English: $\ \frac{\partial}{\partial x}\frac{\partial u}{\partial x} = \left( cos\ \theta\ \frac{\partial}{\partial r} - \frac{sin\ \theta\ }{r}\frac{\partial}{\partial\theta} \right)\left( cos\ \theta\ u_{r} + \frac{sin\ \theta\ }{r}u_{\theta} \right)$ $cos\ \theta\ \frac{\partial}{\partial r}\left( cos\ \theta\ u_{r} + \frac{sin\ \theta\ }{r}u_{\theta} \right) = \theta\ u_{rr} - cos\ \theta\ sin\ \theta\ \left( u_{\theta r}.\frac{1}{r} - \frac{1}{r^{2}}u_{\theta} \right)$ $\frac{sin\ \theta\ }{r}\frac{\partial}{\partial\theta}\left( cos\ \theta\ u_{r} + \frac{sin\ \theta\ }{r}u_{\theta} \right) = \frac{sin\ \theta\ }{r}\left( u_{r\theta}cos\ \theta\ - sin\ \theta\ u_{r} \right) +$ $\frac{sin\ \theta\ }{r^{2}}\left( sin\ \theta\ u_{\theta\theta} + cos\ \theta\ u_{\theta} \right)$ $u_{xx} = \theta\ u_{rr} - \frac{sin\ 2\theta\ }{r}u_{r\theta} + \frac{1}{r^{2}}u_{\theta}cos\ \theta\ sin\ \theta\ + \frac{\theta\ }{r}u_{r} + \frac{\theta\ }{r^{2}}u_{\theta\theta} + \frac{sin\ \theta cos\ \theta\ \ }{r^{2}}u_{\theta}$ $\frac{\partial}{\partial y}\frac{\partial u}{\partial y} = \left( sin\ \theta\ \frac{\partial}{\partial r} + \frac{cos\ \theta\ }{r}\frac{\partial}{\partial\theta} \right)\left( sin\ \theta u_{r}\ + \frac{cos\ \theta\ }{r}u_{\theta} \right)$ $sin\ \theta\ \frac{\partial}{\partial r}\left( sin\ \theta u_{r}\ + \frac{cos\ \theta\ }{r}u_{\theta} \right) = \theta\ u_{rr} + cos\ \theta\ sin\ \theta\ \left( u_{r\theta}.\frac{1}{r} - \frac{1}{r^{2}}u_{\theta} \right)$ $\frac{cos\ \theta\ }{r}\frac{\partial}{\partial\theta}\left( sin\ \theta u_{r}\ + \frac{cos\ \theta\ }{r}u_{\theta} \right)$ $\frac{cos\ \theta\ }{r}\left( cos\ \theta u_{r}\ + sin\ \theta\ u_{r\theta} \right)$+ $\frac{cos\ \theta\ }{r^{2}}\left( u_{\theta\theta}cos\ \theta\ - sin\ \theta\ u_{\theta\theta} \right)$ $u_{yy} = \theta\ u_{rr} + \frac{sin\ 2\theta\ }{r}u_{r\theta} - \frac{1}{r^{2}}u_{\theta}cos\ \theta\ sin\ \theta\ + \frac{\theta\ }{r}u_{r} + \frac{\theta\ }{r^{2}}u_{\theta\theta} - \frac{sin\ \theta cos\ \theta\ \ }{r^{2}}u_{\theta}$ So now the wave equation becomes for 0 < r < R, and 0 ≤ θ ≤ 2π, and t > 0 so these are the three variable you have u(r,θ,t).
Telugu: $\ \frac{\పాక్షిక}{\పాక్షిక x}\frac{\పాక్షిక u}{\పాక్షిక x} = \ఎడమ(cos\ \teta\ \frac{\పాక్షిక}{\పాక్షిక r} - \frac{sin\ \teta\ {{r}\frac{\పాక్షిక}{\పాక్షిక\tta} \కుడి)\ఎడమ(cos\ \teta\ u_{r} + \frac{sin\ \theta\ {{r}$cos u_{\theta} \ \frac{\పాక్షిక}{\పాక్షిక r}\ఎడమ( cos\ \teta\ u_{r} + \frac{sin\ \theta\ }{r}u_{\teta} \కుడి) = \teta\ u_{rr} - cos\ \teta\ sin\ \teta\ \ఎడమ( u_{\teta r}.\frac{1}{r} - \frac{1}{r^{2}}u_{\theta} కుడి)$ $\frac{sin\ \theta\ {{r}\frac{\పాక్షిక}{\పాక్షిక\teta}\ఎడమ(cos\ \theta\ u_{r} + \frac{sin\ \teta\ {{r}u_{\teta} \కుడి) = \frac{sin\ \teta\ {r}\ఎడమ( u_{r\theta}cos\ \theta\ - sin\ \theta\ u_{r} \ {r^{2}}}\sin\ \teta\ u_{\teta\teta} + cos\ \teta\ u_{\teta} \కుడి)$ $u_{xx} = \teta\ u_{rr} - \frac{sin\ 2\teta\ {{r}u_{r\theta} + \frac{1}{r^{2}}u_{\theta}\theta\sin\ frac{\teta\ {{r}u_{r} + \frac{\teta\ {{r^{2}}u_{\teta\teta} + \frac{sin\ \teta cos\ \teta\ \teta\ {{r^{2}}u_{\teta}$ $\frac{\పాక్షిక}{\పాక్షిక y}{\పాక్షిక y} = \ఎడమ(sin\theta\frac\theta\frac\frac\theta\frac{\పాక్షిక y}rac{cos\ \theta\ {{r}\frac{\పాక్షిక}{\పాక్షిక\teta} \కుడి)\ఎడమ(sin\ \theta u_{r}\ + \frac{cos\ \theta\ {r}u_{\theta} \కుడి)$ $sin\teta\ \frac{\పాక్షిక}{\పాక్షిక r}\ఎడమ( sin\ \theta u_{r}\ + \frac{cos\ \theta\ {frac{cos\ \theta\ {u_ frac{cos\ \theta\ {frac{cos\ \theta\ కుడి) = \teta\ u_{rr} + cos\ \theta\ sin\ \theta\ \ఎడమ( u_{r\theta}.\frac{1}{r} - \frac{1}{r^{2}}u_{\theta} \కుడి)$ $\frac{cos\ \theta\ }{r}\frac{\పాక్షిక}{\పాక్షిక\teta}\sin\ \theta}\sin\ \theta u_}\sin\ \theta}\sin\theta\\r}{r}\ \frac{cos\ r}u_{\theta} \కుడి)$ $\frac{cos\ \theta\ {{r}\ఎడమ( cos\ \theta u_{r}\ + sin\ \teta\ u_{r\theta} \కుడి)$\frac{cos\ \teta\ {{r^{2}}\ఎడమ(u_{\theta\theta}cos\ \theta\ - sin\theta\ u_{\theta\tta} \కుడి)$ $u_{ yy} = \theta\ u_{rr} + \frac{sin\ 2\teta\ {{r}u_{r\theta} - \frac{1}{r^{2}}u_{\teta}cos\teta\ \teta\ \frac{\teta\ {r}u_ u_{r} + \frac{r^{2}}u_{\r^{2}}u_{\theta\r}u_{r} + \frac{r^{2}}u_{r {2} r < < R, మరియు 0 ≤ 2θ 2π, మరియు t ≤ 2θ ≤ 2π, మరియు t ≤ 2π, మరియు t > 0 అనే మూడు వేరియబుల్ లు ఉన్నాయి. θ,t).