The equation y = A sin² (kx-wt) represents a wave motion with

1. amplitude A, frequency w/2\(\pi\)

2. amplitude A/2, frequency w/\(\pi\)

3. amplitude 2A, frequency w/4\(\pi\)

4. does not represent a wave motion

Which of the following is a mechanical wave?
1. Radio waves
2. X-rays
3. Light waves
4. Sound waves

A cork floating in a calm pond executes simple harmonic motion of frequency \(\nu\) when a wave generated by a boat passes by it. The frequency of the wave is:
1. \(\nu\)
2. \(\nu/2\)
3. \(2\nu\)
4. \(\sqrt2\)\(\nu\)

Two strings \(A\) and \(B,\) made of same material, are stretched by same tension. The radius of string \(A\) is double of the radius of \(B.\) A transverse wave travels on \(A\) with speed \(v_A\) and on \(B\) with speed \(v_B.\) The ratio \(\frac{v_A}{v_B}=\) ?

Both the strings, shown in the figure, are made of the same material and have the same cross-section. The pulleys are light. The wave speed of a transverse wave in the string \(AB\) is \(v_1\) and in \(CD\) it is \(v_2\). Then \(\frac{v_1}{v_2}\) is:

1. \(1\)
2. \(2\)
3. \(\sqrt2\)
4. \(\frac{1}{\sqrt{2}}\)

Velocity of sound in air is \(332\) m/s. Its velocity in the vacuum will be:
1. \(>332\) m/s
2. \(=332\) m/s
3. \(<332\) m/s
4. meaningless

A wave pulse, travelling on a two-piece string, gets partially reflected and partially transmitted at the junction. The reflected wave is inverted in shape as compared to the incident one. If the incident wave has wavelength \(\lambda\) and the transmitted wave\(\lambda\)',

1. \(\lambda\)' > \(\lambda\)

2. \(\lambda\)' = \(\lambda\)

3. \(\lambda\)' < \(\lambda\)

4. nothing can be said about the relation of \(\lambda\) and \(\lambda\)'

Two waves represented by; \(y=a\text{sin}(\omega t-kx)\) and \(y=a\text{cos}(\omega t-kx)\) are superposed. The resultant wave will have an amplitude:
1. \(a\)
2. \(\sqrt{2} a\)
3. \(2a\)
4. \(0\)

Two wires A and B, having identical geometrical construction, are stretched from their natural length by small but equal amount. The Young modulus of the wires are Y_A and Y_B whereas the densities are ρ_A>ρ_B. A transverse signal started at one end takes a time t₁ to reach the other end for A and t₂ for B.

1. t₁ < t₂

2. t₁ = t₂

3. t₁ > t₂

4. the information is insufficient to find the relation between t₁ and t₂

Consider two waves passing through the same string. Principle of superposition for displacement says that the net displacement of a particle on the string is sum of the displacements produced by the two waves individually. Suppose we state similar principles for the net velocity of the particle and the net kinetic energy of the particle. Such a principle will be valid for: