Question

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

Answer 1

Sonometer is used for sound-related measurements. Using this device, The following quantities can be determined.

1. The frequency of the tuning fork or frequency of the alternating current.
2. The tension in the string.
3. The unknown hanging mass.

Sonometer

Construction:

The sonometer is made up of a hollow box which 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 11.34. Since only one string is used, it is also known as monochord. The weights are added to the free end of the wire to increase 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.

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 then

`l = lambda/2 => lambda = 2l`

Let f be the frequency of the vibrating element, T the tension of in the string and p the mass per unit length of the string. Then using equation, we get

f = `v/lambda = 1/(2l) sqrt("T"/mu)` in Hertz   ...(1)

Let ρ be the density of the material of the string and d be the diameter of the string. Then the mass per unit length μ

`mu = "Area" xx "density" = pi"r"^2rho = (pirho"d"^2)/4`

Frequency f = `"v"/lambda = 1/(2l) sqrt("T"/((pi"d"^2rho)/4))`

f = `1/(l"d") sqrt("T"/(pirho))`   ....(2)