The Wave Equation (Edexcel IGCSE Science (Double Award) (Modular): Physics Unit 2): Revision Note

Visible light has a frequency of about 6 × 10¹⁴ Hz.

How long does it take for one complete cycle of visible light to enter our eyes?

 Answer:

Step 1: List the known values

• Frequency, f = 6 × 10¹⁴ Hz

Step 2: State the relationship between frequency and time period 

• This question involves quantities of time and frequency, so the equation which relates time period and frequency of a wave is:

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

Step 3: Substitute the known values into the equation and calculate the time period 

$T=1÷(6\times {10}^{14})=1.67\times {10}^{-15}\mathrm{s}$

• Therefore, it takes 1.67 × 10^-15 s (to 2 decimal places) for one wave of visible light to pass our eyes

A certain sound wave moves at about 330 m/s and has a time period of 0.0001 seconds.

Calculate:

a) The frequency of the sound wave

b) The wavelength of the sound wave

 Answer:

Part (a)

Step 1: List the known quantities

• Time period, T = 0.0001 s

Step 2: Write out the equation relating time period and frequency

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

Step 3: Rearrange for frequency, f, and calculate the answer

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

$f=\frac{1}{0.0001}$

$f=10000\mathrm{Hz}=1\times {10}^4\mathrm{Hz}$

Part (b)

Step 1: List the known quantities

• Wave speed, v = 330 m/s

• Frequency, f = 1 × 10⁴ Hz

Step 2: Write out the wave speed equation

$v=f\times \lambda$

Step 3: Rearrange the equation to calculate the wavelength

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

Step 4: Use the frequency you calculated in part (a) and put the values into the equation

$\lambda =\frac{330}{\left(1\times {10}^4\right)}$

$\lambda =0.033\mathrm{m}$

A local radio station broadcasts at a frequency of 200 kHz. The wavelength of these radio waves is 1500 m.

Calculate the speed of these radio waves and state an appropriate unit.

 Answer:

Step 1: List the known quantities

• Frequency, f = 200 kHz = 200 000 Hz

• Wavelength, λ = 1500 m

Step 2: Write out the wave speed equation

• This question requires wave speed, so state the equation linking wave speed, wavelength and frequency:

$v=f\times \lambda$

Step 3: Substitute the known values to calculate the wave speed 

$v=200000\times 1500$

$v=300000000=3\times {10}^8$

Step 4: State the unit with the answer

• The units for speed are m/s

• Therefore, the speed of these radio waves is 3 × 10⁸ m/s

When stating equations make sure you use the right letters:

For example, use λ for wavelength, not L or W

If you can’t remember the correct letters, then state the word equations required

Be careful with units: wavelength is usually measured in metres and speed in m/s, but if the wavelength is given in cm you might have to give the speed in cm/s

Likewise, watch out for the frequency given in kHz: 1 kHz = 1000 Hz