The velocity of waves in a string fixed at both ends is $2 \ m/s$. The string forms standing waves with nodes $5.0 \ cm$ apart. The frequency of vibration of the string in $Hz$ is

Write the equation of a stationary wave and obtain the equations of nodes and antinodes by defining them.

In stationary waves,

$A$ standing wave is represented by $Y = A \sin(100t) \cos(0.01x)$,where $Y$ and $A$ are in millimetres,$t$ is in seconds,and $x$ is in metres. The velocity of the wave is ..... $m/s$.

$A$ standing wave exists in a string of length $150 \ cm$,which is fixed at both ends with rigid supports. The displacement amplitude of a point at a distance of $10 \ cm$ from one of the ends is $5\sqrt{3} \ mm$. The nearest distance between two points,within the same loop and having a displacement amplitude equal to $5\sqrt{3} \ mm$,is $10 \ cm$. Find the maximum displacement amplitude of the particles in the string (in $mm$).

Write the amplitude and phase difference for all particles of the same interval for stationary waves.