Two $Cu$ wires of radii $R_{1}$ and $R_{2}$ are such that $(R_{1} > R_{2})$. Then which of the following is true?

$A$ string of length $0.4\, m$ and mass $10^{-2}\, kg$ is tightly clamped at its ends. The tension in the string is $1.6\, N$. Identical wave pulses are produced at one end at equal intervals of time $\Delta t$. The minimum value of $\Delta t$ which allows constructive interference between successive pulses is .... $s$

$A$ wire is under tension of $2 \text{ kg wt}$ and a wave is travelling through it with some speed. Tension in the wire is so increased that the wave travels through it with thrice the original speed. The increase in tension is (in kg wt)

$A$ transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \ kg \ m^{-1}$ is represented by the equation $y = 0.2 \sin (1.5 x + 60 t)$, where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is

The linear density of a vibrating string is $1.3 \times 10^{-4} \, kg/m$. $A$ transverse wave is propagating on the string and is described by the equation $Y = 0.021 \, \sin(x + 30t)$,where $x$ and $y$ are measured in meters and $t$ in seconds. The tension in the string is ..... $N$.

$Assertion :$ Two waves moving in a uniform string having uniform tension cannot have different velocities.
$Reason :$ Elastic and inertial properties of string are same for all waves in same string. Moreover,the speed of a wave in a string depends on its elastic and inertial properties only.