Physics - Sound Wave Question with Solution | TestHub

Displacement equation $y=A\sin \omega t-B\cos \omega t$ Let $A=a\cos \theta$ and $B=a\sin \theta$ So, $A^2+B^2=a^2$ $$a=\sqrt{A^2+B^2}$$ Then, $y=a\cos \theta \sin \omega t-a\sin \theta \cos \omega t$ $$y=a\sin (\omega t-\theta )$$ which is the equation of simple harmonic oscillator. The amplitude of the oscillator $$=a=\sqrt{A^2+B^2}$$