Which of the following is related to Doppler effect?
Sound
The question asks which concept is related to the Doppler effect. The Doppler effect is a fundamental physics principle that describes how the observed frequency of a wave changes when the source of the wave and the observer are moving relative to each other.
Let's break down the Doppler effect and its connection to the given options:
Based on the analysis, the change in wave frequency due to relative motion, known as the Doppler effect, is most directly and commonly associated with sound waves, as demonstrated by the changing pitch of moving sound sources.
The Doppler effect is fundamentally about how the perceived frequency of waves changes with relative motion between the source and the observer. Sound waves provide a very common and audible example of this effect.
The position of a particle in one dimension changes in discrete steps. With each step it moves to the right, however, the length of the step is drawn from a uniform distribution from the interval \(\left[ {{\rm{λ }}\,{\rm{ - }}\,\frac{{\rm{1}}}{{\rm{2}}}{\rm{w,}}\,{\rm{λ }}\,{\rm{ + }}\,\frac{{\rm{1}}}{{\rm{2}}}{\rm{w}}} \right] \) , where λ and w are positive constants. If X denotes the distance from the starting point after N steps, the standard deviation \(\sqrt {\left\langle {{X^2}} \right\rangle \, - {{\left\langle X \right\rangle }^2}} \) for large values of N is
A particle of mass m in one dimension is in the ground state of a simple harmonic oscillator described by a Hamiltonian \(\frac{{{{\rm{P}}^{\rm{2}}}}}{{{\rm{2m}}}}{\rm{ + }}\frac{{\rm{1}}}{{\rm{2}}}{\rm{m}}{{\rm{\omega }}^{\rm{2}}}{{\rm{x}}^{\rm{2}}} \) in the standard notation. An impulsive force at time t = 0 suddenly imparts a momentum P0 = \(\sqrt {{\rm{hm\omega }}} \) to it. The probability that the particle remains in the original ground state is
In an elastic scattering process at an energy E, the phase shifts satisfy δ 0 ≈ 30°, δ 1≈ 10°, while the other phase shifts are zero. The polar angle at which the differential cross-section peaks is closest to
The unnormalized wavefunction of a particle in one dimension in an infinite square well with walls at x = 0 and x = a, is ψ(x) = x (a - x). If ψ (x) is expanded as a linear combination of the energy eigenfunctions, \(\int_0^a {\left| {\psi {{\left( x \right)}^2}} \right|} \) dx is proportional to the infinite series (You may use \(\int_{\rm{0}}^{\rm{a}} {{\rm{t}}\,{\rm{sin}}\,{\rm{t}}\,{\rm{dt}}} \) = -a cos a + sin a and \(\int_{\rm{0}}^{\rm{a}} {{{\rm{t}}^2}\,{\rm{sin}}\,{\rm{t}}\,{\rm{dt}}} \) = -2 - (a 2- 2) cos a + 2a sin a)