The $(x, y)$ coordinates of the corners of a square plate are $(0, 0), (L, 0), (L, L)$ and $(0, L).$ The edges of the plate are clamped and transverse standing waves are set up in it. If $u(x, y)$ denotes the displacement of the plate at the point $(x, y)$ at some instant of time,the possible expression$(s)$ for $u$ is(are) ($a =$ positive constant).

The speed of a stationary wave represented by the equation $y = 0.7 \sin \left(\frac{7 \pi}{4} x\right) \cos (350 \pi t)$ is (In the given equation $x$ and $y$ are in metre and $t$ is in second). (in $m \ s^{-1}$)

The figure shows an incident pulse $P$ reflected from a rigid support. Which one of $A, B, C, D$ represents the reflected pulse correctly?

What are nodes and antinodes?

One end of a taut string of length $3 \ m$ along the $x$-axis is fixed at $x=0$. The speed of the waves in the string is $100 \ m/s$. The other end of the string is vibrating in the $y$-direction so that stationary waves are set up in the string. The possible waveform$(s)$ of these stationary waves is (are):
$(A)$ $y(x,t) = A \sin \frac{\pi x}{6} \cos \frac{50 \pi t}{3}$
$(B)$ $y(x,t) = A \sin \frac{\pi x}{3} \cos \frac{100 \pi t}{3}$
$(C)$ $y(x,t) = A \sin \frac{5 \pi x}{6} \cos \frac{250 \pi t}{3}$
$(D)$ $y(x,t) = A \sin \frac{5 \pi x}{2} \cos 250 \pi t$

On producing the waves of frequency $1000 \,Hz$ in a Kundt's tube, the total distance between $6$ successive nodes is $85 \,cm$. Then, the speed of sound in the gas filled in the tube is (in $\,ms^{-1}$)