What is sonometer ? Give its construction and working. Explain how to determine the frequency fo tuning fork using sonometer.

Explanation

Sonometer is used for sound-related measurements.
Using this device, the following quantities can be determined.
(i) the frequency of the tuning fork or frequency of alternating current.
(ii) The tension in the string.
(iii) The unknow hanging mass.

Sonstruction : The sonometer is made up of a hollow box that is one meter long with a uniform metallic thin string attached to it. One end of the string is connected to a hook and the other end is connected to a weight hanger through a pulley as shown in Figure. Since only one string is used, it is also known as monochord. The weights are added to the free end of the wire to increases the tension of the wire. Two adjustable wooden knives are put over the board and their positions are adjusted to change the vibrating length of the stretched wire.
Procedure : A transverse stationary or standing wave is produced. So, at the knife edges P adn Q, nodes are formed. In between the knife edges, anti-node sare formed. In between the knife edges, anti-nodes are formed.
If the length of the vibrating element is l then
`l=(lambda)/(2) rArr lambda=2l`
Let f be the frequency of the vibrating element, T the tention of in the string and `mu` the mass per unit length of the string. then using the the equation `v=sqrt((T)/(mu))` measured in `ms^(-1)`, we get
`f=(v)/(lambda)=(1)/(2l) sqrt((T)/(mu))` in Hertz.
Let `rho` be the density of the material of the string and d be the diameter of the string. then the mass per unit length `mu`.
`mu="Area"xx"Density"= pir^(2)rho`
`=(pirhod^(2))/(4)`
Frequency `f=(v)/(lambda)`
`=(l)/(2l)sqrt((T)/((pid^(2)rho)/(4)))`
`:.f=(1)/(ld) sqrt((T)/(pirho))`