Q.22 The string of a guitar is 80 cm long and has a fundamental frequency of 112 Hz. If a guitarist wishes to produce a frequency of 160 Hz, where should he press the string?
Best answer
Answer: He should press the string so that the vibrating length is 56 cm, i.e. 24 cm from one end (56 cm from the other end).
For a stretched string \(n = \dfrac{1}{2l}\sqrt{\dfrac{T}{m}}\); with the same tension and mass per unit length, \(n \propto \dfrac{1}{l}\), so \(n_1 l_1 = n_2 l_2\).
\[l_2 = \frac{n_1 l_1}{n_2} = \frac{112 \times 80}{160} = 56\ \text{cm}\]The string should be pressed at a point 56 cm from the bridge, that is, \(80 - 56 = 24\) cm from the other (nut) end, so that only 56 cm of the string vibrates.
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