Question 1:
difficultTwo wires are kept tight between the same pair of support. The tensions in the wires are in the ratio 2 : 1, the radii are in the ratio 3 : 1 and the densities are in the ratio 1 : 2. The ratio of their fundamental frequencies is
Question 2:
difficultA transverse wave is represented by the equation
\[ y= y_{0} sin\frac{2\Pi}{\lambda}(vt-x)\]Â
For what value of λ , the maximum particle velocity equal to two times the wave velocity
Question 3:
difficultA uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2$. The ratio $\lambda_2/\lambda_1$ is:
(2016 – I)
$v = f\lambda \Rightarrow \lambda \propto v \propto \sqrt{T}$. At the bottom, tension $T_1 = m_2 g$. At the top, $T_2 = (m_1+m_2)g$. Thus $\lambda_2/\lambda_1 = \sqrt{T_2/T_1} = \sqrt{\frac{m_1+m_2}{m_2}}$.
Question 4:
difficultA tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27^\circ\text{C}$ two successive resonances are produced at $20 \text{ cm}$ and $73 \text{ cm}$ of column length. If the frequency of the tuning fork is $320 \text{ Hz}$, the velocity of sound in air at $27^\circ\text{C}$ is:
(2018)
$v = 2f(L_2 - L_1) = 2 \times 320 \times (0.73 - 0.20) = 640 \times 0.53 = 339.2 \text{ m/s}$.