MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Stationary Waves Page 4

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6.

Sonometer

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:

1. To determine unknown frequency of a given tuning fork.
2. 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
1. A set of tuning forks of different frequencies n1, n2, … are used and their corresponding vibrating lengths, l1, l2, … are determined. The tension is maintained constant.
It is found that
n1l1 = n2l2 = n3l3 … = constant

This verifies the law of length (n µ

 1 l

)

1. A tuning fork of frequency n1 and its resonant vibrating length l1 for a tension T1 is determined. This vibrating length l1 is maintained constant. For a set of tuning forks of frequencies n2, n3, n4… etc, the tension is adjusted such that resonance is obtained. If T2, T3, T4… are the corresponding tensions, it is observed that
 n1

=

 n2

=

 n3

=… = constant.

1. This verifies the law of tension (n µ )
2. Wires of different mass per unit length m1, m2, m3 … 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 l1, l2, l3 … are the corresponding lengths, it is observed that
 l1 = l2 = l3 … = constant

Þ l µ

 1

for T, n constant.

By first law n µ

 1 l

\ n µ

 1

for constant T and l

1. This verifies the law of mass per unit length.

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