$A$ stretched string fixed at both ends has $m$ nodes,then the length of the string will be

$A$ stationary 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 constituent wave is ........... $m/s$.

The equation of a stationary wave is $Y = 10 \sin \left( \frac{\pi x}{4} \right) \cos (20 \pi t)$. The distance between two consecutive nodes in metres is

$(i)$ For the wave $y(x, t) = 0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The length of the string is $1.5 \, m$ and its mass is $3.0 \times 10^{-2} \, kg$. Do all the points on the string oscillate with the same $(a)$ frequency,$(b)$ phase,$(c)$ amplitude? Explain your answers.
$(ii)$ What is the amplitude of a point $0.375 \, m$ away from one end?

In the standing wave shown,particles at the positions $A$ and $B$ have a phase difference of

Stationary waves are produced in a $10\,m$ long stretched string. If the string vibrates in $5$ segments and the wave velocity is $20\,m/s$,the frequency is ..... $Hz$.