The 0.3 power law of Stevens in Psycho - Acoustics

A series of stimuli were presented in an irregular order and the person was asked to assign numbers to them; he could assign any number he liked to the first stimulus, but thereafter the ratios of the numbers he assigned should correspond to the ratios of his subjective impressions.


When Smitty (S.S. Stevens) plotted the data obtained in this manner against the stimulus intensity, he repeatedly found not a logarithmic function but a power function.


When loudness was the attribute to be judged, for example, every time the intensity was increased by 10 dB, the number assigned to it doubled. Whereas Frechner would have predicted that logarithmic increments in intensity would be judged as constant increments in loudness, Stevens found that they yielded contrast ratios in loudness.


The loudness, L, was proportional to the energy to the 0.3 power: L=k(I to the 0.3). From this it follows that the underlying invariance is the simple principle that equal stimulus ratios produce equal subjective ratios.


Αν κατάλαβε καλα η Κανελινα...


Οταν η ισχύς για παράδειγμα δεκαπλασιαζεται (+10dB) η ακουστοτητα διπλασιάζεται.


Ο Στηβενς βρήκε λοιπόν πειραματικά οτι η ακουστοτητα ειναι αναλογη της ενέργειας είσαι την δύναμη του 0,3. L=k(I στην 0,3).


Έβαλαν τους αριθμούς στην εξίσωση η Κανελινα και οι σοφοί γλάροι και είδαν οτι ένας ενισχυτής 10 Watt πρεπει να ακούγεται διπλάσια δυνατά απο έναν ενισχυτη 1 Watt. Ένας ενισχυτής 100W διπλάσια απο έναν 10W.  Και ένας 1000W διπλάσια απο έναν 100W.


Αυτιά ειναι ο νόμος του Στηβενς στην ψυχο-ακουστική.


Reference, πηγή:


Stanley Smith Stevens, a Biographical Memoir by George A. Miller, National Academy of Sciences