If the length of a vibrating string is changed from l1 to l2=l1/3 while keeping tension and linear density constant, what is the new frequency f2 in terms of the original frequency f1?

March 18, 2026Physics

ScanSolve AI Answer

March 18, 2026

Answer

$f_2 = 3f_1$

Step 1: The fundamental frequency is given by
$f = \frac{1}{2l} \sqrt{\frac{T}{\mu}}$

Step 2: Assuming $T$ and $\mu$ are constant,
$f \propto \frac{1}{l}$

Step 3: Therefore, for two cases,
$f_1 l_1 = f_2 l_2$

Step 4: Given $l_2 = \frac{l_1}{3}$ , substitute:
$f_1 l_1 = f_2 \left( \frac{l_1}{3} \right)$

Step 5: Solve for $f_2$ :
$f_2 = f_1 l_1 \div \frac{l_1}{3}$
$f_2 = f_1 l_1 \times \frac{3}{l_1}$
$f_2 = 3 f_1$

$\boxed{f_2 = 3f_1}$

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The fundamental frequency is given by f = (1)/(2l) sqrt((T)/()) Step 2: Assuming T and are constant, f (1)/(l) Step 3: Therefore, for two cases, f_1 l_1 = f_2 l_2 Step 4: Given l_2 = (l_1)/(3), substitute: f_1 l_1 = f_2 ( (l_1)/(3) ) Step 5: Solve for…

Asked on March 18, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

ScanSolve AI AnswerAnswered on March 18, 2026

Step 1: The fundamental frequency is given by f = (1)/(2l) sqrt((T)/()) Step 2: Assuming T and are constant, f (1)/(l) Step 3: Therefore, for two cases, f_1 l_1 = f_2 l_2 Step 4: Given l_2 = (l_1)/(3), substitute: f_1 l_1 = f_2 ( (l_1)/(3) ) Step 5: Solve for f_2: f_2 = f_1 l_1 ÷ (l_1)/(3) f_2 = f_1 l_1 × (3)/(l_1) f_2 = 3 f_1 f_2 = 3f_1