Starting from the definitions of wavelength and period, derive the relation $v=f\lambda$ connecting a wave's speed, frequency, and wavelength.

Starting from the definitions of wavelength and period, derive the relation v=fλ connecting a wave's speed, fr

Exercise · Q10

v=f\lambda

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✓ Free question

By definition, the wavelength $\lambda$ is the distance the wave pattern must shift, along the direction of propagation, for it to look exactly the same again (one full wavelength); the period $T$ is the time taken for any one particle -- and hence the whole pattern -- to complete exactly one such cycle.

Since the wave travels a distance of one wavelength $\lambda$ in exactly one period $T$ , its speed (distance travelled per unit time) is:

v = \frac{\text{distance travelled in one period}}{\text{time for one period}} = \frac{\lambda}{T}

Using the definition of frequency, $f=1/T$ , this becomes:

v = \lambda\times\frac{1}{T} = f\lambda

✓Final answer

v=\lambda/T=f\lambda

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Q.Starting from the definitions of wavelength and period, derive the relation $v=f\lambda$ connecting a wave's speed, frequency, and wavelength.

Concept understanding — Wavelength, Frequency and Wave Speed

Q.Starting from the definitions of wavelength and period, derive the relation v=fλv=f\lambdav=fλ connecting a wave's speed, frequency, and wavelength.

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Q.Starting from the definitions of wavelength and period, derive the relation $v=f\lambda$ connecting a wave's speed, frequency, and wavelength.

Unlock everything free for 14 days