
A
sonometer is a hollow, rectangular wooden box, about a metre long, and
provided with two or three holes. A thin uniform metallic wire is
supported at one end of the box, which passes over a pulley fixed at the
other end of the box. The free end of the wire supports a pan. A suitable
tension can be applied to the wire by placing appropriate weights in the
pan. The wire is supported by two movable bridges or knife edges along
its length. The vibrating length of the wire can be changed by moving
these bridges.
The sonometer is used:
 To
determine unknown frequency of a given tuning fork.
 To
verify the laws of vibrating strings.
 Experiments Using the Sonometer
Determination of Unknown Frequency
The frequency of the tuning fork is determined by using a
sonometer and a paper rider utilising the resonance phenomenon.
The length of the vibrating wire is adjusted so that the paper rider
placed at the middle of the vibrating wire is thrown off when the
stem of the vibrating tuning fork is brought in contact with the
sonometer.
The frequency is determined using the formula
n =

1


2l



where,




l:

Vibrating length of the wire (measured)


T:

Tension applied = M'g



where M': load applied to the pan


m:

linear density of the wire = M/L
where M: mass of the wire of total length L.

 Verification of Laws of Vibrating String
 A set of tuning forks of different frequencies n_{1}, n_{2}, … are used and their
corresponding vibrating lengths, l_{1}, l_{2}, … are determined.
The tension is maintained constant.
It is found that n_{1}l_{1} = n_{2}l_{2} = n_{3}l_{3} … = constant
This verifies the law of length (n µ

1


l


)

 A tuning fork of frequency n_{1} and its resonant
vibrating length l_{1} for a tension T_{1} is determined.
This vibrating length l_{1} is maintained
constant. For a set of tuning forks of frequencies n_{2}, n_{3}, n_{4}… etc, the tension is
adjusted such that resonance is obtained. If T_{2}, T_{3},
T_{4}… are the corresponding tensions, it is observed that
n_{1}




=

n_{2}




=

n_{3}




=… = constant.

 This verifies the law of tension (n µ )
 Wires of different mass per unit length m_{1}, m_{2}, m_{3} … etc. are taken and the same tension T is applied to
these wires. Using the same tuning fork of frequency n, the vibrating length
for each wire is determined. If l_{1}, l_{2}, l_{3} … are the
corresponding lengths, it is observed that
l_{1}


=
l_{2}


=
l_{3 }


… = constant

Þ l
µ

1




for T, n constant.

By first law n µ

1


l


\ n µ

1




for constant T and l

 This verifies the law of mass per unit length.

