Physics-
General
Easy
Question
Two strings
and
of a sitar produce a beat frequency
When the tension of the string
is slightly increased the beat frequency is found to be
If the frequency of
is
then the original frequency of
was
- 296 Hz
- 298 Hz
- 302 Hz
- 302 Hz
The correct answer is: 296 Hz
![n subscript x end subscript equals 300 H z comma blank n subscript y end subscript equals blank ?](data:image/png;base64,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)
beat frequency
which is decreasing
after increasing the tension of the string ![y.](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAMCAYAAABSgIzaAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAIFJREFUeNpjYICAuUAczoAJCoC4lQEPiAfiLjQxLiC+BcTC+DR6AfEqNLF6IK5lIABApl5B4osC8V0g5mAgAnxDYvdB/UcUOAzESlAMso2JWI0LgdgPiJcCcSwDCaAAGi2X8Kj5D8UoIAAq6EeqRpCG4wxkgG1AbEmqJh0g3kKKBgB7chfCym7+RQAAAFN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+eTwvbWk+PG1vPi48L21vPjwvbWF0aD6pmM29AAAAAElFTkSuQmCC)
Also tension of wire
increasing so ![n subscript y end subscript upwards arrow left parenthesis because n proportional to square root of T right parenthesis](data:image/png;base64,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)
Hence ![n subscript x end subscript minus n subscript y end subscript upwards arrow equals x downwards arrow blank rightwards arrow C o r r e c t](data:image/png;base64,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)
![n subscript y end subscript upwards arrow negative n subscript x end subscript equals x downwards arrow blank rightwards arrow W r o n g](data:image/png;base64,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)
![rightwards double arrow n subscript y end subscript equals n subscript x end subscript minus x equals 300 minus 4 equals 296 H z](data:image/png;base64,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)
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A transverse sinusoidal wave moves along a string in positive x-direction at a speed of 10
. The wavelength of the wave is 0.5 m and its amplitude is 10.cm at a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is
![](data:image/png;base64,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)
A transverse sinusoidal wave moves along a string in positive x-direction at a speed of 10
. The wavelength of the wave is 0.5 m and its amplitude is 10.cm at a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is
![](data:image/png;base64,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)
physics-General
maths-
The point on the line x – y + 2 = 0 from which the tangent to the parabola y2 = 8x is perpendicular to the given line is (a, b), then the line ax + by + c = 0 is
The point on the line x – y + 2 = 0 from which the tangent to the parabola y2 = 8x is perpendicular to the given line is (a, b), then the line ax + by + c = 0 is
maths-General
Maths-
The equation of normal in terms of slope m to the parabola (y – 2)2 = 4 (x – 3)
The equation of normal in terms of slope m to the parabola (y – 2)2 = 4 (x – 3)
Maths-General
maths-
The condition that the parabolas y2 = 4c (x – d) and y2 = 4ax have a common normal other then x-axis (a
0, c
0) is
The condition that the parabolas y2 = 4c (x – d) and y2 = 4ax have a common normal other then x-axis (a
0, c
0) is
maths-General
physics-
If the speed of the wave shown in the figure is
in the given medium, then the equation of the wave propagating in the positive
-direction will be (all quantities are in M.K.S. units)
![](data:image/png;base64,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)
If the speed of the wave shown in the figure is
in the given medium, then the equation of the wave propagating in the positive
-direction will be (all quantities are in M.K.S. units)
![](data:image/png;base64,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)
physics-General
Maths-
The circle
touches the parabola y2 = 4x externally. Then
The circle
touches the parabola y2 = 4x externally. Then
Maths-General
physics-
The displacement-time graphs for two sound waves
and
are shown in the figure, then the ratio of their intensities
is equal to
![](data:image/png;base64,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)
The displacement-time graphs for two sound waves
and
are shown in the figure, then the ratio of their intensities
is equal to
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)
physics-General
Maths-
The equations of the normals at the ends of the latus rectum of the parabola y2 = 4ax are given by
The equations of the normals at the ends of the latus rectum of the parabola y2 = 4ax are given by
Maths-General
physics-
The driver of a car travelling with speed 30 metres per second towards a hill sounds a horn of frequency
If the velocity of sound in air is 330 metres per second, the frequency of the reflected sound as heard by the driver is
The driver of a car travelling with speed 30 metres per second towards a hill sounds a horn of frequency
If the velocity of sound in air is 330 metres per second, the frequency of the reflected sound as heard by the driver is
physics-General
physics-
An Indian submarine and an enemy submarine move towards each other during maneuvers in motionless water in the Indian ocean. The Indian submarine moves at
and the enemy submarine at
The Indian sub sends out a sonar signal (sound wave in water) at
Sonar waves travel at
What is the frequency detected by the Indian submarine
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)
An Indian submarine and an enemy submarine move towards each other during maneuvers in motionless water in the Indian ocean. The Indian submarine moves at
and the enemy submarine at
The Indian sub sends out a sonar signal (sound wave in water) at
Sonar waves travel at
What is the frequency detected by the Indian submarine
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)
physics-General