The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4\, \%$,will be ......... $\%$

$A$ string of length $1 \,m$ and mass $490 \,g$ is put under a tension of $25 \,N$. $A$ wave of frequency $120 \,Hz$ is sent along it. The speed of this wave is (in $\,m/s$)

$A$ string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of a transverse wave along the string at a distance $x$ from the free end will be:

$A$ wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $50 \, Hz$. The mass of the wire is $30 \, g$ and its linear density is $4 \times 10^{-2} \, kg/m$. The speed of the transverse wave on the string is ...... $m/s$.

$A$ 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 .... $s$

Two strings with circular cross section and made of same material are stretched to have the same amount of tension. $A$ transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section $R$ is $v_1$,and that in the other string having radius of cross section $R/2$ is $v_2$. Then $\frac{v_2}{v_1} = $