wavefunction is QM
Source Link
Qmechanic
  • 178.4k
  • 37
  • 454
  • 2032

Why is whatdo we hear the square of the wave function?

Assume we superpose two waves of frequencies $\omega_1, \omega_2$. Then what we get are beats. Adding the two sines gives us $$\psi = A\sin(\omega_1 t) + A\sin(\omega_2 t) = 2 \sin \left(\frac{\omega_1 + \omega_2}2\right)\cos \left(\frac{\omega_1 - \omega_2}2\right)$$$$\psi = A\sin(\omega_1 t) + A\sin(\omega_2 t) = 2 \sin \left(\frac{\omega_1 + \omega_2}2\right)\cos \left(\frac{\omega_1 - \omega_2}2\right).$$

Then I'd say that the frequency of beats we'd hear is $\frac{\omega_1 - \omega_2}2$. On the other hand, someone told me that it's ${\omega_1 - \omega_2}$ in fact, because what we hear is the square of the wave function $\psi^2$.

Why?

Why is what we hear the square of the wave function

Assume we superpose two waves of frequencies $\omega_1, \omega_2$. Then what we get are beats. Adding the two sines gives us $$\psi = A\sin(\omega_1 t) + A\sin(\omega_2 t) = 2 \sin \left(\frac{\omega_1 + \omega_2}2\right)\cos \left(\frac{\omega_1 - \omega_2}2\right)$$

Then I'd say that the frequency of beats we'd hear is $\frac{\omega_1 - \omega_2}2$. On the other hand, someone told me that it's ${\omega_1 - \omega_2}$ in fact, because what we hear is the square of the wave function $\psi^2$.

Why?

Why do we hear the square of the wave?

Assume we superpose two waves of frequencies $\omega_1, \omega_2$. Then what we get are beats. Adding the two sines gives us $$\psi = A\sin(\omega_1 t) + A\sin(\omega_2 t) = 2 \sin \left(\frac{\omega_1 + \omega_2}2\right)\cos \left(\frac{\omega_1 - \omega_2}2\right).$$

Then I'd say that the frequency of beats we'd hear is $\frac{\omega_1 - \omega_2}2$. On the other hand, someone told me that it's ${\omega_1 - \omega_2}$ in fact, because what we hear is the square of the wave $\psi^2$.

Why?

Source Link
marmistrz
  • 557
  • 3
  • 19

Why is what we hear the square of the wave function

Assume we superpose two waves of frequencies $\omega_1, \omega_2$. Then what we get are beats. Adding the two sines gives us $$\psi = A\sin(\omega_1 t) + A\sin(\omega_2 t) = 2 \sin \left(\frac{\omega_1 + \omega_2}2\right)\cos \left(\frac{\omega_1 - \omega_2}2\right)$$

Then I'd say that the frequency of beats we'd hear is $\frac{\omega_1 - \omega_2}2$. On the other hand, someone told me that it's ${\omega_1 - \omega_2}$ in fact, because what we hear is the square of the wave function $\psi^2$.

Why?