The Wave Equation Flashcards

All 5 cards in this deck

State the wave equation, naming each quantity and its unit.

$v = f\lambda$: wave speed $v$ in m/s, frequency $f$ in Hz, wavelength $\lambda$ in m.

What are the steps to find the wavelength of a wave from its speed and frequency?
e.g. a wave of frequency 5 Hz travelling at 10 m/s

1. Write $v = f\lambda$
2. Rearrange: $\lambda = \dfrac{v}{f}$
3. Substitute: $\lambda = \dfrac{10}{5} = 2$ m

What are the steps to find the speed of a wave from its wavelength and period?
e.g. $\lambda = 6$ m, $T = 0.5$ s

1. Find frequency: $f = \dfrac{1}{T} = \dfrac{1}{0.5} = 2$ Hz
2. Use $v = f\lambda$
3. $v = 2 \times 6 = 12$ m/s

Which unit conversions must you do before substituting into $v = f\lambda$?

Frequency into Hz ($1$ kHz $= 1000$ Hz, $1$ MHz $= 1\,000\,000$ Hz), wavelength into metres ($1$ cm $= 0.01$ m) and speed into m/s ($1$ km/s $= 1000$ m/s).

True or false? If the frequency of a wave doubles while its speed stays the same, the wavelength halves.

True. In $v = f\lambda$, at constant $v$ the frequency and wavelength are inversely proportional.