Groan

Groan(Groan) with, pitch (pitch of sound, sound high) Two which barely differs sound has sounded, at each fundamental tone frequency. This time the sound of two has been audible as been one sound,, but when pitch leaves is to, both are audible as another two sounds.

It will try considering the groan mathematically. As the simplest case, two whose strength and phase are equalSign waveYou think. Angular frequency < Math> \omega< /math> On center, on front and back width < Math> 2\alpha< /math> When just of two sounds where angular frequency slips are thought, the sound which is synthesized becomes as follows.

< Math> \sin (\omega-\alpha) t + \sin (\omega+\alpha) t< /math>

< Math> = (\sin\omega t \cos\alpha t - \cos\omega t \sin\alpha t)

+ (\sin\omega t \cos\alpha t + \cos\omega t \sin\alpha t) < /math>

< Math> = 2 \sin\omega t \cos\alpha t< /math>

As for result, angular frequency < Math> \omega< /math> In sound, angular frequency < Math> \alpha< /math> The wave is piled. Because of this as for strength < Math> 2\alpha< /math> So to fluctuate, thisGroanSo it is.

Furthermore, here < Math> T< /math> It is time. As for deformation of formula trigonometric function. In addition, in order for numerical formula to become easy to see, angular frequency was used, but angular frequency < Math> \omega< /math> Frequency < Math> F< /math> As for relationship < Math> \omega = 2\pi f< /math> Because is, thinking at frequency, it is the same.

For example, frequency the sound of 440Hz ( pitch name, A), you hear one one wave in the human and cannot divide. But, 4Hz (4 times) being to be in 1 seconds, you hear the frequency of the groan of 438Hz and 442Hz can divide easily and.

Red the wave of frequency 15Hz, green is the wave of frequency 17Hz and the wave which blue superposes and you can see the groan of 2Hz, in order (in the figure for the wave to be visible clearly, extremely low frequency is chosen).

Related item

• sound wave
• frequency modulation
• Tuning (music)

Flange effect

When two sound sources whose frequency is close relatively are repeated, frequency amount of that frequency The wave of sound per second occurs. Furthermore, when complicated frequency and the formant is included mainly, Also the new timbre occurs, with respect to hearing becomes beautiful sound.

As for the Beatles who can know this empirically, the recording tape of music The edge (the flange) by touching by the hand, feed rate of the tape While changing delicately, repeating two same musics, you recorded. As a result, it became the strangely beautiful timbre. To call this, the flange effect, in especially music industry, that effect The equipment which brings is named フランジャー.