A wire of length 10 m and mass 3 kg is suspended from a rigid support. The wire has uniform cr

step 1 In this question we will learn about some basic concept of the oscillation and waves. The questi

A wire of length 10 m and mass 3 kg is suspended from a...

A wire of length $10 \mathrm{~m}$ and mass $3 \mathrm{~kg}$ is suspended from a rigid support. The wire has uniform cross sectional area. Now a block of mass $1 \mathrm{~kg}$ is suspended at the free end of the wire and a wave having wavelength $0.05 \mathrm{~m}$ is produced at the lower end of the wire. What will be the wavelength of this wave when it reached the upper end of the wire? (A) $0.12 \mathrm{~m}$ (B) $0.18 \mathrm{~m}$ (C) $0.14 \mathrm{~m}$ (D) $0.10 \mathrm{~m}$

A wire of length $10 \mathrm{~m}$ and mass $3 \mathrm{~kg}$ is suspended from a rigid support. The wire has uniform cross sectional area. Now a block of mass $1 \mathrm{~kg}$ is suspended at the free end of the wire and a wave having wavelength $0.05 \mathrm{~m}$ is produced at the lower end of the wire. What will be the wavelength of this wave when it reached the upper end of the wire?
(A) $0.12 \mathrm{~m}$
(B) $0.18 \mathrm{~m}$
(C) $0.14 \mathrm{~m}$
(D) $0.10 \mathrm{~m}$

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Key Concepts

Wave Propagation on a String

This concept explains that waves traveling along a string or wire are disturbances that propagate due to the tension in the medium. Their behavior is governed by properties such as tension, mass per unit length, and the medium’s rigidity, which together determine how fast the wave moves.

Tension Variation Along the Wire

For a suspended wire, the tension is not uniform throughout its length; it increases toward the top because each point must support the weight of the material below it in addition to any attached masses. This variation in tension affects the local wave speed along the wire.

Wave Speed Dependence on Tension

The speed at which a wave travels in a string is given by the square root of the tension divided by the linear mass density, a relationship expressed as v = ?(T/?). This means that in regions of higher tension the wave travels faster. Since tension increases upward in a hanging wire, the wave speed will be greater at the upper end.

Frequency Invariance in a Medium

When a wave travels along a single medium, the frequency remains constant even when other parameters such as tension vary. This invariance of frequency implies that changes in wave speed are accompanied by proportional changes in wavelength, as the relation v = f? must hold.

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