-->

Mechanical Properties Of Fluids

Question
CBSEENPH11018889

The fundamental frequency of a sonometer wire increases by 7Hz on increasing the tension by 10-25%. Find the fundamental frequency of sonometer wire.

Solution
We know that fundamental frequency of sonometer wire is directly proportional to the square root of tension in the string.
straight i. straight e. comma space space space space space straight nu space proportional to space square root of straight T space space space space space space space space space space space space space... space left parenthesis 1 right parenthesis thin space

When space the space tension space is space increased space by space 10.25 space percent sign comma
straight i. straight e. comma space by space 0.1025 space straight T comma space the space fundamnetal space frequency space
becomes space straight nu space plus space 7.

Therefore comma space

straight nu space plus space 7 space proportional to space square root of 1.1025 space straight T end root space space space space space space space space... space left parenthesis 2 right parenthesis space

Now comma space dividing space left parenthesis 2 right parenthesis space by space left parenthesis 1 right parenthesis comma space we space get

fraction numerator straight nu space plus space 7 over denominator space space straight nu end fraction space equals space square root of 1.1025 space straight T end root space equals space 1.05 space

rightwards double arrow space straight nu space plus space 7 space equals space 1.05 space space space straight nu space

rightwards double arrow space 0.05 space straight nu space space equals space 7 space

rightwards double arrow space straight nu space space equals space 140 space Hz
140 Hz is the fundamental frequency of sonometer wire.