Physics

Problem

A sinusoidal wave of frequency

500\,\text{Hz}

travels along a wire. Points

A

and

B

on the wire are

12\,\text{cm}

apart. Point

A

attains maximum positive displacement and,

0.60\,\text{ms}

later, point

B

attains its maximum positive displacement for the first time. Calculate the speed of the wave. a)

120\,\text{m s}^{-1}

200\,\text{m s}^{-1}

133\,\text{m s}^{-1}

267\,\text{m s}^{-1}

Intuitive explanation

The key is recognizing that the time delay between two points reaching the same phase tells you how the wave is propagating through space. Since point $B$ reaches its maximum $0.60\,\text{ms}$ after point $A$ , the wave has traveled some distance in that time—but that distance might be the separation plus extra wavelengths. Use the period (from frequency) to figure out what fraction of a wavelength corresponds to the time delay, then solve for wave speed using $v = f\lambda$ .

Intuitive explanation

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