JEE Main & Advanced Physics Wave Mechanics Sonometer

(1) It is an apparatus, used to produce resonance (matching frequency) of tuning fork (or any source of sound) with stretched vibrating string.

(2) It consists of a hollow rectangular box of light wood. The experimental fitted on the box as shown.

(3) The box serves the purpose of increasing the loudness of the sound produced by the vibrating wire.

(4) If the length of the wire between the two bridges is l, then the frequency of vibration is \[n=\frac{1}{2l}\sqrt{\frac{T}{m}}=\sqrt{\frac{T}{\pi {{r}^{2}}d}}\]

(r = Radius of the wire, d = Density of material of wire) m = mass per unit length of the wire)

(5) Resonance : When a vibrating tuning fork is placed on the box, and if the length between the bridges is properly adjusted then if \[{{(n)}_{Fork}}={{(n)}_{String}}\to \] rider is thrown off the wire.

(6) Laws of string

(i) Law of length : If T and m are constant then \[n\propto \frac{1}{l}\]

\[\Rightarrow \] nl = constant \[\Rightarrow \] \[{{n}_{1}}{{l}_{1}}={{n}_{2}}{{l}_{2}}\]

(ii) Law of mass : If T and l are constant then \[n\propto \frac{1}{\sqrt{m}}\]

\[\Rightarrow \] \[n\sqrt{m}=\]constant \[\Rightarrow \] \[\frac{{{n}_{1}}}{{{n}_{2}}}=\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\]

(iii) Law of density : If T, l and r are constant then \[n\propto \frac{1}{\sqrt{d}}\]

\[\Rightarrow \] \[n\sqrt{d}=\] constant \[\Rightarrow \] \[\frac{{{n}_{1}}}{{{n}_{2}}}=\sqrt{\frac{{{d}_{2}}}{{{d}_{1}}}}\]

(iv) Law of tension : If l and m are constant then \[n\propto \sqrt{T}\] \[\Rightarrow \] \[\frac{n}{\sqrt{T}}=\]constant

\[\Rightarrow \] \[\frac{{{n}_{1}}}{{{n}_{2}}}=\sqrt{\frac{{{T}_{2}}}{{{T}_{1}}}}\]