Question
Give any three differences between progressive waves and stationary waves. A stationary wave is $\text{y}=12\sin300\text{t}\cos^2\text{x}.$ What is the distance between two nearest nodes?
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Answer
| S. No. | Progressive Wave | Stationary Wave |
| 1. | All particles have same phase and amplitude. | Amplitude varies with position. |
| 2. | Speed of motion is same. | Speed varies with position. |
| 3. | Energy is transported. | Energy is not transported. |
| 4. | Same change in pressure and density is with every point. | Pressure and density varies with point. |
$\text{y}=12\sin300\text{t}\cos2\text{x}$
Comparing with equation of stationary wave
$\text{y}=2\text{A}\sin\omega\text{t}\cos\text{kx}$
$\text{k}=2$
Distance between two consecutive nodes $=\frac{\lambda}{2}$ Where $\lambda$ is wavelength
$\text{k}=\frac{2\pi}{\lambda}$
$\Rightarrow\frac{\pi}{\Big(\frac{\lambda}{2}\Big)}=2$
$\therefore \frac{\lambda}{2}=\frac{\pi}{2}$
So, the distance between two nearest nodes is $\frac{\pi}{2}.$
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