Superposition of Transverse Waves
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PHXI15:WAVES

355070 Two waves of nearly same amplitude, same frequency travelling with same velocity are superimposing to give phenomenon of interference. If \(a_{1}\) and \(a_{2}\) be their amplitudes, \(\omega\) be the frequency for both, \(v\) be the velocity for both and \(\Delta \phi\) is the phase difference between the two waves then, incorrect statement among the following

1 The resultant intensity varies periodically with distance
2 \(\dfrac{I_{\text {min }}}{I_{\text {max }}}=\left(\dfrac{a_{1}-a_{2}}{a_{1}+a_{2}}\right)^{2}\)
3 Both the waves must have been travelling in the same direction and must be coherent
4 \(I_{R}=I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \cos (\Delta \phi)\), where constructive interference is obtained for path difference that are odd multiple of \(\dfrac{\lambda}{2}\) and destructive interference is obtained for path difference that are even multiple of \(\dfrac{\lambda}{2}\)
PHXI15:WAVES

355071 Two waves represented by
\({y_{1}=10 \sin (2000 \pi t+2 x)}\) and
\({y_{2}=10 \sin \left(2000 \pi t+2 x+\dfrac{\pi}{2}\right)}\)
are superimposed at any point at a particular instant. The resultant amplitude is

1 10 units
2 20 units
3 14.1 units
4 zero
PHXI15:WAVES

355072 Assertion :
Velocity of particles, while crossing mean position (in stationary waves) varies from maximum at antinodes to zero at nodes.
Reason :
Amplitude of vibration at antinodes is maximum and at nodes, the amplitude is zero, and all particles between two successive nodes cross the mean position together.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

355073 The displacement-time graphs for two sound waves \(A\) and \(B\) are shown in the figure, then the ratio of their intensities \(I_{A} / I_{B}\) is equal to
supporting img

1 \(1: 4\)
2 \(1: 1\)
3 \(1: 2\)
4 \(1: 16\)
PHXI15:WAVES

355074 The superposing waves are represented by the following equations
\(y_{1}=5 \sin 2 \pi(10 t-0.1 x), y_{2}=10 \sin 2 \pi(10 t-0.1 x)\)
Ratio of intensities \(\dfrac{I_{\max }}{I_{\text {min }}}\) will be

1 16
2 1
3 9
4 4
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PHXI15:WAVES

355070 Two waves of nearly same amplitude, same frequency travelling with same velocity are superimposing to give phenomenon of interference. If \(a_{1}\) and \(a_{2}\) be their amplitudes, \(\omega\) be the frequency for both, \(v\) be the velocity for both and \(\Delta \phi\) is the phase difference between the two waves then, incorrect statement among the following

1 The resultant intensity varies periodically with distance
2 \(\dfrac{I_{\text {min }}}{I_{\text {max }}}=\left(\dfrac{a_{1}-a_{2}}{a_{1}+a_{2}}\right)^{2}\)
3 Both the waves must have been travelling in the same direction and must be coherent
4 \(I_{R}=I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \cos (\Delta \phi)\), where constructive interference is obtained for path difference that are odd multiple of \(\dfrac{\lambda}{2}\) and destructive interference is obtained for path difference that are even multiple of \(\dfrac{\lambda}{2}\)
PHXI15:WAVES

355071 Two waves represented by
\({y_{1}=10 \sin (2000 \pi t+2 x)}\) and
\({y_{2}=10 \sin \left(2000 \pi t+2 x+\dfrac{\pi}{2}\right)}\)
are superimposed at any point at a particular instant. The resultant amplitude is

1 10 units
2 20 units
3 14.1 units
4 zero
PHXI15:WAVES

355072 Assertion :
Velocity of particles, while crossing mean position (in stationary waves) varies from maximum at antinodes to zero at nodes.
Reason :
Amplitude of vibration at antinodes is maximum and at nodes, the amplitude is zero, and all particles between two successive nodes cross the mean position together.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

355073 The displacement-time graphs for two sound waves \(A\) and \(B\) are shown in the figure, then the ratio of their intensities \(I_{A} / I_{B}\) is equal to
supporting img

1 \(1: 4\)
2 \(1: 1\)
3 \(1: 2\)
4 \(1: 16\)
PHXI15:WAVES

355074 The superposing waves are represented by the following equations
\(y_{1}=5 \sin 2 \pi(10 t-0.1 x), y_{2}=10 \sin 2 \pi(10 t-0.1 x)\)
Ratio of intensities \(\dfrac{I_{\max }}{I_{\text {min }}}\) will be

1 16
2 1
3 9
4 4
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PHXI15:WAVES

355070 Two waves of nearly same amplitude, same frequency travelling with same velocity are superimposing to give phenomenon of interference. If \(a_{1}\) and \(a_{2}\) be their amplitudes, \(\omega\) be the frequency for both, \(v\) be the velocity for both and \(\Delta \phi\) is the phase difference between the two waves then, incorrect statement among the following

1 The resultant intensity varies periodically with distance
2 \(\dfrac{I_{\text {min }}}{I_{\text {max }}}=\left(\dfrac{a_{1}-a_{2}}{a_{1}+a_{2}}\right)^{2}\)
3 Both the waves must have been travelling in the same direction and must be coherent
4 \(I_{R}=I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \cos (\Delta \phi)\), where constructive interference is obtained for path difference that are odd multiple of \(\dfrac{\lambda}{2}\) and destructive interference is obtained for path difference that are even multiple of \(\dfrac{\lambda}{2}\)
PHXI15:WAVES

355071 Two waves represented by
\({y_{1}=10 \sin (2000 \pi t+2 x)}\) and
\({y_{2}=10 \sin \left(2000 \pi t+2 x+\dfrac{\pi}{2}\right)}\)
are superimposed at any point at a particular instant. The resultant amplitude is

1 10 units
2 20 units
3 14.1 units
4 zero
PHXI15:WAVES

355072 Assertion :
Velocity of particles, while crossing mean position (in stationary waves) varies from maximum at antinodes to zero at nodes.
Reason :
Amplitude of vibration at antinodes is maximum and at nodes, the amplitude is zero, and all particles between two successive nodes cross the mean position together.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

355073 The displacement-time graphs for two sound waves \(A\) and \(B\) are shown in the figure, then the ratio of their intensities \(I_{A} / I_{B}\) is equal to
supporting img

1 \(1: 4\)
2 \(1: 1\)
3 \(1: 2\)
4 \(1: 16\)
PHXI15:WAVES

355074 The superposing waves are represented by the following equations
\(y_{1}=5 \sin 2 \pi(10 t-0.1 x), y_{2}=10 \sin 2 \pi(10 t-0.1 x)\)
Ratio of intensities \(\dfrac{I_{\max }}{I_{\text {min }}}\) will be

1 16
2 1
3 9
4 4
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PHXI15:WAVES

355070 Two waves of nearly same amplitude, same frequency travelling with same velocity are superimposing to give phenomenon of interference. If \(a_{1}\) and \(a_{2}\) be their amplitudes, \(\omega\) be the frequency for both, \(v\) be the velocity for both and \(\Delta \phi\) is the phase difference between the two waves then, incorrect statement among the following

1 The resultant intensity varies periodically with distance
2 \(\dfrac{I_{\text {min }}}{I_{\text {max }}}=\left(\dfrac{a_{1}-a_{2}}{a_{1}+a_{2}}\right)^{2}\)
3 Both the waves must have been travelling in the same direction and must be coherent
4 \(I_{R}=I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \cos (\Delta \phi)\), where constructive interference is obtained for path difference that are odd multiple of \(\dfrac{\lambda}{2}\) and destructive interference is obtained for path difference that are even multiple of \(\dfrac{\lambda}{2}\)
PHXI15:WAVES

355071 Two waves represented by
\({y_{1}=10 \sin (2000 \pi t+2 x)}\) and
\({y_{2}=10 \sin \left(2000 \pi t+2 x+\dfrac{\pi}{2}\right)}\)
are superimposed at any point at a particular instant. The resultant amplitude is

1 10 units
2 20 units
3 14.1 units
4 zero
PHXI15:WAVES

355072 Assertion :
Velocity of particles, while crossing mean position (in stationary waves) varies from maximum at antinodes to zero at nodes.
Reason :
Amplitude of vibration at antinodes is maximum and at nodes, the amplitude is zero, and all particles between two successive nodes cross the mean position together.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

355073 The displacement-time graphs for two sound waves \(A\) and \(B\) are shown in the figure, then the ratio of their intensities \(I_{A} / I_{B}\) is equal to
supporting img

1 \(1: 4\)
2 \(1: 1\)
3 \(1: 2\)
4 \(1: 16\)
PHXI15:WAVES

355074 The superposing waves are represented by the following equations
\(y_{1}=5 \sin 2 \pi(10 t-0.1 x), y_{2}=10 \sin 2 \pi(10 t-0.1 x)\)
Ratio of intensities \(\dfrac{I_{\max }}{I_{\text {min }}}\) will be

1 16
2 1
3 9
4 4
Join With Us for More Updates
PHXI15:WAVES

355070 Two waves of nearly same amplitude, same frequency travelling with same velocity are superimposing to give phenomenon of interference. If \(a_{1}\) and \(a_{2}\) be their amplitudes, \(\omega\) be the frequency for both, \(v\) be the velocity for both and \(\Delta \phi\) is the phase difference between the two waves then, incorrect statement among the following

1 The resultant intensity varies periodically with distance
2 \(\dfrac{I_{\text {min }}}{I_{\text {max }}}=\left(\dfrac{a_{1}-a_{2}}{a_{1}+a_{2}}\right)^{2}\)
3 Both the waves must have been travelling in the same direction and must be coherent
4 \(I_{R}=I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \cos (\Delta \phi)\), where constructive interference is obtained for path difference that are odd multiple of \(\dfrac{\lambda}{2}\) and destructive interference is obtained for path difference that are even multiple of \(\dfrac{\lambda}{2}\)
PHXI15:WAVES

355071 Two waves represented by
\({y_{1}=10 \sin (2000 \pi t+2 x)}\) and
\({y_{2}=10 \sin \left(2000 \pi t+2 x+\dfrac{\pi}{2}\right)}\)
are superimposed at any point at a particular instant. The resultant amplitude is

1 10 units
2 20 units
3 14.1 units
4 zero
PHXI15:WAVES

355072 Assertion :
Velocity of particles, while crossing mean position (in stationary waves) varies from maximum at antinodes to zero at nodes.
Reason :
Amplitude of vibration at antinodes is maximum and at nodes, the amplitude is zero, and all particles between two successive nodes cross the mean position together.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

355073 The displacement-time graphs for two sound waves \(A\) and \(B\) are shown in the figure, then the ratio of their intensities \(I_{A} / I_{B}\) is equal to
supporting img

1 \(1: 4\)
2 \(1: 1\)
3 \(1: 2\)
4 \(1: 16\)
PHXI15:WAVES

355074 The superposing waves are represented by the following equations
\(y_{1}=5 \sin 2 \pi(10 t-0.1 x), y_{2}=10 \sin 2 \pi(10 t-0.1 x)\)
Ratio of intensities \(\dfrac{I_{\max }}{I_{\text {min }}}\) will be

1 16
2 1
3 9
4 4