What is wavelength? Definition and examples

Wavelength is the size of a sound wave, measured from any point on one wave to the same point on the next wave.

Sound waves are a form of pressure wave, best understood by visualising a wave of water: a series of alternating crests or peaks (compressions) and troughs (rarefactions). This sort of sequence produces a sinusoidal shape: smooth, repeated geometric curves, otherwise known as a sine wave. The spacing of the crests and troughs in a sine wave – pressure variations – is dictated by the vibration of the source of the sound wave. Plotted as a graph with a vertical axis showing pressure, the crests of the waves correspond to regions of higher pressure, and the troughs to regions of lower pressure. 

Wavelength is the size of a wave, measured from any point on one wave to the same point on the next wave. It may be easiest to conceptualise measuring from the top of one crest to the top of the next – that is, the distance between one high-pressure region to the next (or one trough to the next; one low-pressure region to the next). Imagine measuring between the crest of one breaker and another; a distance of, say, a meter means that the wavelength equals one meter. Wavelength can also be expressed as the distance a wave travels before the next wave starts. 

Typically, audible sine waves have wavelengths ranging from just a few centimetres to several meters: the wavelengths of low-frequency waves can reach as much as 17 meters (20 Hertz [Hz]), while the highest frequency wavelengths can be as small as 1.7 centimeters (20,000 Hz). Compared to the wavelengths of visible light (430-790 nanometers), the audible sound wavelengths covers a much larger range – larger by four orders of magnitude (another term for power of 10). 

Wavelength is directly related to frequency and sound speed. Frequency is the amount of waves per second, measured in Hertz – that is, the number of complete cycles that occurs in a particular span of time (typically one second). Sound speed is how fast a wave travels. Therefore, because of the direct relation between wavelength, frequency, and speed, speed divided by frequency equals wavelength; in mathematics, this is rendered as λ = v/f, where wavelength equals λ (the Greek letter lambda), wave speed (or velocity) equals v, and frequency equals f. 

Frequency determines the pitch of a sound, and is inversely proportional to the wavelength of the sound – meaning that, as frequency increases, wavelength decreases. So, the higher the frequency, the shorter the time between waves (ie, the wavelength gets shorter). The reverse is also true: the lower the frequency, the longer the time between waves.

Wavelength is significant because it dictates a sound’s type and characteristics. Long-wavelength sounds, for example, are perceived as low-frequency (bass) sounds. Correspondingly, short-wavelength sounds are perceived as high-frequency (treble) sounds. 

Examples of low-frequency sounds include:

• Thunder
• Large diesel engines
• Bass notes in music
• Vocalizations produced by some of the largest animals, like whales, elephants, and hippos
• Those generated by the ground vibrating at very low frequencies during an earthquake.

Examples of high-frequency sounds include:

• The chirping of birds
• Whistling (caused by air passing through a small opening); this includes dog whistles, which produce such high-frequency sounds that they are inaudible to humans
• The buzzing of mosquitos’ rapidly flapping wings
• Musical triangles
• Screaming children: high-pitched because of the tension and tightness in the vocal cords.

Wavelength also dictates waves’ behavior, with factors affected by frequency including:

• Directionality: lower frequency sounds, with their longer wavelengths, are more omni-directional than sounds with higher frequencies; they spread out in different directions and are audible from greater distances. By contrast, because higher frequency sounds are more directional, they are more likely to be reflected or absorbed by their surroundings
• Reflection and diffraction: in the case of long wavelengths (low frequency sounds), these will bend around objects smaller than themselves – as a result, they are able to travel further without being absorbed or reflected. On the other hand, even when encountering the same objects, short wavelengths (higher frequency sounds) will be reflected off or absorbed. (See also sound diffraction.)

Therefore, a sound with a wavelength of, say, 34 cm in air (1,000 Hz), will not be obstructed by any object with a diameter of less than 34 cm – but a larger object could interfere with or even entirely block this wave.

In practical terms, the effect of wavelength on the behavior of sound can be demonstrated by the experience of sharing a wall with a noisy neighbor. The bass of their music – low frequency sounds, with very long wavelengths – may be clearly audible through the wall. The higher notes, on the other hand, with their short wavelengths, will be less able to pass through the wall, causing it to be muffled.

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Featured photo by A Chosen Soul on Unsplash