Question

Suppose you have a string that is being made to vibrate at a specific frequency, f. The speed of waves on the string is v. The length of the string that is vibrating, L, is adjustable. When the length of the string has been adjusted so that the fundamental standing wave pattern forms, write the expression for L in terms of f and v. (The fundamental standing wave pattern corresponds to nodes at each end of the string and an antinode in the middle.)

L = ?

Is L = v/f the correct answer?

Answer 1

wavelength = twice string length to get node at each end and bulge in middle.

L = (1/2) wavelength

wavelength = speed * period = speed/frequency

so

L = (1/2) v/f