# Wave speed

Wave speed is the speed (velocity) at which a wave is travelling.

The formula for calculating wave speed is:

Wave speed = f λ or v = f λ

Speeding along she frequently (frequency) waved at length.

**NOTE:**

This does not only relate to waves in water but all waves, including light waves and electromagnetic waves.

v = f λ where:

v = wave speed (measured in metres per second – m/s)

f = frequency (measured in hertz – Hz)

λ (pronounced lambda) = wavelength (measured in metres)

**Example 1**

A wave at sea travels with a velocity of 25m/s. If it has a wavelength of 10m, what is its frequency?

**Answer**

Wave speed = frequency x wave length

Divide both sides by wavelength to make frequency the subject,

\frac{Wave\ speed}{wavelength}\ =\ \frac{\strike{wavelength\ }\times frequency}{\strike{wavelength}}

Frequency\ =\frac{Wave\ speed\ }{wavelength}=\ \frac{25}{10}\ =\ 2.5Hz

**Example 2**

Lizzy reads the back label of her microwave oven. It says frequency = 2,450MHz. If the speed of microwaves is 3.00 x 10^{8} m/s, what wavelength are they?

**Answer**

The first thing you must do to answer this question is convert the frequency to the standard units, which means converting from MHz to Hz (1 MHz = 10^{6} Hz). So 2,450 MHz = 2,450 x 10^{6} Hz.

Wave speed = frequency x wave length

Divide both sides by frequency to make wavelength the subject:

\frac{Wave\ speed}{frequency}\ =\ \frac{\strike{frequency}\ \times wavelength}{\strike{frequency}}

wavelength=\frac{Wave\ speed\ }{frequency}=\frac{3\ \times10^{^8}}{2,450\ \times10^6}\ =\ 0.122m

0.122m = 12.2cm

**Example 3**

An electromagnetic wave travels at a speed of 300,000,000 m/s and has a wavelength of 15cm. Calculate the frequency of the electromagnetic wave.

**Answer**

Wave speed = frequency x wave length

Divide both sides by wavelength to make frequency the subject,

\frac{Wave\ speed\ }{wavelength}=\ \frac{\strike{wavelength}\times frequency}{\strike{wavelength}}

Frequency\ =\frac{\ Wave\ speed}{wavelength}

However the wavelength given in the question is not in the standard unit and so must first be converted from cm to metres.

15cm = 0.15m So:

Frequency\ =\ \frac{Wave\ speed\ }{wavelength}=\frac{300,000,000}{0.15}=2,000,000,000\ Hz\ =\ 2GHz

**NOTE:**

We have converted the answer to GHz in this case. There are 1 billion Hz (10^{9}) in 1 GHz, so 2 billion Hz = 2GHz.

**Example 4**

A TV station broadcasts at 500,000 kHz. The waves travel through the air at 300,000,000 m/s. Calculate the wavelength of the waves broadcast by this station.

**Answer**

Wave speed = frequency x wave length

Divide both sides by frequency to make wavelength the subject,

Wave\ speed\ =\ \frac{\strike{frequency}\ \times\ wavelength}{\strike{frequency}}

Wavelength\ =\ \frac{Wave\ speed}{frequency}

Beware, the question gives the frequency in kHz so you will need to convert this to Hz before you can put the figures into the formula.

500,000 kHz = 500,000,000 Hz So:

Wavelength\ =\frac{\ 300,000,000\ }{500,000,000}=\ 0.6m