Show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3 loops, and 4 loops, the frequencies are in the ratio 1:2:3:4.

Answer:

When n = 1,

f1 = v/2L

This is known as the fundamental frequency.

When n = 2,

f2 = 2(v/2L)

This is known as the first overtone.

When n = 3,

f3 = 3(v/2L)

This is known as the second overtone.

When n = 4,

f4 = 4(v/2L)

This is known as the third overtone.

The tone is always the same as the fundamental frequency.