NEET Practice Questions (MCQs) with Answers & Solutions

The two displacements can be written as $y_1 = A cos (k_1x - \omega_1t)$ and $ y_2 = A cos (k_2x - \omega_ 2 t)$ compare this equation with given equation and get solution.

$ Beat frequency f_1 - f_2 = { \omega_1 \over 2 \pi } - { \omega_2 \over 2 \pi } $

The resultant displacement is given by $y = y_1 + y_2$ $ = A cos ( k_1x - \omega_1t) + A cos (k_2x - \omega_2t) $ For x = 0 we have $ y =A cos \omega_1 t + A cos \omega_2 t $ $ \therefore y = 0.10 cos (96 \pi t) cos (4 \pi t) $ Between t = 0 and t = 1 s, $Cos 96 \pi t $ becomes zero 96times and $cos 4 \pi t$ becomes zero 4 times. Hence the resultant displacement Y at x = 0 becomes zero 100 times between t = 0 and t = 15.

$ y_1 = A sin (kx + \omega t) $ $ y_r = A sin ( kx -\omega t ) \Rightarrow y = yi + yr $ $ \therefore y = 2 A sin kx cos \omega t $ Here $ 2A = 10 , \therefore A = 5 $

The given equation represents a stationary wave, which is of the form $ y = 2A ext{sin}(kx) ext{cos}( ext{wt}) $. For a stationary wave, the distance between two consecutive nodes is given by $ rac{ ext{wavelength}}{2} $. Here, $ k = rac{ ext{Ï€}}{4} $, so $ ext{wavelength} = rac{2 ext{Ï€}}{k} = rac{2 ext{Ï€}}{ ext{Ï€}/4} = 8 ext{cm} $. Hence, the separation between consecutive nodes is $ rac{8}{2} = 4 ext{cm} $.

Physics is categorized as a natural science because it involves the study of the natural world and the laws that govern it. Natural sciences include fields such as physics, chemistry, biology, and earth sciences.

The word 'Physics' is derived from the Greek word 'physikē,' meaning nature. The term was used by ancient Greek philosophers to describe the study of nature and natural phenomena.

The range of time scales in physics and cosmology can span from extremely small fractions of a second, such as those involved in particle physics, to extremely long durations, such as the age of the universe. The given range $10^{-22}$ seconds to $10^{18}$ seconds covers this broad spectrum, from the smallest measurable quantities to timescales associated with cosmic events.