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Sound Waves: Characteristics and Applications

Wavelength, frequency and time period

Find a sound wave's wavelength, frequency and time period.

Wavelength (λ, "lambda") is the distance from one crest to the next (or one trough to the next). It is measured in metres. On the graph it is one full wave: from a point back to the same height, moving the same way. Two points at the same height but one going up and the other going down are only half a wave apart.

One oscillation is one full cycle at a point: the density goes from highest, to lowest, and back to highest.

Frequency (ν, "nu") is how many oscillations happen at a point each second. It is measured in hertz (Hz): 1 Hz = one oscillation per second. Like the rpm written on a fan: how many turns each second.

Time period (T) is the time for one complete oscillation, in seconds.

Linking them: ν = 1/T. If one cycle takes T seconds, then in one second you get 1/T cycles. A shorter time period means a higher frequency. Example: 10 oscillations in 2 s means frequency = 10 ÷ 2 = 5 Hz, and time period = 1 ÷ 5 = 0.2 s.

Reading a picture: waves packed tightly together mean a high frequency; waves stretched out mean a low frequency.

Everyday sounds mix many frequencies. A tuning fork, or whistling, gives nearly one frequency.

Try it on a phone. With an app such as Phyphox, sing Sa, Re, Ga, Ma, Pa, Dha, Ni, Sa. You'll see the frequency is lowest for the first Sa and rises with each note.

Frequency = oscillations ÷ time, in hertz. Time period = 1 ÷ frequency.
Wavelength, amplitude, frequency and time period.

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