Two equations calculate wave speed
Definition
Wave speed
The distance travelled by a wavefront per unit time.
- The frequency-wavelength equation is v=fλv=f\lambdav=fλ.
- The distance-time equation is v=xtv=\dfrac{x}{t}v=tx.
- Use vvv in m/s\text{m/s}m/s, fff in Hz\text{Hz}Hz, λ\lambdaλ and xxx in m\text{m}m, and ttt in s\text{s}s.
Rearrange before substituting
- From v=fλv=f\lambdav=fλ, use f=vλf=\dfrac{v}{\lambda}f=λv or λ=vf\lambda=\dfrac{v}{f}λ=fv.
- From v=xtv=\dfrac{x}{t}v=tx, use x=vtx=vtx=vt or t=xvt=\dfrac{x}{v}t=vx.
- Convert units first: 1 kHz=103 Hz1\ \text{kHz}=10^3\ \text{Hz}1 kHz=103 Hz, 1 MHz=106 Hz1\ \text{MHz}=10^6\ \text{Hz}1 MHz=106 Hz and 1 cm=10−2 m1\ \text{cm}=10^{-2}\ \text{m}1 cm=10−2 m.
Example
Calculating wave speed
- A wave has frequency 8.0 Hz8.0\ \text{Hz}8.0 Hz and wavelength 0.75 m0.75\ \text{m}0.75 m.
- Use v=fλv=f\lambdav=fλ.
- v=8.0×0.75=6.0 m/sv=8.0\times0.75=6.0\ \text{m/s}v=8.0×0.75=6.0 m/s.
Example
Calculating wavelength
- Sound travels at 340 m/s340\ \text{m/s}340 m/s with frequency 680 Hz680\ \text{Hz}680 Hz.
- Use λ=vf\lambda=\dfrac{v}{f}λ=fv.
- λ=340680=0.50 m\lambda=\dfrac{340}{680}=0.50\ \text{m}λ=680340=0.50 m.
Frequency and wavelength vary inversely
- Wave speed is approximately constant for a wave travelling in a fixed medium.
- Because v=fλv=f\lambdav=fλ, doubling frequency halves wavelength when speed is constant.
Common Mistake
- Do not add frequency and wavelength; their product gives wave speed.
- Do not substitute non-SI units without converting them.
Exam technique
- Write the equation, substitute consistent units, calculate and state the final unit.
- Visible stages preserve method marks if an arithmetic error occurs.
Self review
- State both wave speed equations.
- State the SI units of vvv, fff and λ\lambdaλ.
- Rearrange v=fλv=f\lambdav=fλ for λ\lambdaλ.
- What happens to wavelength when frequency doubles at constant speed?
- Why must centimetres be converted?
