354532
The equation of a progressive wave is \(y=0.02 \sin 2 \pi\left[\dfrac{t}{0.01}-\dfrac{x}{0.3}\right]\), where \(x\) and \(y\) are in meters and \(t\) is in second. The velocity of propagation of the wave is
354533
A wave is represented by the equation \({y=7 \sin \left(7 \pi t-0.04 x+\dfrac{\pi}{3}\right)}\)where \({x}\) is in meters and \({t}\) is in seconds. The speed of the wave is
354534
The equation of a transverse wave is given by \(y=0.05 \sin \pi(2 t-0.02 x)\), where \(x\), \(y\) are in metre and \(t\) is in second. The minimum distance of separation between two particles which are in phase and the wave velocity are respectively.....
1 \(50\;m,50\;m{s^{ - 1}}\)
2 \(100\;m,100\;m{s^{ - 1}}\)
3 \(50\;m,100\;m{s^{ - 1}}\)
4 \(100\;m,50\;m{s^{ - 1}}\)
Explanation:
The given equation of a transverse wave is \(y = 0.05\sin \pi (2t - 0.02x)\) \( \Rightarrow y = 0.05\sin (2\pi t - 0.02\pi x)\) Comparing it with the standard equation \(y = A\sin (\omega t - kx),\) we get \(A = 0.05\;m,\omega = 2\pi \,rad\,{s^{ - 1}}\) \(k = 0.02\pi \,rad\,{m^{ - 1}}\) The minimum distance between points having the same phase is known as wavelength \((\lambda)\) of the wave. \(\therefore \;\;\;{\mkern 1mu} {\kern 1pt} \lambda = \frac{{2\pi }}{k} = \frac{{2\pi }}{{0.02\pi }} = 100\;m\) Wave velocity, \(v = \frac{\omega }{k} = \frac{{2\pi }}{{0.02\pi }} = 100\;m{s^{ - 1}}\)
PHXI15:WAVES
354535
The equation of transverse wave in a stretched string is \(y=5 \sin 2 \pi\left[\dfrac{t}{0.04}-\dfrac{x}{50}\right]\) where \({y}\) and \({x}\) are in \({c m}\) and \({t}\) is in second. The wavelength of wave is
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PHXI15:WAVES
354532
The equation of a progressive wave is \(y=0.02 \sin 2 \pi\left[\dfrac{t}{0.01}-\dfrac{x}{0.3}\right]\), where \(x\) and \(y\) are in meters and \(t\) is in second. The velocity of propagation of the wave is
354533
A wave is represented by the equation \({y=7 \sin \left(7 \pi t-0.04 x+\dfrac{\pi}{3}\right)}\)where \({x}\) is in meters and \({t}\) is in seconds. The speed of the wave is
354534
The equation of a transverse wave is given by \(y=0.05 \sin \pi(2 t-0.02 x)\), where \(x\), \(y\) are in metre and \(t\) is in second. The minimum distance of separation between two particles which are in phase and the wave velocity are respectively.....
1 \(50\;m,50\;m{s^{ - 1}}\)
2 \(100\;m,100\;m{s^{ - 1}}\)
3 \(50\;m,100\;m{s^{ - 1}}\)
4 \(100\;m,50\;m{s^{ - 1}}\)
Explanation:
The given equation of a transverse wave is \(y = 0.05\sin \pi (2t - 0.02x)\) \( \Rightarrow y = 0.05\sin (2\pi t - 0.02\pi x)\) Comparing it with the standard equation \(y = A\sin (\omega t - kx),\) we get \(A = 0.05\;m,\omega = 2\pi \,rad\,{s^{ - 1}}\) \(k = 0.02\pi \,rad\,{m^{ - 1}}\) The minimum distance between points having the same phase is known as wavelength \((\lambda)\) of the wave. \(\therefore \;\;\;{\mkern 1mu} {\kern 1pt} \lambda = \frac{{2\pi }}{k} = \frac{{2\pi }}{{0.02\pi }} = 100\;m\) Wave velocity, \(v = \frac{\omega }{k} = \frac{{2\pi }}{{0.02\pi }} = 100\;m{s^{ - 1}}\)
PHXI15:WAVES
354535
The equation of transverse wave in a stretched string is \(y=5 \sin 2 \pi\left[\dfrac{t}{0.04}-\dfrac{x}{50}\right]\) where \({y}\) and \({x}\) are in \({c m}\) and \({t}\) is in second. The wavelength of wave is
354532
The equation of a progressive wave is \(y=0.02 \sin 2 \pi\left[\dfrac{t}{0.01}-\dfrac{x}{0.3}\right]\), where \(x\) and \(y\) are in meters and \(t\) is in second. The velocity of propagation of the wave is
354533
A wave is represented by the equation \({y=7 \sin \left(7 \pi t-0.04 x+\dfrac{\pi}{3}\right)}\)where \({x}\) is in meters and \({t}\) is in seconds. The speed of the wave is
354534
The equation of a transverse wave is given by \(y=0.05 \sin \pi(2 t-0.02 x)\), where \(x\), \(y\) are in metre and \(t\) is in second. The minimum distance of separation between two particles which are in phase and the wave velocity are respectively.....
1 \(50\;m,50\;m{s^{ - 1}}\)
2 \(100\;m,100\;m{s^{ - 1}}\)
3 \(50\;m,100\;m{s^{ - 1}}\)
4 \(100\;m,50\;m{s^{ - 1}}\)
Explanation:
The given equation of a transverse wave is \(y = 0.05\sin \pi (2t - 0.02x)\) \( \Rightarrow y = 0.05\sin (2\pi t - 0.02\pi x)\) Comparing it with the standard equation \(y = A\sin (\omega t - kx),\) we get \(A = 0.05\;m,\omega = 2\pi \,rad\,{s^{ - 1}}\) \(k = 0.02\pi \,rad\,{m^{ - 1}}\) The minimum distance between points having the same phase is known as wavelength \((\lambda)\) of the wave. \(\therefore \;\;\;{\mkern 1mu} {\kern 1pt} \lambda = \frac{{2\pi }}{k} = \frac{{2\pi }}{{0.02\pi }} = 100\;m\) Wave velocity, \(v = \frac{\omega }{k} = \frac{{2\pi }}{{0.02\pi }} = 100\;m{s^{ - 1}}\)
PHXI15:WAVES
354535
The equation of transverse wave in a stretched string is \(y=5 \sin 2 \pi\left[\dfrac{t}{0.04}-\dfrac{x}{50}\right]\) where \({y}\) and \({x}\) are in \({c m}\) and \({t}\) is in second. The wavelength of wave is
354532
The equation of a progressive wave is \(y=0.02 \sin 2 \pi\left[\dfrac{t}{0.01}-\dfrac{x}{0.3}\right]\), where \(x\) and \(y\) are in meters and \(t\) is in second. The velocity of propagation of the wave is
354533
A wave is represented by the equation \({y=7 \sin \left(7 \pi t-0.04 x+\dfrac{\pi}{3}\right)}\)where \({x}\) is in meters and \({t}\) is in seconds. The speed of the wave is
354534
The equation of a transverse wave is given by \(y=0.05 \sin \pi(2 t-0.02 x)\), where \(x\), \(y\) are in metre and \(t\) is in second. The minimum distance of separation between two particles which are in phase and the wave velocity are respectively.....
1 \(50\;m,50\;m{s^{ - 1}}\)
2 \(100\;m,100\;m{s^{ - 1}}\)
3 \(50\;m,100\;m{s^{ - 1}}\)
4 \(100\;m,50\;m{s^{ - 1}}\)
Explanation:
The given equation of a transverse wave is \(y = 0.05\sin \pi (2t - 0.02x)\) \( \Rightarrow y = 0.05\sin (2\pi t - 0.02\pi x)\) Comparing it with the standard equation \(y = A\sin (\omega t - kx),\) we get \(A = 0.05\;m,\omega = 2\pi \,rad\,{s^{ - 1}}\) \(k = 0.02\pi \,rad\,{m^{ - 1}}\) The minimum distance between points having the same phase is known as wavelength \((\lambda)\) of the wave. \(\therefore \;\;\;{\mkern 1mu} {\kern 1pt} \lambda = \frac{{2\pi }}{k} = \frac{{2\pi }}{{0.02\pi }} = 100\;m\) Wave velocity, \(v = \frac{\omega }{k} = \frac{{2\pi }}{{0.02\pi }} = 100\;m{s^{ - 1}}\)
PHXI15:WAVES
354535
The equation of transverse wave in a stretched string is \(y=5 \sin 2 \pi\left[\dfrac{t}{0.04}-\dfrac{x}{50}\right]\) where \({y}\) and \({x}\) are in \({c m}\) and \({t}\) is in second. The wavelength of wave is