A sine wave is travelling in a medium. The minimum distance between the two particles, always having the same speed, is:
1. \(\lambda/4\)
2. \(\lambda/3\)
3. \(\lambda/2\)
4. \(\lambda\)

A sine wave is travelling in a medium. A particular particle has zero displacement at a certain instant. The particle closest to it having zero displacement is at a distance:
1. \(\lambda\)/4
2. \(\lambda\)/3
3. \(\lambda\)/2
4. \(\lambda\)

Which of the following equations represents a wave travelling along \(\mathrm{Y}\)-axis?
1. \(x=A ~sin(ky-\omega t)\)
2. \(y=A ~sin(kx-\omega t)\)
3. \(y=A ~sinky~ cos \omega t\)
4. \(y=A ~cosky~ sin \omega t\)

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

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 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

Two sine waves travel in the same direction in a medium. The amplitude of each wave is \(A\) and the phase difference between the two waves is \(120^\circ.\) The resultant amplitude will be:
1. \(A\)
2. \(2A\)
3. \(4A\)
4. \(\sqrt2 A\)

A mechanical wave propagates in a medium along the X-axis. The particles of the medium

(a) must move on the X-axis

(b) must move on the Y-axis

(c) may move on the X-axis

(d) may move on the Y-axis

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these

A transverse wave travels along the Z-axis. The particles of the medium must move: