Standing Waves on a string lab help! Here is a description of what the lab was i

Question

Standing Waves on a string lab help!

Here is a description of what the lab was in case you need it: In this lab, waves on a string with two fixed ends will be generated by a string vibrator. The student will determine the frequency of the generator and keep this frequency for the remainder of the experiment. Wavelength=velocity/frequency. Since the frequency is fixed, the wavelength of the waves can only be changed by chaining the speed of the waves. Students will adjust the tension in the string until 1, 2, or 3 half wavelength of a wave fit into the length of the string. Then frequency of the string and the vibrator drives the string into resonance. The amplitude increases and the standing waves can easily be observed.

the directions say "now make generalized observations to help you explain the following:"

a) as mass (or tension) increases what do you have to do to the frequency of the vibrator to get the string to vibrate at its fundamental frequency (as a single piece? Explain why this happens with physic reasoning and equations.

b) As length decreases what do you have to do to frequency of the vibrator to get the string to vibrate at its fundamental frequency (as a single piece)? Use physics reasoning and equations to explain why this happens.

I'm very confused! If you could explain the answer and why its the answer that would be very helpful.

Explanation / Answer

fundamnetal frequency of a string is given by

f = (1/2L) * sqrt (T/u)

where T is tension

u is mass per unilt

f is directly prop to T and

f is inversly proportioal to mass

so to have same ff,

if m is increased , f of vibrator has to be decreased

---------------------------------------------

f is directly proportioal to l ) from above formula

so

as L decrases, to keep same fundamental freq, f has to be decreased

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