dependence of fundamental frequency of vibration of a stretched string on the medium in which it is kept suppose a stretched wire's fundamental frequency in air is 280 Hz. What would be it's fundamental frequency in water ?
(all other conditions of the string remain same)
I looked into the laws of vibrations of stretched strings,  but all of them give information on characteristics of string, but nothing about the surrounding medium.
Please help.
The answer to the question is 243.2 Hz, but I am unable to calculate it myself.  I read all the texts of fundamental modes and harmonics but found no way forward.
 A: the surrounding medium has a characteristic acoustic impedance which can be calculated. if that characteristic impedance is close to that of the vibrating string, then two things will occur: first, the string will be strongly damped and second, the mass of the surrounding medium will begin to couple to the mass of the string and the string will act as if its vibrating mass is increased relative to its tension. both of these effects will reduce the natural frequency of the string. 
Per Sammy Gerbil's suggestion, I will enlarge upon my answer in this edit:
When a resonant system is coupled to a load that extracts power from it, the width of its resonant response peak is broadened and the location of that frequency peak shifts down to a slightly lower frequency. Immersion in water will extract power from the vibrating string and dissipate it by a variety of mechanisms and therefore its resonant frequency will certainly be reduced upon immersion. The first thing I would try is plugging the string's characteristics into the resonance equation and add progressive amounts of damping, to see how strong the damping effect is and whether or not it can account for the frequency shift. 
I'm going off-line now to search for resources and will edit again if I find clues to share.
