Question

The string of a violin has a frequency of $440cps$. If the violin string is shortend by one fifth, its frequency will be changed to

• A. $440cps$
• B. $880cps$
• C. $550cps$
• D. $2200cps$

Answer 1

Answer: (D)

$2200cps$

F = frequency of wave

n = order of harmonic

c = speed of wave

l = length of string

$f=440$

$l_2=\frac{1}{5}{l}_1$

$f=\frac{nc}{2l}$

$\therefore f\propto \frac{1}{l}$

$\therefore \frac{f_1}{f_2}=\frac{l_2}{l_1}$

$\frac{f_1}{f_2}=\frac{l_2}{l_1}\Rightarrow \frac{440}{f_2}=\frac{\frac{1}{5}{l}_1}{l_1}$

$\frac{440}{f_2}=\frac{1}{5}\Rightarrow f_2=5\times 440$

$=2200$ Hz