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

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