Question

Standing waves on a 1.0m long string that is fixed at both ends are seen at successive frequencies of 24 hz and 36hz. what is the fundamental frequency and wave speed

Answer 1

The multiples of the fundamental frequency are the standing wave frequencies for a string.

Since 24 Hz and 36 Hz are consecutive frequencies, the fundamental frequency must be 36 −12 = 12 Hz. Meaning that the standing wave with frequency 36 Hz is the third harmonic (i.e., m = 3),

The wave speed fulfills the equation f1 = v / 2L where f1 is the fundamental frequency and L is the length of the string

So we can say that:

v = 2Lf1

= 2(1.0)(12)

= 24 m/s