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)

1 : 2 : 3 : 4

Answer 2

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 loop, 3 loops and 4 loops, the frequencies are in the ratio 1 : 2 : 3 : 4.