Q. No.Which of the following equations represents a wave travelling along the \(y\text-\)axis?
1. \(x=A \sin(ky-\omega t)\)
2. \(y=A \sin(kx-\omega t)\)
3. \(y=A \sin (ky)\cos \omega t\)
4. \(y=A \cos (ky) \sin \omega t\)
1. \(x=A \sin(ky-\omega t)\)
2. \(y=A \sin(kx-\omega t)\)
3. \(y=A \sin (ky)\cos \omega t\)
4. \(y=A \cos (ky) \sin \omega t\)
The equation; \(y = A \sin^2 (kx-\omega t)\) represents a wave motion with:
| 1. | \(\text{amplitude} ~(A),~\text{frequency}~\left(\omega/2\pi\right)\) |
| 2. | \(\text{amplitude} ~\left(A/2\right),~\text{frequency}~\left(\omega/\pi\right)\) |
| 3. | \(\text{amplitude} ~(2A),~\text{frequency}~\left(\omega/4\pi\right)\) |
| 4. | does not represent a wave motion |
Which of the following is a mechanical wave?
1. Radio waves
2. \(X\text-\)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 the same material, are stretched by the same tension. The radius of string \(A\) is double of the radius of \(B.\) A transverse wave that travels on \(A\) with a speed \(v_A\) and on \(B\) with a speed \(v_B.\) The ratio of \(\frac{v_A}{v_B}\) is:
| 1. | \(\frac{1}{2}\) | 2. | \(2\) |
| 3. | \(\frac{1}{4}\) | 4. | \(4\) |
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 \(\dfrac{v_1}{v_2}\) is:
| 1. | \(1\) | 2. | \(2\) |
| 3. | \(\sqrt2\) | 4. | \({1}/{\sqrt{2}}\) |
1. \(>332~\text{m/s}\)
2. \(=332~\text{m/s}\)
3. \(<332~\text{m/s}\)
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 are 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 YA and YB whereas the densities are ρA>ρB. 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
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