Physics

Problem

Transverse waves are generated in two uniform steel wires

A

and

B

by attaching their free ends to a fork of frequency 500 Hz. The diameter of wire

A

is half that of

B

and tension in wire

A

is half the tension in wire

B

. What is the ratio of velocities of waves in

A

and

B

? a.

1 : 2

\sqrt{2} : 1

2 : 1

1 : \sqrt{2}

Intuitive explanation

Wave velocity in a string depends on both the tension pulling it tight and the mass per unit length resisting that motion—heavier strings move slower for the same tension. Here, wire $A$ has half the diameter (so one-quarter the cross-sectional area and mass per unit length) but also half the tension. The key is recognizing that velocity scales as $v \propto \sqrt{T/\mu}$ , where $T$ is tension and $\mu$ is mass per unit length, so you need to track how both quantities change between the wires.

Intuitive explanation

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