.
For example- Movement in strings of a guitar, Ripples on the surface of water.
2. Longitudinal wave- It is defined as the wave in which displacement of particles of the medium is parallel to the direction of propagation of the wave. It travels in the form of compression and rarefractions
.
For example - Sound, Ultrasound.
Standing waves- When two waves of same amplitude and frequency moving in opposite directions combine then standing waves are formed. It is also known as stationary wave.
For example- Musical instruments having strings form stationary waves.
Calculation:
\(v\) is speed of the wave
\(l'\) is length of open organ pipe
Fundamental frequency for open organ pipe is \( \frac{{v}}{{2l}}\)
For closed organ pipe, third harmonic
\( = \frac{{3v}}{{4l}}\)
For open organ pipe, fundamental frequency
\( = \frac{v}{{2l'}}\)
Given,
\(\frac{{3v}}{{4l}} = \frac{v}{{2l'}}\)
\(\Rightarrow l' = \frac{{4l}}{{3 \times 2}} = \frac{{2l}}{3}\)
\(= \frac{{2 \times 20}}{3}\)
= 13.2 cm
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