$n _{1}= n \left(\frac{ v - u }{ v }\right)=\left(1-\frac{ u }{ v }\right) n$
for $2^{nd}$ source
$n _{2}= n \left(\frac{ v + u }{ v }\right)=\left(1+\frac{ u }{ v }\right) n$
Beat freq. $=\left| n _{1}- n _{2}\right|= n +\frac{ nu }{ v }- n +\frac{ nu }{ v }$
$=\frac{2 nu }{ v }=2 \frac{ u }{\lambda}\left[\because v = n \lambda \quad \therefore \frac{1}{\lambda}=\frac{ n }{ v }\right]$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
[Boltzmann’s constant ${k_B} = 1.38 \times {10^{ - 23}}J/K]$
| column $I$ | column $II$ |
| $(A)$ $U _1( x )=\frac{ U _0}{2}\left[1-\left(\frac{ x }{ a }\right)^2\right]^2$ | $(P)$ The force acting on the particle is zero at $x = a$. |
| $(B)$ $U _2( x )=\frac{ U _0}{2}\left(\frac{ x }{ a }\right)^2$ | $(Q)$ The force acting on the particle is zero at $x=0$. |
| $(C)$ $U _3( x )=\frac{ U _0}{2}\left(\frac{ x }{ a }\right)^2 \exp \left[-\left(\frac{ x }{ a }\right)^2\right]$ | $(R)$ The force acting on the particle is zero at $x =- a$. |
| $(D)$ $U _4( x )=\frac{ U _0}{2}\left[\frac{ x }{ a }-\frac{1}{3}\left(\frac{ x }{ a }\right)^3\right]$ | $(S)$ The particle experiences an attractive force towards $x =0$ in the region $| x |< a$. |
| $(T)$ The particle with total energy $\frac{ U _0}{4}$ can oscillate about the point $x=-a$. |
$y = 2A\,\,\sin \,\left( {\frac{{2\pi ct}}{\lambda }} \right)\,\cos \,\,\,\left( {\frac{{2\pi x}}{\lambda }} \right)$
Which statement is not true?