Wave speed calculator: v = f × λ

• Speed: a sound wave has a frequency of 50 Hz and a wavelength of 6.8 m. $v = 50 \times 6.8 = 340$ m/s.
• Wavelength: a radio station broadcasts at 100 MHz. Radio waves travel at $3 \times 10^8$ m/s, so $\lambda = 3 \times 10^8 \div (100 \times 10^6) = 3$ m.
• Frequency: a water wave travels at 2 m/s with a wavelength of 0.5 m. $f = 2 \div 0.5 = 4$ Hz.

• All electromagnetic waves travel at $3 \times 10^8$ m/s in a vacuum (and almost that in air).
• Sound in air travels at about 330 to 340 m/s, depending on temperature, and faster in liquids and solids.

If a question involves light or radio and doesn't give the speed, it's usually $3 \times 10^8$ m/s.

The period $T$ is the time for one complete wave: $T = \dfrac{1}{f}$. A wave with a frequency of 50 Hz has a period of $1 \div 50 = 0.02$ s. This comes up with oscilloscope traces, where you read the period from the screen and then find the frequency.

Convert before you substitute, or let the calculator do it and check its conversion step.

• Forgetting to convert MHz or kHz.
• Dividing the wrong way round when rearranging.
• Mixing up wavelength (a distance) and amplitude (the height of the wave).

For transverse and longitudinal waves and more examples, see the wave equation explained.

1. A sound wave has a frequency of 500 Hz and a wavelength of 0.68 m. What is its speed?
2. Red light has a wavelength of about 600 nm. What is its frequency? (Speed of light: $3 \times 10^8$ m/s.)
3. A water wave travels at 1.2 m/s with a frequency of 3 Hz. What is its wavelength?

Answers: 340 m/s; $5 \times 10^{14}$ Hz; 0.4 m.