Why is pitch inversely proportional to length of an instrument? I think i know meaning of frequency but if anyone can also explain frequency according to higher level physics it shall be great.


1 Answer 1


When making a sound with an instrument, what you hear is the base frequency and higher harmonic frequencies which have increasing frequencies. The frequencies of the higher harmonic frequencies are multiples of the base frequency. And since the lowest frequency wave is usually the most energetic, it's the frequency that one would consider the pith of the tone. Then, you may ask what causes the base frequency to increase when we shrink the instrument. This is caused by decreasing the wavelength. If we take a string that's attached on its ends, the base wavelength is going to be twice the length of the string. This is better visualized on the following image:

higher harmonics

When you shrink the instrument you lower the base wavelength $L$ and the frequency increases like $f\sim\frac{1}{L}$. So it is an inverse relation to the size, just like you wrote.


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