Wave speed equation

Using the formulae covered in these chapters:

• wave speed
• wave frequency
• wavelength

…we can do some example calculations!

A reminder of the equation

\text{wave speed} = \text{Frequency} \times \text{wavelength}

With symbols:

v = f\lambda

Examples

Calculate the wave speed of a wave with a frequency of 500 Hz and a wavelength of 2 m.

• v=f\lambda (write our formula)
• v=500\times2 (substitute in the values)
• v=1000 m/s (calculate)
• Answer: 1000 m/s.

Calculate the frequency of a wave with a speed of 340 m/s and a wavelength of 0.5 m.

• v=f\lambda (write our formula)
• f=\frac{v}{\lambda} (rearrange it)
• f=\frac{340}{0.5} (substitute in the values)
• f=680 Hz (calculate)
• Answer: 680 Hz.

Calculate the wavelength of a wave with a speed of 1500 m/s and a frequency of 3000 Hz.

• v=f\lambda (write our formula)
• \lambda=\frac{v}{f} (rearrange it)
• \lambda=\frac{1500}{3000} (substitute in the values)
• \lambda=0.5 m (calculate)
• Answer: 0.5 m.

A wave has a frequency of 100 Hz and a wavelength of 3 m. What is its speed?

• v=f\lambda (write our formula)
• v=100\times3 (substitute in the values)
• v=300 m/s (calculate)
• Answer: 300 m/s.

A wave travels at a speed of 600,000 mm/s and has a wavelength of 4 cm. What is its frequency?

• 600,000 mm/s = 600 m/s (convert speed to metres per second)
• 4 cm = 0.04 m (convert wavelength to metres)
• v=f\lambda (write our formula)
• f=\frac{v}{\lambda} (rearrange it)
• f=\frac{600}{0.04} (substitute in the values)
• f=15,000 Hz (calculate)
• Answer: 15,000 Hz.

A wave has a speed of 2 km/s and a frequency of 500 Hz. What is its wavelength?

• 2 km/s = 2000 m/s (convert speed to metres per second)
• v=f\lambda (write our formula)
• \lambda=\frac{v}{f} (rearrange it)
• \lambda=\frac{2000}{500} (substitute in the values)
• \lambda=4 m (calculate)
• Answer: 4 m.