NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXI15:WAVES
355156
If \(n_{1}, n_{2}\) and \(n_{3}\) are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency \(n\) of the string is given by
355157
The equation of a stationary wave is given by \(y=6 \sin (\pi x / 3) \cos 40 \pi t\) where \(y\) and \(x\) are given in \(cm\) and time \(t\) in second, then the amplitude of progressive wave is
1 \(2\;cm\)
2 \(6\;cm\)
3 \(3\;cm\)
4 \(12\;cm\)
Explanation:
For the given standing wave \(2A = 6{\text{ or }}A = 3\;cm\)
PHXI15:WAVES
355158
Two wires are kept tight between the same pair of supports. The ratio of tension in the two wires are \(2: 1\), radii are \(3: 1\) and that of densities are \(1: 2\). What is the ratio of their fundamental frequencies?
1 \(2: 3\)
2 \(1: 2\)
3 \(4: 3\)
4 \(3: 4\)
Explanation:
Fundamental frequency is \(\begin{aligned}& f=\dfrac{1}{2 \ell} \sqrt{\dfrac{T}{\mu}}=\dfrac{1}{2 \ell} \sqrt{\dfrac{T}{\rho A}} \\& f=\dfrac{1}{2 \ell} \sqrt{\dfrac{T}{\rho \pi d^{2}}} \\& \dfrac{f_{1}}{f_{2}}=\sqrt{\dfrac{T_{1}}{T_{2}} \times \dfrac{\rho_{2} \times d_{2}^{2}}{\rho_{1} \times d_{1}^{2}}} \\& \dfrac{f_{1}}{f_{2}}=\sqrt{\dfrac{2}{1} \times \dfrac{1}{9} \times \dfrac{2}{1}}=\dfrac{2}{3}\end{aligned}\)
PHXI15:WAVES
355159
A wave equation is represented as \(r=A \sin \left[\alpha\left(\dfrac{x-y}{2}\right)\right] \cos \left[\omega t-\alpha\left(\dfrac{x+y}{2}\right)\right]\) where \(x\) and \(y\) are in meters and \(t\) is in seconds. Then
1 The wave is a stationary wave
2 The wave is a progressive wave propagating along \(+x-a\) axis
3 The wave is a progressive wave propagating at right angle to the \(+x\)-axis
4 All points lying on line \(y=x-\dfrac{2 \pi}{\alpha}\) are always at rest.
Explanation:
The given equation represents the superposition of two progressive waves travelling along \(x\) and \(y\) axes given by \({r_1} = - \frac{A}{2}\sin (\omega t - \alpha x)\,\& \) \({r_2} = \frac{A}{2}\sin (\omega t - \alpha y)\) \(r = {r_1} + {r_2}\) \(=A \sin \left[\alpha \dfrac{(x-y)}{2}\right] \cos \left[\omega t-\alpha \dfrac{(x+y)}{2}\right]\) from the given equation the amplitude of the wave is \(A_{R}=A \sin \left[\alpha\left(\dfrac{x-y}{2}\right)\right]\) The amplitude becomes zero \({A_R} = A\sin \left[ {\alpha \left( {\frac{{x - y}}{2}} \right)} \right] = 0\) \(\alpha \left( {\frac{{x - y}}{2}} \right) = n\pi \;\;\;{\mkern 1mu} {\kern 1pt} (n = 0,1,2, \ldots .)\) \(\alpha \left( {\frac{{x - y}}{2}} \right) = \pi \Rightarrow x - y = \frac{{2\pi }}{\alpha }\) \(y = x - \frac{{2\pi }}{\alpha }\) All the points that lie on the line \(y=x-\dfrac{2 \pi}{\alpha}\) are always at rest.
355156
If \(n_{1}, n_{2}\) and \(n_{3}\) are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency \(n\) of the string is given by
355157
The equation of a stationary wave is given by \(y=6 \sin (\pi x / 3) \cos 40 \pi t\) where \(y\) and \(x\) are given in \(cm\) and time \(t\) in second, then the amplitude of progressive wave is
1 \(2\;cm\)
2 \(6\;cm\)
3 \(3\;cm\)
4 \(12\;cm\)
Explanation:
For the given standing wave \(2A = 6{\text{ or }}A = 3\;cm\)
PHXI15:WAVES
355158
Two wires are kept tight between the same pair of supports. The ratio of tension in the two wires are \(2: 1\), radii are \(3: 1\) and that of densities are \(1: 2\). What is the ratio of their fundamental frequencies?
1 \(2: 3\)
2 \(1: 2\)
3 \(4: 3\)
4 \(3: 4\)
Explanation:
Fundamental frequency is \(\begin{aligned}& f=\dfrac{1}{2 \ell} \sqrt{\dfrac{T}{\mu}}=\dfrac{1}{2 \ell} \sqrt{\dfrac{T}{\rho A}} \\& f=\dfrac{1}{2 \ell} \sqrt{\dfrac{T}{\rho \pi d^{2}}} \\& \dfrac{f_{1}}{f_{2}}=\sqrt{\dfrac{T_{1}}{T_{2}} \times \dfrac{\rho_{2} \times d_{2}^{2}}{\rho_{1} \times d_{1}^{2}}} \\& \dfrac{f_{1}}{f_{2}}=\sqrt{\dfrac{2}{1} \times \dfrac{1}{9} \times \dfrac{2}{1}}=\dfrac{2}{3}\end{aligned}\)
PHXI15:WAVES
355159
A wave equation is represented as \(r=A \sin \left[\alpha\left(\dfrac{x-y}{2}\right)\right] \cos \left[\omega t-\alpha\left(\dfrac{x+y}{2}\right)\right]\) where \(x\) and \(y\) are in meters and \(t\) is in seconds. Then
1 The wave is a stationary wave
2 The wave is a progressive wave propagating along \(+x-a\) axis
3 The wave is a progressive wave propagating at right angle to the \(+x\)-axis
4 All points lying on line \(y=x-\dfrac{2 \pi}{\alpha}\) are always at rest.
Explanation:
The given equation represents the superposition of two progressive waves travelling along \(x\) and \(y\) axes given by \({r_1} = - \frac{A}{2}\sin (\omega t - \alpha x)\,\& \) \({r_2} = \frac{A}{2}\sin (\omega t - \alpha y)\) \(r = {r_1} + {r_2}\) \(=A \sin \left[\alpha \dfrac{(x-y)}{2}\right] \cos \left[\omega t-\alpha \dfrac{(x+y)}{2}\right]\) from the given equation the amplitude of the wave is \(A_{R}=A \sin \left[\alpha\left(\dfrac{x-y}{2}\right)\right]\) The amplitude becomes zero \({A_R} = A\sin \left[ {\alpha \left( {\frac{{x - y}}{2}} \right)} \right] = 0\) \(\alpha \left( {\frac{{x - y}}{2}} \right) = n\pi \;\;\;{\mkern 1mu} {\kern 1pt} (n = 0,1,2, \ldots .)\) \(\alpha \left( {\frac{{x - y}}{2}} \right) = \pi \Rightarrow x - y = \frac{{2\pi }}{\alpha }\) \(y = x - \frac{{2\pi }}{\alpha }\) All the points that lie on the line \(y=x-\dfrac{2 \pi}{\alpha}\) are always at rest.
355156
If \(n_{1}, n_{2}\) and \(n_{3}\) are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency \(n\) of the string is given by
355157
The equation of a stationary wave is given by \(y=6 \sin (\pi x / 3) \cos 40 \pi t\) where \(y\) and \(x\) are given in \(cm\) and time \(t\) in second, then the amplitude of progressive wave is
1 \(2\;cm\)
2 \(6\;cm\)
3 \(3\;cm\)
4 \(12\;cm\)
Explanation:
For the given standing wave \(2A = 6{\text{ or }}A = 3\;cm\)
PHXI15:WAVES
355158
Two wires are kept tight between the same pair of supports. The ratio of tension in the two wires are \(2: 1\), radii are \(3: 1\) and that of densities are \(1: 2\). What is the ratio of their fundamental frequencies?
1 \(2: 3\)
2 \(1: 2\)
3 \(4: 3\)
4 \(3: 4\)
Explanation:
Fundamental frequency is \(\begin{aligned}& f=\dfrac{1}{2 \ell} \sqrt{\dfrac{T}{\mu}}=\dfrac{1}{2 \ell} \sqrt{\dfrac{T}{\rho A}} \\& f=\dfrac{1}{2 \ell} \sqrt{\dfrac{T}{\rho \pi d^{2}}} \\& \dfrac{f_{1}}{f_{2}}=\sqrt{\dfrac{T_{1}}{T_{2}} \times \dfrac{\rho_{2} \times d_{2}^{2}}{\rho_{1} \times d_{1}^{2}}} \\& \dfrac{f_{1}}{f_{2}}=\sqrt{\dfrac{2}{1} \times \dfrac{1}{9} \times \dfrac{2}{1}}=\dfrac{2}{3}\end{aligned}\)
PHXI15:WAVES
355159
A wave equation is represented as \(r=A \sin \left[\alpha\left(\dfrac{x-y}{2}\right)\right] \cos \left[\omega t-\alpha\left(\dfrac{x+y}{2}\right)\right]\) where \(x\) and \(y\) are in meters and \(t\) is in seconds. Then
1 The wave is a stationary wave
2 The wave is a progressive wave propagating along \(+x-a\) axis
3 The wave is a progressive wave propagating at right angle to the \(+x\)-axis
4 All points lying on line \(y=x-\dfrac{2 \pi}{\alpha}\) are always at rest.
Explanation:
The given equation represents the superposition of two progressive waves travelling along \(x\) and \(y\) axes given by \({r_1} = - \frac{A}{2}\sin (\omega t - \alpha x)\,\& \) \({r_2} = \frac{A}{2}\sin (\omega t - \alpha y)\) \(r = {r_1} + {r_2}\) \(=A \sin \left[\alpha \dfrac{(x-y)}{2}\right] \cos \left[\omega t-\alpha \dfrac{(x+y)}{2}\right]\) from the given equation the amplitude of the wave is \(A_{R}=A \sin \left[\alpha\left(\dfrac{x-y}{2}\right)\right]\) The amplitude becomes zero \({A_R} = A\sin \left[ {\alpha \left( {\frac{{x - y}}{2}} \right)} \right] = 0\) \(\alpha \left( {\frac{{x - y}}{2}} \right) = n\pi \;\;\;{\mkern 1mu} {\kern 1pt} (n = 0,1,2, \ldots .)\) \(\alpha \left( {\frac{{x - y}}{2}} \right) = \pi \Rightarrow x - y = \frac{{2\pi }}{\alpha }\) \(y = x - \frac{{2\pi }}{\alpha }\) All the points that lie on the line \(y=x-\dfrac{2 \pi}{\alpha}\) are always at rest.
355156
If \(n_{1}, n_{2}\) and \(n_{3}\) are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency \(n\) of the string is given by
355157
The equation of a stationary wave is given by \(y=6 \sin (\pi x / 3) \cos 40 \pi t\) where \(y\) and \(x\) are given in \(cm\) and time \(t\) in second, then the amplitude of progressive wave is
1 \(2\;cm\)
2 \(6\;cm\)
3 \(3\;cm\)
4 \(12\;cm\)
Explanation:
For the given standing wave \(2A = 6{\text{ or }}A = 3\;cm\)
PHXI15:WAVES
355158
Two wires are kept tight between the same pair of supports. The ratio of tension in the two wires are \(2: 1\), radii are \(3: 1\) and that of densities are \(1: 2\). What is the ratio of their fundamental frequencies?
1 \(2: 3\)
2 \(1: 2\)
3 \(4: 3\)
4 \(3: 4\)
Explanation:
Fundamental frequency is \(\begin{aligned}& f=\dfrac{1}{2 \ell} \sqrt{\dfrac{T}{\mu}}=\dfrac{1}{2 \ell} \sqrt{\dfrac{T}{\rho A}} \\& f=\dfrac{1}{2 \ell} \sqrt{\dfrac{T}{\rho \pi d^{2}}} \\& \dfrac{f_{1}}{f_{2}}=\sqrt{\dfrac{T_{1}}{T_{2}} \times \dfrac{\rho_{2} \times d_{2}^{2}}{\rho_{1} \times d_{1}^{2}}} \\& \dfrac{f_{1}}{f_{2}}=\sqrt{\dfrac{2}{1} \times \dfrac{1}{9} \times \dfrac{2}{1}}=\dfrac{2}{3}\end{aligned}\)
PHXI15:WAVES
355159
A wave equation is represented as \(r=A \sin \left[\alpha\left(\dfrac{x-y}{2}\right)\right] \cos \left[\omega t-\alpha\left(\dfrac{x+y}{2}\right)\right]\) where \(x\) and \(y\) are in meters and \(t\) is in seconds. Then
1 The wave is a stationary wave
2 The wave is a progressive wave propagating along \(+x-a\) axis
3 The wave is a progressive wave propagating at right angle to the \(+x\)-axis
4 All points lying on line \(y=x-\dfrac{2 \pi}{\alpha}\) are always at rest.
Explanation:
The given equation represents the superposition of two progressive waves travelling along \(x\) and \(y\) axes given by \({r_1} = - \frac{A}{2}\sin (\omega t - \alpha x)\,\& \) \({r_2} = \frac{A}{2}\sin (\omega t - \alpha y)\) \(r = {r_1} + {r_2}\) \(=A \sin \left[\alpha \dfrac{(x-y)}{2}\right] \cos \left[\omega t-\alpha \dfrac{(x+y)}{2}\right]\) from the given equation the amplitude of the wave is \(A_{R}=A \sin \left[\alpha\left(\dfrac{x-y}{2}\right)\right]\) The amplitude becomes zero \({A_R} = A\sin \left[ {\alpha \left( {\frac{{x - y}}{2}} \right)} \right] = 0\) \(\alpha \left( {\frac{{x - y}}{2}} \right) = n\pi \;\;\;{\mkern 1mu} {\kern 1pt} (n = 0,1,2, \ldots .)\) \(\alpha \left( {\frac{{x - y}}{2}} \right) = \pi \Rightarrow x - y = \frac{{2\pi }}{\alpha }\) \(y = x - \frac{{2\pi }}{\alpha }\) All the points that lie on the line \(y=x-\dfrac{2 \pi}{\alpha}\) are always at rest.
