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

Explanation

Explain how to determine the frequency of tuning for k using sonometer.
Working: A transverse stationary or standing wave is produced and hence, at the knife edges P and Q, nodes are formed. In between the knife edges, anti-nodes are formed. If the length of the vibrating element is l then
`l = lamda/2 rArr lamda = 2l`
Let f be the frequency of the vibrating element, T the tension of in the string and `mu` the mass per unit length of the string. Then using equation ,we get
` f = v/lamda = (1)/(2l) sqrt(T/mu)` in Hz ....(1)
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 x density ` =pi r^2 rho = (pi rhod^2)/(4)`
Frequency ` f = v/lamda = (1)/(2l) sqrt( (T)/( (pi d^2 rho)/(4) )`
`therefore f = (1)/(ld) sqrt( (T)/(pid) `