Question

A stretched string is vibrating at $500$ hertz. If the tension is increased four times, the frequency shall become.

• A. $1,000$ hertz
• B. $500$ hertz
• C. $250$ hertz
• D. $1,500$ hertz

Answer 1

The correct option is A $1,000$ hertz

As frequency $\left(f\right)$ is directly proportional to the square root of tension$\left(t\right)$.

$f\propto \sqrt{t}$

$\frac{f_1}{f_2}=\sqrt{\frac{t_1}{t_2}}$

$\frac{500}{f_2}=\sqrt{\frac{1}{4}}$

$⟹f=1,000$ hertz