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

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. \(0\)