## To use a sonometer to determine the frequency of tuning fork

OBJECT:- To use a sonometer to determine the frequency of a given tuning fork.

**(A) APPARATUS REQUIRED**

- A sonometer
- Tuning fork
- Rubber pad
- Kilogram weights
- Micrometer screw gauge

**(B) THEORY**

The fundamental frequency of vibration of stretched spring is given by,

$$f=\frac1{2L}\sqrt{\frac T\mu}$$

$$f=\frac1{2L}\sqrt{\frac T{m/l}}$$

$$f=\frac1{2L}\sqrt{\frac{T\times l}m}$$

$$f=\frac1{2L}\sqrt{\frac{T\times l}{\rho\times v}}$$

$$f=\frac1{2L}\sqrt{\frac{T\times l}{\rho\times A\times l}}$$

$$f=\frac1{2L}\sqrt{\frac{T\times4}{\pi d^2}}$$

**Where**,

T=tension in the wire.

l=resonating length of the wire.

ρ=density of the material of the wire.

d=diameter of the material of the wire.

**(C) OBSERVATION:- **

- Frequency of the tunning fork=319Hz.
- The density of the material of the wire(ρ)=8890kg\m^3
- Diameter of the wire(d)=0.488mm=4.8*10^(-4)m

**OBSERVATION TABLE**

No. of obs | Load(m) in kg | Tension (t=mg) in | Resonating length ‘L’ in ‘m’ | $$f=\frac1{2l}\sqrt{\frac{T\times4}{\rho\times\pi d^2}}$$ |

1) | 1 | 10 | 0.126 | 312.742 |

2) | 1.5 | 15 | 0.153 | 315.436 |

3) | 2 | 20 | 0.174 | 320.275 |

4) | 2.5 | 25 | 0.19 | 327.924 |

Mean |

1276.377 |

319.04 |

**(D) CONCLUSION:-**

Hence, by using the sonometer, we can determine the frequency of the given tuning fork.

**(E) RESULT:- **

Hence, the frequency of the given tuning fork was found to be 319.04Hz.

**(F) PRECAUTIONS:-**

- Wires should not be plucked with nails.
- The fork should be gently stroked on a rubber pad.
- After the end of the experiment, do not leave the wire in a stretched condition.
- The weight should be put below the exact limit. Being overweight may cross the elastic limit.