Question

If the length of an A string on a violin is decreased by one quarter, what is the resonant frequency of the string, rounded to the nearest Hz?

• A. $587$
• B. $564$
• C. $765$
• D. $248$

Answer 1

The correct option is A $587$

It is given that $f=\frac{v}{2l}$

Now, when Length is decreased by Quarter ,remaining length will be $=l-\frac{l}{4}=\frac{3l}{4}$

New frequency $f^{\prime }=\frac{v}{2\left(\frac{3l}{4}\right)}$

$f^{\prime }=\frac{4}{3}\frac{v}{2l}$

$f^{\prime }=\frac{4}{3}f$

$f^{\prime }=\frac{4}{3}\times 440$

$f^{\prime }=586.6$ which is close to $587$

Therefore Answer is $\left(A\right)$