Reasoning: Wave intensity is directly proportional to the square of amplitude:
$\mathbf{I}\mathbf{\propto}\mathbf{A}^{\mathbf{2}}$
If amplitude becomes $\mathbf{2A}$. $\mathbf{\Longrightarrow}$ $\mathbf{I}^{\mathbf{'}}\mathbf{=}{\mathbf{(2A}\mathbf{)}}^{\mathbf{2}}\mathbf{= 4}\mathbf{A}^{\mathbf{2}}$ Therefore, the intensity becomes four times.

Reasoning: During constructive interference, the amplitudes of waves in phase are added. $\mathbf{\Longrightarrow}$ $\mathbf{A}_{\mathbf{R}}\mathbf{=}\mathbf{A}_{\mathbf{1}}\mathbf{+}\mathbf{A}_{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{A}_{\mathbf{R}}\mathbf{= 0.5 + 0.5 = 1}\mathbf{\ }\mathbf{m}$

Reasoning: Beat frequency is $\mathbf{f}_{\mathbf{b}}\mathbf{=}\left| \mathbf{f}_{\mathbf{1}}\mathbf{-}\mathbf{f}_{\mathbf{2}} \right|$. The human ear can clearly distinguish beats only when the frequency difference is approximately $\mathbf{10\ Hz}$ or less. For a larger difference, the rapid beats cannot be heard separately.

Reasoning: $\mathbf{f}_{\mathbf{b}}\mathbf{=}\left| \mathbf{f}_{\mathbf{1}}\mathbf{-}\mathbf{f}_{\mathbf{2}} \right|$ $\mathbf{\Longrightarrow}$ $\mathbf{f}_{\mathbf{b}}\mathbf{=}\left| \mathbf{203 - 199} \right|\mathbf{= 4}\mathbf{\ }\mathbf{Hz}$

Reasoning: Higher harmonics are whole-number multiples of the fundamental frequency. $\mathbf{\Longrightarrow}$ $\mathbf{f}_{\mathbf{n}}\mathbf{= n}\mathbf{f}_{\mathbf{1}}$
For $\mathbf{f}_{\mathbf{1}}\mathbf{= 150}\mathbf{\ }\mathbf{Hz}\mathbf{\ }$,
$\mathbf{f}_{\mathbf{2}}\mathbf{= 2(150) = 300}\mathbf{\ }\mathbf{Hz}$ ; $\mathbf{f}_{\mathbf{4}}\mathbf{= 4(150) = 600}\mathbf{\ }\mathbf{Hz}$

Reasoning: For a string fixed at both ends: $\mathbf{\lambda}_{\mathbf{n}}\mathbf{=}$ $\frac{\mathbf{2L}}{\mathbf{n}}$ $\mathbf{\Longrightarrow}$ $\mathbf{\lambda}_{\mathbf{3}}\mathbf{=}$ $\frac{\mathbf{2(3)}}{\mathbf{3}}\mathbf{= 2}\mathbf{\ }\mathbf{m}$

Reasoning: A node is a point of zero displacement. It is formed when two waves of equal amplitude meet in opposite phases and undergo complete destructive interference.

Reasoning: Interference is the phenomenon in which two or more waves overlap in the same medium and produce a resultant wave.

Reasoning: First calculate wavelength: $\mathbf{\lambda =}$ $\frac{\mathbf{v}}{\mathbf{f}}$ $\mathbf{\Longrightarrow}$ $\mathbf{\lambda =}$ $\frac{\mathbf{128}}{\mathbf{256}}\mathbf{= 0.5}\mathbf{\ }\mathbf{m}$
The distance between consecutive nodes is:
$\mathbf{d =}$ $\frac{\mathbf{\lambda}}{\mathbf{2}}\mathbf{=}\frac{\mathbf{0.5}}{\mathbf{2}}\mathbf{= 0.250}\mathbf{\ }\mathbf{m}$

Reasoning: For the shortest resonating air column closed at one end: $\mathbf{L =}$ $\frac{\mathbf{\lambda}}{\mathbf{4}}$
Therefore, $\mathbf{\lambda = 4L = 4(0.25) = 1.0}\mathbf{\ }\mathbf{m}$ Now, $\mathbf{v = f\lambda}$
$\mathbf{v = 329.6}\mathbf{\ }\mathbf{(1.0) = 329.6}\mathbf{\ }\mathbf{m}\mathbf{s}^{\mathbf{- 1}}$ $\mathbf{\Longrightarrow}$ $\mathbf{v \approx 3.30 \times}\mathbf{10}^{\mathbf{2}}\mathbf{\ }\mathbf{m}\mathbf{s}^{\mathbf{- 1}}$

Reasoning: When unpolarized light passes through a polarizer, only the component vibrating along the transmission axis passes through.
Its intensity becomes: $\mathbf{I =}$ $\frac{\mathbf{I}_{\mathbf{o}}}{\mathbf{2}}$ Therefore, the observed intensity is decreased.