# Relationship Between Sound Wavelength and Reflections

In many ways, the phenomenon of reflection is simple to understand. We are familiar with reflections from mirrors, as well as echoes from a distant rock cliff. Light or sound bounces from a surface, returning to the source or another position. This is specular reflection. However, not all reflections are so simple.

First, reflection is wavelength dependent. Wavelength, denoted as λ, measures the literal length of a waveform, that is, one complete cycle of a sound wave. A waveform can be measured between any two corresponding points on the cycle such as peaks or where the waveform crosses the zero axis. Looked at another way, wavelength is the distance a wave travels in the time it takes to complete one cycle. Frequency, denoted as f, is the number of cycles per second (or hertz). Frequency and wavelength are related:

λ = c/f

where λ = wavelength, ft

c = speed of sound = 1130 ft/sec

f = frequency, Hz

From this relationship, for example, we see that a 20-Hz waveform is about 56.5-ft long, and a 20,000-Hz waveform is a little less than 3/4 in long. Depending on the problem at hand, it is proper to refer to a sound in terms of either its wavelength or its frequency.

Wavelength of sound is important because it determines how large a surface must be to reflect a sound. Sound of a certain wavelength (or frequency) will only reflect from a surface that is sufficiently large. In particular, this is shown in the expression:

x > 4λ

where x = surface dimension, ft λ = wavelength, ft

This shows us that sound reflects from a surface if the surface length or width dimension is greater than 4 times the wavelength of the sound. For example, a 1-kHz sine wave is about 1.1-ft long; thus it will reflect from a surface with dimension of 4.4 ft. Also, clearly, signals higher in frequency than 1 kHz will reflect from this surface. It is interesting to note that reflecting panels can thus act as high-pass filters, only reflecting frequencies that are above a certain cutoff frequency. Also, note that in this kind of specular reflection, the angle of reflection equals the angle of incidence. As we will see in other post related to diffusion, when x = λ, sound is not reflected; instead, it is diffused.

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December 9, 2016 @ 7:06 pm

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