Question

When a string fixed at its both ends vibrates in $1$ loop, $2$ 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

Answer: (B)

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