Question

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

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

Answer 1

Answer: (A)

13.5 cm

The relation between the frequency and the length of the string is

$n\propto \frac{1}{l}$

$\Rightarrow \frac{l_2}{l_1}=\frac{n_1}{n_2}$

$\Rightarrow l_2=l_1\left(\frac{n_1}{n_2}\right)$

$=50\times \frac{270}{1000}=13.5cm$