(i) Yes, except at the nodes
Yes, except at the nodes
No, 0.042 m
Explanation:
(i) All the points on the string oscillate with the same frequency, except at the nodes which have zero frequency.
All the points in any vibrating loop have the same phase, except at the nodes.
All the points in any vibrating loop have different amplitudes of vibration.
The given equation is:
y(x,t)=0.06 sin \((\frac{2\pi}{3}x)\) cos (120 πt)
For x = 0.375 m and t = 0
Amplitude= Displacement= 0.06 sin \((\frac{2\pi}{3}x)\) cos 0
= 0.06 sin \((\frac{2\pi}{3}× 0,375)×1\)
= 0.06 sin (0.25 π)=0.06 sin \((\frac{\pi}{4})\)
= 0.06× \(\frac{1}{\sqrt2}=0.042\, m\)
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 |