Q. No.Two loudspeakers (\(L_1 \) and \(L_2\)) are placed with a separation of \(10~\text{m}, \) as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point \(A, \) at equidistance to both loud speakers, is moved by \(25~\text{m}, \) along the line AB while monitoring the audio signal. The measured signal was found to undergo \(10\) cycles of minima and maxima during the movement. The frequency of the input signal is: (in Hz)
(Speed of sound in air is \(324~\text{m/s}\) and \(\sqrt{5}=2.23\))
1. \(100\)
2. \(300\)
3. \(400\)
4. \(600\)
(Speed of sound in air is \(324~\text{m/s}\) and \(\sqrt{5}=2.23\))
1. \(100\)
2. \(300\)
3. \(400\)
4. \(600\)
Subtopic: Superposition Principle |
Level 3: 35%-60%
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When two harmonic travelling waves,
\(y_1(x, t) = 4\sin(kx - ωt) \) & \(y_2(x, t) = 2\sin \left(kx \ – ωt \ + \dfrac{2π}{3}\right)~\)
superpose, what are the amplitude and phase difference of the resultant wave relative to the first wave? Assume both waves have the same angular frequency \(\omega.\)
\(y_1(x, t) = 4\sin(kx - ωt) \) & \(y_2(x, t) = 2\sin \left(kx \ – ωt \ + \dfrac{2π}{3}\right)~\)
superpose, what are the amplitude and phase difference of the resultant wave relative to the first wave? Assume both waves have the same angular frequency \(\omega.\)
| 1. | \( \left [6,\dfrac{2\pi}{3} \right ] ~\) | 2. | \( \left [6,\dfrac{\pi}{3} \right ] ~\) |
| 3. | \( \left [\sqrt{3},\dfrac{\pi}{6} \right ] ~\) | 4. | \( \left [2\sqrt3,\dfrac{\pi}{6} \right ] ~\) |
Subtopic: Superposition Principle |
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Two monochromatic light beams have intensities in the ratio \(1:9\). An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is:
1. \(9:1\)
2. \(4:1\)
3. \(8:1\)
4. \(3:1\)
1. \(9:1\)
2. \(4:1\)
3. \(8:1\)
4. \(3:1\)
Subtopic: Superposition Principle |
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Level 1: 80%+
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Two coherent monochromatic light beams of intensities \(4I \) and \(9I \) are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is \(xI \). The value of \(x \) is:
1. \(24\)
2. \(35\)
3. \(15\)
4. \(20\)
1. \(24\)
2. \(35\)
3. \(15\)
4. \(20\)
Subtopic: Superposition Principle |
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Level 1: 80%+
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Two plane polarized light waves combine at a certain point whose electric filed components are:
\(\begin{aligned} & E_1=E_0 \sin \omega t \\ & E_2=E_0 \sin \left(\omega t+\dfrac{\pi}{3}\right) \end{aligned} \)
Find the amplitude of the resultant wave:
1. \(0.9 {E}_0 \)
2. \(3.4 {E}_0 \)
3. \({E}_0 \)
4. \(1.7 {E}_0 \)
\(\begin{aligned} & E_1=E_0 \sin \omega t \\ & E_2=E_0 \sin \left(\omega t+\dfrac{\pi}{3}\right) \end{aligned} \)
Find the amplitude of the resultant wave:
1. \(0.9 {E}_0 \)
2. \(3.4 {E}_0 \)
3. \({E}_0 \)
4. \(1.7 {E}_0 \)
Subtopic: Superposition Principle |
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A particle is subjected to two simple harmonic motions as:
\(x_1=\sqrt 7 \sin 5 t ~\text{cm} \)
and \(x_2=2 \sqrt{7} \sin (5 t+\pi / 3) ~\text{cm} \)
where \(x\) is displacement and \(t\) is time in seconds. The maximum acceleration of the particle is \(x \times 10^{-2}~ \text{ms}^{-2}. \) The value of \(x\) is:
1. \(125\)
2. \(5 \sqrt7 \)
3. \(25 \sqrt7 \)
4. \(175\)
\(x_1=\sqrt 7 \sin 5 t ~\text{cm} \)
and \(x_2=2 \sqrt{7} \sin (5 t+\pi / 3) ~\text{cm} \)
where \(x\) is displacement and \(t\) is time in seconds. The maximum acceleration of the particle is \(x \times 10^{-2}~ \text{ms}^{-2}. \) The value of \(x\) is:
1. \(125\)
2. \(5 \sqrt7 \)
3. \(25 \sqrt7 \)
4. \(175\)
Subtopic: Superposition Principle |
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The width of one of the two slits in a Young's double slit experiment is \(4\) times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is –
1. \(1:1\)
2. \(16:1\)
3. \(9:1\)
4. \(4:1\)
1. \(1:1\)
2. \(16:1\)
3. \(9:1\)
4. \(4:1\)
Subtopic: Superposition Principle |
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Two coherent waves of equal intensity, originating from sources in phase, superpose at a point. If the resultant intensities are \(I_0,I_1,\) and \(I_2\) for path differences of \(0,\dfrac{\lambda}{2},\) and \(\dfrac{\lambda}{4},\) respectively, what is the value of \(\dfrac{I_{1}+I_{2}}{I_{0}},\) where \(\lambda\) is the wavelength of the waves?
1. \(0\)
2. \(2\)
3. \(4\)
4. \(0.5\)
1. \(0\)
2. \(2\)
3. \(4\)
4. \(0.5\)
Subtopic: Superposition Principle |
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Two coherent waves of amplitude \(8\text{ cm}\) each are superimposed on one another. If the amplitude of a resultant wave is \(8\text{ cm},\) then the phase difference between the two waves is:
| 1. | \(\dfrac{2\pi}{3}\) | 2. | \(\dfrac{\pi}{3}\) |
| 3. | \(\dfrac{\pi}{4}\) | 4. | \(\dfrac{3\pi}{4}\) |
Subtopic: Superposition Principle |
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The interference pattern is obtained with two coherent light sources of intensity ratio 4 :1. And the ratio \(\frac{I_{\max }+I_{\min }}{I_{\max }-I_{\min }} \text { is } \frac{5}{x}\). Then, the value of x will be equal to:
1. 3
2. 4
3. 2
4. 1
1. 3
2. 4
3. 2
4. 1
Subtopic: Superposition Principle |
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