![]() ![]() The exact mixture of waves determines the precise shape of the total wave different mixtures produce waves of different forms.Ī deeper answer to the question can now be given. The other waves have frequencies $f = 2$, $f=3$, and $f = 4$, so that they oscillate twice, three times, and four times as fast as the dominant wave, respectively these are the harmonics, or overtones, of the fundamental frequency. The dominant frequency is by definition the lowest, and in the plot it is set to $f = 1$. ![]() In each case the wave is synthesized from four simple waves of the form $\sin(2\pi f t)$, in which $f$ is the frequency. Waves of the same (dominant) frequency but of different forms are shown in Fig. ![]() Different mixtures produce different wave forms. In each case the wave (shown on the right) is synthesized from four elementary sine waves (shown on the left). Figure 7.1: Waves of the same (dominant) frequency, but of different forms. ![]() A violin and a flute sound different because they produce different wave forms. And waves of different forms are easily distinguished by the ear. But our ears know nothing of the construction and playing of instruments how do they actually distinguish the sounds? The answer is that the sound waves generated by different instruments come with different forms, even when they come with the same (dominant) frequency. It is not surprising, therefore, that different instruments should produce different sounds. Shouldn't these waves make the same impression on our ears and be heard as identical sounds?Īn element of answer is that the violin and the flute are made from different materials - wood for the violin, brass for the flute - and use different methods to produce the sound - a bowed string for the violin, a column of air for the flute. Why do a violin and a flute playing the same note sound so different? They are, after all, generating sounds waves of the same frequency. The material covered in this chapter is also presented in Boas Chapter 7, Sections 3, 4, 5, 7, 8, and 9. NOTE: Math will not display properly in Safari - please use another browser ![]()
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