![]() If we go down a note to G we get $392\times 2^$ Hz $= 431$ THz, which is just into the infra-red. This can't be played as a sound wave (air can't vibrate at frequencies that are too high) but as an electromagnetic wave it's a slightly reddish orange. If we go forty octaves up from A we get a note of 483 THz. The A an octave above is 880Hz, and in general if we go $n$ octaves up we get a frequency of $440\times 2^n$. ![]() The A above middle C is defined, for modern instruments, as 440Hz. This is really more or less a coincidence, but because of it, I can point out a relationship between light and colours, just for fun. Having said that, it does happen to be the case that the range of frequencies we can see is just a little short of an octave, ranging from about 440-770 THz. (Are indigo and violet really different colours? Why don't we count aquamarine, right between green and blue?) The seven colours in the rainbow are also somewhat arbitrary. pentatonic scales in blues music) or more (e.g. It's not entirely arbitrary as you say, but there are many other choices that could have been made, and there are other cultures who use fewer notes (e.g. ![]() The seven primary notes in an octave is specific to the western musical tradition. GPT-4 vs ChatGPT.On the most basic level, the answer is a flat no.Teenagers prove Pythagoras using Trigonometry.If you enjoyed this post you might also like:įourier Transforms – the most important tool in mathematics? – how we can use advanced mathematics to understand waves – with applications for everything from WIFI, JPEG compression, DNA analysis and MRI scans. So, modelling waves using trig graphs is an essential part of understanding the physical world. See if you can hear this file – warning it’s a bit painful!Īs well as sound waves, the whole of the electromagnetic spectrum (radio waves, microwaves, infrared, visible light, ultraviolet, x rays and gamma rays) can also be thought of in terms of waves of different frequencies. Which has the equation, y = sin(40,000πt). Babies have a ability to hear higher pitched sounds, and we gradually lose this higher range with age. Again you can listen to this sound file on Wolfram Alpha.Īt the top end of the sound spectrum for adults is around 16,000 – 20,000Hz. Which has the equation, y = sin(1643.84πt). The middle C on a piano is modeled with a wave of 261.626Hz. 20Hz is regarded as the lower range of hearing spectrum for adults – and is a very low bass sound. You can plot this graph using Wolfram Alpha, and then play the sound file to hear what 20Hz sounds like. Sine waves with different Hertz values will each have a distinct sound – so we can cycle through scales in music through sine waves of different periods.Ģ0Hz means 20 periods per second (i.e 1 period per 1/20 second) so we can find the equivalent sine wave by using When modeling sound waves we normally work in Hertz – where Hertz just means full cycles (periods) per second. b is then connected to the period of the function by the formula period = 2π/b. Musical notes can be thought of in terms of sine curves where we have the basic formula: Sine and cosine waves are incredibly important for understanding all sorts of waves in physics.
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