This Is the Sine Wave!!

1. Wow, This is the Sine Wave.

The graph below is the sine wave of 500Hz frequency. Sine waves are also called a pure tone, and they are used in audiometric exams, etc.

The frequency of 500Hz means, if the sound continues for 1 second, the wave of the same shape is repeated 500 times. That is, the length of one wave is "1 second divided by 500," or 0.002 second, or 2ms (milliseconds). The graph below shows the 10ms period, and the wave of the same shape is repeated 5 times within.

2. What if You Change the Frequency...

Now, let's change the frequency. The left graph shows the 250Hz sine wave, the center one shows the 500Hz sine wave (the same as the above graph), and the right one shows the 1000Hz sine wave. The smaller the figure of Hz is, the lower the sound is, and the bigger the figure is, the higher the sound is.

3. What if You Change the Amplitude...

Now, let's change the amplitude (the size of the wave). If the wave is small the sound is small, and if the wave is big the sound is big.

4. What if You Mix 2 Sine Waves...

Now, let's add up 2 sine waves. At a certain time t, given that the amplitude of wave 1 is x1 and the amplitude of wave 2 is x2, the amplitude of the compound wave of waves 1 and 2 is x1 + x2. The graphs below shows the adding of 250Hz and 500Hz sine waves mentioned above.

250Hz sine wave500Hz sine waveCompound wave
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In the above example, the amplitudes of the 2 sine waves were the same. Now, let's add up 2 sine waves with different amplitudes.

250Hz sine wave500Hz sine wave with small amplitudeCompound wave
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Now, let's add a sine wave of other frequency.

250Hz sine wave1000Hz sine waveCompound wave
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You can make various waves (various sounds) by changing the amplitude and frequency of added sine waves. You see?

5. What if You Mix a Bit More...

Well, do you wanna mix one more wave? OK, let's mix 3 sine waves. Now, try mixing sine waves of various frequencies. You can get waves of more complicated shapes.

Mixed wavesResultant waves
100Hz
 300Hz
 2300Hz
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100Hz
 500Hz
 2100Hz
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100Hz
 700Hz
 1300Hz
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100Hz
 500Hz
 1100Hz
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100Hz
 400Hz
 1300Hz
 make

Well, the resultant waves, from top to bottom, sound like /i/(the vowel of eat), /e/(the vowel of get), /a/(the vowel of ah), /o/(the vowel of oh) and /u/(the vowel of do), don't they? No?, mmm...

Written in July 1997.
Masahiko Komatsu koma2@twics.com