1. The two plane polarized waves are $E_1=E_0\,\sin \omega t, \qquad E_2=E_0\,\sin\left(\omega t+\frac{\pi}{3}\right)$

2. Since both waves have the same frequency and same amplitude, and differ only by phase, the amplitude of the resultant is given by phasor addition: $R=\sqrt{E_0^2+E_0^2+2E_0\cdot E_0\cos\phi}$ where the phase difference is $\phi=\frac{\pi}{3}$

3. Substitute: $R=E_0\sqrt{1+1+2\cos\frac{\pi}{3}}$

4. Now, $\cos\frac{\pi}{3}=\frac{1}{2}$ so $R=E_0\sqrt{2+2\cdot \frac{1}{2}}=E_0\sqrt{3}$

5. Numerically, $\sqrt{3}\approx 1.732$ Hence, $R\approx 1.7E_0$

6. Checking options:

   • A: $1.7E_0$ ✅
   • B: $E_0$ ❌
   • C: $0.9E_0$ ❌
   • D: $3.4E_0$ ❌

Therefore, the amplitude of the resultant wave is $\boxed{1.7E_0}$.