Two identical strings, \(X\) and \(Z,\) made of the same material, have tensions \(T_X\)​ and \(T_Z\)​ respectively. If their fundamental frequencies are \(450\) Hz and \(300\) Hz, respectively, the ratio \(\dfrac{T_X}{T_Z}=\)
1. \(0.44\)
2. \(1.5\)
3. \(2.25\)
4. \(1.25\)

A uniform thin rope of length \(12~\text{m}\) and mass \(6\) kg hangs vertically from a rigid support and a block of mass \(2\) kg is attached to its free end. A transverse short wave-train of wavelength \(6~\text{cm}\) is produced at the lower end of the rope. What is the wavelength of the wavetrain \((\text{in cm})\) when it reaches the top of the rope?
1. \(12\)
2. \(9\)
3. \(3\)
4. \(6\)

The percentage increase in the speed of transverse waves produced in a stretched string when the tension is increased by \(4\%\) is:
1. \(4\%\)
2. \(3\%\)
3. \(2\%\)
4. \(1\%\)

The mass per unit length of a uniform wire is \(0.135\) g/cm. A transverse wave of the form \(y=-0.21 \sin (x+30 t)\) is produced in it, where \(x\) is in meter and \(t\) is in second. The expected value of the tension in the wire is:
1. \(12.15\) N
2. \(30.12\) N
3. \(45.35\) N
4. \(50.24\) N