Question

When a string fixed at its both ends vibrates in $1$ loops, $2$ loops $3$ loops and $4$ loops, the frequencies are in the ratio:

• A. $1:1:1:1$
• B. $1:2:3:4$
• C. $4:3:2:1$
• D. $1:4:9:16$

Answer 1

The correct option is B $1:2:3:4$

When the string vibrates in loops $n$, its frequency is, ${\upsilon }_n=\frac{n\nu }{2L}$
where $L$ is the length of the string and $\nu$ is the velocity of the wave.
$\therefore$ When the string fixed at its both ends vibrates in $1$ loops, $2$ loops $3$ loops and $4$ loops, the frequencies are in the ratio $1:2:3:4$.