All the waves have different phases.
The given transverse harmonic wave is:
\(y(x,t)=3.0\,sin(36\,t+0.018x+\frac{\pi}{4})...(i)\)
For x = 0, the equation reduces to:
\(y(0,t)=3.0\,sin(36\,t+\frac{\pi}{4})\)
Also, ω=\(\frac{2\pi}{T}=36\,rad/s^{-1}\)
\(∴T=\frac{\pi}{8}s\)
Now, plotting y vs. t graphs using the different values of t, as listed in the given table.
t(s) | 0 | \(\frac{7}{8}\) | \(\frac{2T}{8}\) | \(\frac{3T}{8}\) | \(\frac{4T}{8}\) | \(\frac{5T}{8}\) | \(\frac{6T}{8}\) | \(\frac{7T}{8}\) |
y(cm) | \(\frac{3\sqrt2}{2}\) | 3 | \(\frac{3\sqrt2}{2}\) | 0 | \(\frac{-3\sqrt2}{2}\) | -3 | \(\frac{-3\sqrt2}{2}\) | 0 |
For x = 0, x = 2, and x = 4, the phases of the three waves will get changed. This is because amplitude and frequency are invariant for any change in x. The y-t plots of the three waves are shown in the given figure.
A sub-atomic particle of mass \( 10^{-30} \) kg is moving with a velocity of \( 2.21 \times 10^6 \) m/s. Under the matter wave consideration, the particle will behave closely like (h = \( 6.63 \times 10^{-34} \) J.s)
Find the mean and variance for the following frequency distribution.
Classes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
Frequencies | 5 | 8 | 15 | 16 | 6 |