Question

A string on a musical instrument is 50 cm long and its fundamental frequency is 270 Hz. If the desired frequency of 1000 Hz is to be produced, the required length of the string is

• A. 13.5 cm
• B. 2.7 cm
• C. 5.4 cm
• D. 10.3 cm

Answer 1

Answer: (A)

13.5 cm

Answer 2

$n \propto \frac{1}{l} \Rightarrow \frac{l_{2}}{l_{1}} = \frac{n_{1}}{n_{2}} \Rightarrow l_{2} = l_{1}\left( \frac{n_{1}}{n_{2}} \right) = 50 \times \frac{270}{1000} = 13.5cm$