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Calculations with wave speed, frequency and wavelength

Use the same method for every wave calculation. Write down the equation, substitute the values with their units, then calculate. The main equation is wave speed = frequency × wavelength. Rearranged, wavelength = speed ÷ frequency and frequency = speed ÷ wavelength.

Always convert to standard units first. Frequency must be in hertz and wavelength in metres. To change kHz to Hz multiply by 1000, and to change cm to m divide by 100. For example, a 3 kHz note is 3000 Hz. A sound of frequency 440 Hz travelling at 330 m/s has a wavelength of 330 ÷ 440 = 0.75 m. Ripples with frequency 5 Hz and wavelength 0.03 m have a speed of 5 × 0.03 = 0.15 m/s. A wave with a speed of 60 m/s and a frequency of 50 Hz has a wavelength of 1.2 m. A 5 Hz wave with a wavelength of 4 m has a speed of 20 m/s, and a 7 cm wavelength is 0.07 m.

Two more relationships help. The period is 1 ÷ frequency, so a wave of frequency 5 Hz has a period of 0.2 s, and a wave of frequency 10 Hz has a period of 0.1 s. A wave also travels a distance = speed × time, so at 0.15 m/s it covers 1.5 m in 10 s.

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