The equation of a stationary wave along a stretched string is given by $y = 5 \sin \left( \frac{\pi x}{3} \right) \cos (40 \pi t)$. Here $x$ and $y$ are in $cm$ and $t$ is in seconds. The separation between two adjacent nodes is: (in $cm$)

$A$ string fixed at both the ends forms a standing wave with a node separation of $5 \,cm$. If the velocity of the wave on the string is $2 \,m/s$, then the frequency of vibration of the string is (in $\,Hz$)

$A$ suspension bridge is to be built across a valley where it is known that the wind can gust at $5 \,s$ intervals. It is estimated that the speed of transverse waves along the span of the bridge would be $400 \,m/s$. The danger of resonant motions in the bridge at its fundamental frequency would be greater if the span had a length of .......... $m$.

$A$ transverse displacement of a vibrating string is given by $y = 0.06 \sin \left( \frac{2 \pi}{3} x \right) \cos (120 \pi t)$. If the mass per unit length of the string is $4 \times 10^{-2} \ kg/m$,then the tension in the string will be: (in $N$)

Which two of the given transverse waves will produce stationary waves when superimposed?
${z_1} = a\cos(kx - \omega t)$.....$(A)$
${z_2} = a\cos(kx + \omega t)$.....$(B)$
${z_3} = a\cos(ky - \omega t)$.....$(C)$

The correct statement about stationary waves is that