Properties of Waves (DP IB Physics: HL): Revision Note

The graph below shows a travelling wave.

Determine:

(a) The amplitude A of the wave, in m.

(b) The frequency f of the wave, in Hz.

Answer:

(a) Identify the amplitude A of the wave on the graph 

• The amplitude is defined as the maximum displacement from the equilibrium position (x = 0)

• The amplitude must be converted from centimetres (cm) into metres (m)

A = 0.1 m

(b) Calculate the frequency of the wave

Step 1: Identify the period T of the wave on the graph 

• The period is defined as the time taken for one complete oscillation to occur

• The period must be converted from milliseconds (ms) into seconds (s)

T = 1 × 10^–3 s

Step 2: Write down the relationship between the frequency f and the period T 

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

Step 3: Substitute the value of the period determined in Step 1

$f=\frac{1}{1\times {10}^{-3}}=1000\mathrm{Hz}$

The wave in the diagram below has a speed of 340 m s^–1.

Determine the wavelength of the wave.

Answer:

A travelling wave has a period of 1.0 μs and travels at a velocity of 100 cm s^–1.

Calculate the wavelength of the wave, in m.

Answer:

Step 1: Write down the known quantities

• Period, T = 1.0 μs = 1.0 × 10^–6 s

• Velocity, v = 100 cm s^–1 = 1.0 m s^–1

Note the conversions:

• The period must be converted from microseconds (μs) into seconds (s)

• The velocity must be converted from cm s^–1 into m s^–1

Step 2: Write down the relationship between the frequency f and the period T 

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

Step 3: Substitute the value of the period into the above equation to calculate the frequency 

$f=\frac{1}{1\times {10}^{-6}}=1\times {10}^6$

Step 4: Write down the wave equation

$v=f\lambda$

Step 5: Rearrange the wave equation to calculate the wavelength λ

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

Step 6: Substitute the numbers into the above equation 

$\lambda =\frac{1.0}{1.0\times {10}^6}=1.0\times {10}^{-6}\mathrm{m}$

You must be able to interpret different properties of waves from a variety of graphs. You may recognise that calculating the time period and wavelength looks very similar (the distance for one full wave). This is the time period if the x-axis is time. If the x-axis is distance, then this distance is the wavelength.

Pay very close attention to units. If you want a frequency in Hertz, then the time period must be in seconds and not milliseconds.