Wave Speed

Key Stage 3

Meaning

Wave Speed is how quickly a wave travels through a medium.

About Wave Speed

Wave Speed is measured in metres per second.

The wave speed states how quickly energy and information can be transferred by a wave.

Equation

Equation 1

\(v = \dfrac{x}{t}\)

Where:

v = Wave Speed

x = distance traveled

t = time taken to travel

Equation 2

\(v = f \lambda\)

\(v = f \times \lambda\)

Where:

v = Wave Speed

f = frequency of the wave

λ = wavelength of the wave

Key Stage 4

Meaning

Wave Speed is how quickly a wave travels through a medium.

About Wave Speed

Wave speed is a scalar because it has magnitude only.

The SI Unit of wave speed is metres per second.

The wave speed states how quickly energy and information can be transferred by a wave.

Wave speed can change depending on the medium the wave is travelling through.

When a wave enters a new medium it will change in speed.

Equation

Equation 1

\(v = \dfrac{x}{t}\)

Where

v = Wave Speed

x = distance traveled

t = time taken to travel

Equation 2

\(v = f \lambda\)

Where:

v = Wave Speed

f = frequency of the wave

λ = wavelength of the wave

Example Calculations

Finding Wave Speed from Distance Travelled and Time Taken

A scientist observes a wave in a ripple tank. The length of the tank is 0.75m and it takes the wave 1.2 seconds to get from one end of the tank to the other. Calculate the wave speed of the wave correct to two significant figures.	A surfer wants to know how fast the waves are travelling on a windy day. The surfer observes a wave takes 15 seconds to travel between two buoys. The surfer knows the distance between the buoys is 63m. Calculate the speed of the wave correct to two significant figures.
1. State the known quantities x = 0.75m t = 1.2s	1. State the known quantities x = 63m t = 15s
2. Substitute the numbers into the equation and solve. \(v = \dfrac{x}{t}\) \(v = \dfrac{0.75}{1.2}\) \(v = 0.625m/s\) \(v \approx 0.63m/s\)	2. Substitute the numbers into the equation and solve. \(v = \dfrac{x}{t}\) \(v = \dfrac{63}{15}\) \(v = 4.2m/s\)

Finding Wave Speed from Wavelength and Frequency

A water wave has a wavelength of 1.6m and a frequency of 1.5Hz. Calculate the speed of the wave.	A ray of ultraviolet light with a frequency of 7.5x10¹⁴Hz and wavelength of 0.30μm in an optical fibre. Calculate the speed of the wave through that optical fibre correct to 2 significant figures.
1. State the known quantities f = 1.5Hz λ = 1.6m	1. State the known quantities f = 7.5x10¹⁴Hz λ = 0.30μm = 0.30x10^-6m
2. Substitute the numbers into the equation and solve. \(v = f \lambda\) \(v = 1.5 \times 1.6\) \(v = 2.4m/s\)	2. Substitute the numbers into the equation and solve. \(v = f \lambda\) \(v = 7.5 \times 10^14 \times 0.30 \times 10^{-6}\) \(v = 225000000m/s\) \(v \approx 2.3 \times 10^8 m/s\)

Finding Wavelength using Wave Speed and Frequency

A wave with frequency 700Hz travels at a speed of 340m/s. Calculate the wavelength of the wave correct to two significant figures.	A 630MHz radiowave travels at 300,000,000m/s in a vacuum. Calculate the wavelength of this radiowave correct to two significant figures.
1. State the known quantities f = 700Hz v = 340m/s	1. State the known quantities f = 630MHz = 630x10⁶Hz v = 300,000,000m/s = 3x10⁸m/s
2. Substitute the numbers and evaluate. \(v = f \lambda\) \(340 = 700 \times \lambda\)	2. Substitute the numbers and evaluate. \(v = f \lambda\) \(3 \times 10^8 = 630 \times 10^6 \times \lambda\)
3. Rearrange the equation and solve. \( \lambda = \dfrac{340}{700}\) \( \lambda = 0.48571m\) \( \lambda \approx 0.48m\)	3. Rearrange the equation and solve. \( \lambda = \dfrac{630 \times 10^6}{3 \times 10^8}\) \( \lambda = 2.1m\)

Finding Frequency using Wave Speed and Wavelength

A microwave travelling at a speed of 3.0x10⁸m/s has a wavelength of 0.051m. Calculate the frequency of the wave correct to two significant figures.	An ultrasound wave of wavelength 0.125m passes through an Iron block at a speed of 5000m/s. Calculate the frequency of the wave correct to two significant figures.
1. State the known quantities v = 3.0x10⁸m/s λ = 0.051m	1. State the known quantities v = 5000m/s λ = 0.125m
2. Substitute the numbers and evaluate. \(v = f \lambda\) \(3.0 \times 10^8 = f \times 0.051\)	2. Substitute the numbers and evaluate. \(v = f \lambda\) \(5000 = f \times 0.125\)
3. Rearrange the equation and solve. \( f = \dfrac{3.0 \times 10^8}{0.051}\) \( f = 5882352941Hz\) \( f \approx 5900000000Hz\)	3. Rearrange the equation and solve. \( f = \dfrac{5000}{0.125}\) \( f = 40000Hz\)