# I am stuck with standing waves mathematical treatment when I am using a complex function

$$f=Ae^{i\omega t}\big(e^{-ikz}-e^{ikz}\big) = -2iAe^{i\omega t}\sin(kz)$$

This is the displacement equation I got. As it is complex, I used the real part to represent the nth normal mode of standing wave which is having both position and time dependent term as sine function. At $$t=0$$ , this gives me zero amplitude at any point $$z$$. I am following H. J. Pain, The Physics of waves and vibrations book.

• It can be correct! Please notice that the time derivative does not vanish at $t=0$. If this does not help, please clarify what is the difficulty. Feb 4, 2022 at 16:27
• How is this zero at t=0?
– nasu
Feb 4, 2022 at 16:34
• What are you stuck with? Feb 4, 2022 at 16:40
• Hi Tarun. I've replaced the picture of your equation with MathJax; if you need a reference to do this yourself in the future, you can find one here. Feb 4, 2022 at 16:41

The displacement of the standing wave vanishes for any point $$z$$ twice every period. There is nothing wrong here