Waves Test - 82...

A harmonic wave has been set up on a very long string which travels along the length of the string. The wave has frequency of $$50 \,Hz,$$ amplitude $$1 \,cm$$ and wavelength $$0.5 \,m.$$ For the above-described wave.
$$Statement \ I :$$ Time taken by the wave to travel a distance of $$8 \,m$$ along the length of the string is $$0.32 \,s.$$
$$Statement \ II :$$ Time taken by a point on the string to travel a distance of $$8 \,m,$$ once the wave has reached at that point and sets it into motion is $$0.32 \,s.$$

The initial phase angle observed by a rider in the elevator,taking downward direction to be positive and positive extreme position to have $$\pi/2$$ phase constant, is equal to:

Two particles execute simple harmonic motion of the same amplitude and frequency along close parallel lines. They pass each other moving in opposite direction each time their displacement us half their amplitude. Their phase difference is :

A standing wave arises on a string when two waves of equal amplitude, frequency, and wavelength traveling in opposite directions superimpose. If the frequency of two-component wäves is doubled, then the frequency of oscillation of the standing waves

The space density of the potential energy $$PE = E_p(x, t)$$ at a point (x, t) in the space is

Figure shows the standing wave pattern at t = 0 due to superposition of waves given by $$y_1\space and\space y_2$$. N is anode and A an antinode. At this instant say t = 0, instantaneous velocity of points on the string

The following equations represent progressive transverse waves
$$z_1 = A \cos (\omega t - kx)$$
$$z_2 = A \cos (\omega t + kx)$$
$$z_3 = A \cos (\omega t + ky)$$
$$z_4 = A \cos (2\omega t - 2ky)$$
A stationary wave will be formed by superposing

Amplitude of simple harmonic motion of a point on the string that is located at x = 1.8 cm will be

The  space density of the kinetic energy, $$KE = E_k(x, t)$$ at the point (x, t) is given by

Maximum value of the y-position coordinate in the simple harmonic motion of an element of the string that is located at an antinode will be