Question

For a certain organ pipe, three successive resonance frequencies are observed at 425, 595 and 765, Hz respectively. Taking the speed of sound in air to be 340 m/s the fundamental frequency of the pipe (in Hz) is

Answer 1

Hint Resonance is defined as the phenomenon where there is the increment of the amplitude that occurs when the frequency of a periodically applied force and is equal to or we can say close to the natural frequency of the system on which it is acting. Based on this concept we can solve this question.

Complete step-by-step answer:
We don’t know which organ pipe is used for it. So, first of all we should take the ratio of all three harmonics.
E.g., 425Hz: 595Hz: 765Hz
$\Rightarrow 5 \times 85Hz:7 \times 85Hz:9 \times 85Hz$
$\Rightarrow (2 \times 2 + 1)85Hz:(2 \times 3 + 1)85Hz:(2 \times 4 + 1)85Hz$
When we saw, each successive harmonic is an odd number.
This is possible only when the organ pipe is closed.
And 85 is common for all harmonics, so the fundamental frequency is 85Hz.

Hence, the answer is 85Hz.

Note It should be known to us that the natural frequency or the fundamental frequency is defined as the lowest possible frequency of a periodic waveform. In case of music, the note is defined as the lowest partial present that can be perceived by us.