The Wave Equation (Cambridge (CIE) IGCSE Physics): Revision Note

A wave has a wavelength of 5 cm and a frequency of 6.6 kHz. Calculate its wave speed.

[4]

Answer:

Step 1: List the known quantities

• Wavelength, $\lambda$ = 5 cm

• Frequency, $f$ = 6.6 kHz

Step 2: Write out the wave speed equation

$v=f\times \lambda$ [1 mark]

Step 3: Convert the wavelength into metres

$\lambda =\frac{5}{100}=0.05\mathrm{m}$ [1 mark]

Step 4: Convert the frequency into hertz

$f=6.6\times 1000=6600\mathrm{Hz}$ [1 mark]

Step 4: Calculate the wave speed

$v=6600\times 0.05$

$v=330\mathrm{m}/\mathrm{s}$ [1 mark]

Be careful with units: speed is usually measured in m/s, so make sure to convert wavelength into metres and frequency into hertz before substituting.

Watch for wavelengths in cm, speeds in km/s, and frequencies in kHz or MHz — 1 kHz = 1000 Hz and 1 MHz = 1 000 000 Hz.

A wave has a speed of 0.27 m/s and the distance from a crest to the nearest trough is 0.75 cm. Calculate:

a) The frequency of the wave [3]

b) The period of the wave [2]

Answer:

Part (a)

Step 1: List the known quantities

• Wave speed, $v$ = 0.27 m/s

• Distance from a crest to the nearest trough, $d$ = 0.75 cm

Step 2: Calculate the wavelength in metres

• The wavelength can be measured from one crest to the next crest, so

$\lambda =2\times 0.75=1.5\mathrm{cm}$

$\lambda =\frac{1.5}{100}=0.015\mathrm{m}$ [1 mark]

Step 3: Write out the wave speed equation

$v=f\times \lambda$

Step 4: Rearrange the equation to calculate the frequency

$f=\frac{v}{\lambda }$

Step 5: Put the values into the equation

$f=\frac{0.27}{0.015}$ [1 mark]

$f=18\mathrm{Hz}$ [1 mark]

Part (b)

Step 1: List the known quantities

• Frequency, $f$ = 18 Hz (from part (a))

Step 2: State the equation relating time period and frequency

$T=\frac{1}{f}$

Step 3: Calculate the answer

$T=\frac{1}{18}$ [1 mark]

$T=0.056s\left(2\mathrm{s}.\mathrm{f}.\right)$ [1 mark]

When stating equations make sure you use the right letters. For example, use $\lambda$ for wavelength, not L or W.

If you cannot recall the symbols under pressure, a word equation will still earn the first mark — but $v$, $f$ and $\lambda$ are the forms used in the question papers, so learn them.