# Relation between frequency of vibrator generator and frequency of waves in a stretched string

Imagine a vibration generator is attached to a stretched string. Will the frequency of the vibration generator be equal to the frequency of the waves produced in the stretched string?

Also, a similar follow up question, imagine I have a tuning fork of a specific frequency forming sound waves in an air column. Will the frequency of that tuning fork be the same as the frequency of the sound waves in the air column? Or will they be different?

Some people have said the frequencies of the waves of the string/of the sound waves will be equal to the vibration generator/tuning fork, respectively. But this doesn't make sense, because the frequency of standing waves changes with temperature. So if the temperature changes, won't the frequency of the standing waves also change, and thus become different from the frequency of the tuning fork/vibration generator? What am I getting wrong here?

Simple answers would be very appreciated, as I am only in Grade 11, and we do not need to go into excessive details about this topic in our syllabus.

• Frequency is determined by the device that is generating that frequency, not by the medium that the frequency is being transmitted through. Mar 31 at 16:41

These natural frequencies are given by $$f_n= nv_t/2L$$, $$f_n=v_l(2n+1)/4L$$, ($$n = 1, 2, 3 ...)$$in which $$v_t$$ is the speed of transverse waves on the string and $$v_l$$ is the speed of longitudinal waves in air. [The air column is assumed to be a pipe open at one end and closed at the other.] It is these natural frequencies which are somewhat temperature-dependent because $$v_t$$ and $$v_l$$ are temperature-dependent. And the frequency of the vibration generator has to be set, or the frequency of the fork has to be chosen, so as to match the natural frequency of the string or column in order to ge the maximum amplitude of standing wave.