\( \frac{2\pi \lambda}{a}\)
\( \frac{2\pi a}{\lambda}\)
\( \frac{\lambda}{a}\)
\( \frac{a}{\lambda}\)
The general equation for a travelling wave is:
y = A sin(kx − ωt)
where:
A is the amplitude.
k is the wave number ($k = \frac{2\pi}{\lambda}$).
ω is the angular frequency ($\omega = 2\pi f$).
f is the frequency.
Comparing this with given equation: y = C sin($\frac{2\pi}{\lambda}$(at − x)), we get ω = $\frac{2\pi a}{\lambda}$.
Since ω = 2πf: 2πf = $\frac{2\pi a}{\lambda}$
$f = \frac{a}{\lambda}$
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)
List I | List II | ||
A | Down’s syndrome | I | 11th chormosome |
B | α-Thalassemia | II | ‘X’ chromosome |
C | β-Thalassemia | III | 21st chromosome |
D | Klinefelter’s syndrome | IV | 16th chromosome |
The velocity (v) - time (t) plot of the motion of a body is shown below :
The acceleration (a) - time(t) graph that best suits this motion is :