Question

how does the frequescy change in a stringed instrument if length of the vibration string is decreased
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Answer 1

The basic formula for the frequency is $\frac{1}{2l} \sqrt{\frac{Tesion}{\pi r^{2} d} }$ .

So, we observe that Frequency is directly proportional to $\frac{1}{2l}$

=>Frequency is inversely proportional to length of string.

=> So, if the length of vibrating string is decreased, the frequency will increase.

=> The sound will be of a higher frequency and of a greater pitch if the length of vibrating string is decreased.