MHT CET202617 April 2026Evening ShiftPhysicsWaves and SoundActual
In a sonometer experiment, the fundamental frequency of vibration of wire is ' n₁ ' when wire is stretched by hanging a metal bob. If the bob is completely immersed in water, the frequency of vibration of wire becomes ' n₂ '. The relative density of the metal of the bob is
Options
- An₁ n₁ - n₂
- Bn₁ - n₂ n₂
- Cn₁^2 n₁^2 - n₂^2
- Dn₂^2 n₁^2 - n₂^2
Correct answer
C. n₁^2 n₁^2 - n₂^2
Step-by-step solution
The fundamental frequency of a sonometer wire is given by n = 1 2L T m , where T is the tension and m is the linear mass density. When the bob is in air, the tension is T₁ = V g , where V is the volume and is the density of the bob. n₁ = 1 2L V g m When the bob is completely immersed in water, the tension becomes T₂ = V g - V _w g = V( - _w)g , where _w is the density of water. n₂ = 1 2L V( - _w)g m Squaring and taking the ratio of the frequencies: n₁^2 n₂^2 = T₁ T₂ = V g V( - _w)g = - _w Dividing the numerator and