The ends of a stretched wire of length $L$ are fixed at $x=0$ and $x=L$. In one experiment the displacement of the wire is $y_1=A \sin \left(\frac{\pi x}{L}\right) \sin \omega t$ and energy is $E_1$ and in other experiment its displacement is $y_2=A \sin \left(\frac{\mathrm{2\pi }x}{L}\right) \sin \mathrm{2\omega }t$  and energy is $E_2$. Then

Two symmetrical and identical pulses in a stretched string, whose centres are initially $8 \mathrm{cm}$ apart, are moving towards each other as shown in the figure. The speed of each pulse is $2 \mathrm{cm} {\mathrm{s}}^{-1}$. After $2 \mathrm{seconds}$, the total energy of the pulses will be

A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9$ $ \mathrm{kg}$ is suspended from the wire. When this mass is replaced by a mass ${M}$, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of ${M}$ is,

Assertion : Electromagnetic waves exert pressure called radiation pressure.

Reason : This is because they carry energy.

Assertion : In a small segment of string carrying sinusoidal wave, total energy is conserved.

Reason: Every small part moves in $\mathrm{SHM}$ and in SHM total energy is conserved.

Assertion : Two waves moving in a uniform string having uniform tension can have different velocities.
Reason : Elastic and inertial properties of string are same for all waves in same string. Moreover, speed of wave in a string depends on its elastic and inertial properties only.

Assertion :In standing wave pattern particle of medium between two consecutive nodes vibrates in same phase but with different amplitude.

Reason : In stationary wave the amplitude of vibration does not depend on the position of the particle.

Assertion : The transverse wave is travelling along a string in the positive $x$ axis as shown

Points $\left(A\&P_1\right)$ moving $\downarrow$ (downward) and points $\left(C\&P_2\right)$ moving (upward).

Reason : In a wave propagating in positive $x$ direction the points with $+ve$ slope move downward and vice versa.

Assertion : In transverse wave particle velocity is perpendicular to the direction of wave velocity.

Reason : In wave motion energy always transferred in the direction of wave propagation.