Question

A 1 cm long string vibrates with fundamental frequency of 256 Hz. If the length is reduced to $\frac{1}{4}cm$ keeping the tension unaltered, the new fundamental frequency will be

• A. 64
• B. 256
• C. 512
• D. 1024

Answer 1

Answer: (D)

1024

Answer 2

$n \propto \frac{1}{l}$⇒ $\frac{n_{2}}{n_{1}} = \frac{l_{1}}{l_{2}}$⇒ $n_{2} = \frac{l_{1}}{l_{2}}n_{1} = \frac{1 \times 256}{1/4} = 1024Hz$