Question

Explain the construction and working of sonometer hence explain its use to verify first law of vibrating string (Law of length).

Answer 1

Construction: A sonometer is a rectangular hollow wooden sound box. As indicated in the image, a thin uniform metal wire fastened at one end ran over two movable bridges P and Q, then a pulley horizontally, and finally hung vertically with slotted weights attached to the other free end.

Working: Sonometers operate on the resonance principle. The waves on the wire can be made by vibrating a tuning fork while remaining close to it, which produces transverse waves. The reflection of the transverse wave from the bridges generates stationary waves between the two bridges. The distance between the bridges is gradually increased as the vibrating length increases and the fundamental frequency decreases. When the frequency of vibrating length equals the frequency of. tuning fork resonance occurs, as evidenced by increased agitation of the papilla.

Sonometer can be used to verify the laws of a vibrating string.

Verification of first law of vibrating string: The number of tuning forks of known frequencies determines the vibrating lengths in unison (at resonance). n₁, n₂, n₃ ... as l₁, l₂, l₃ ... If the tension and wire are the same (i.e. T and m are constant), then the product n₁l₁, n₂l₂, n₃l₃ ... is determined in each case. It is observed that,

n₁l₁ = n₂l₂ = n₃l₃ = ... = constant

∴ nl =constant

∴ `n ∝ 1/l`  at constant T and m

Thus, law of length is verified.