172282
Among the following equations, which one represents the spherical progressive wave?
1 $y=r \sin \omega t$
2 $y=\frac{a}{r} \sin (\omega t-k x)$
3 $y=\frac{a}{\sqrt{r}} \sin (\omega t-k x)$
4 $y=\sqrt{\frac{a}{r}} \sin (\omega t-k x)$
Explanation:
B $y=\frac{a}{r} \sin (\omega t-k x)$ In case of spherical progressive wave, the amplitude of a wave is inversely proportional to the distance of the source from the point of consideration i.e. Amplitude $\propto \frac{1}{\mathrm{r}}$. Hence, $\quad y=\frac{a}{r} \sin (\omega t-k x) \quad$ represents equation of spherical progressive wave.
UP CPMT-2012
WAVES
172286
Which of the following equations represents a wave travelling along $y$-axis?
1 $y=A \sin (k x-\omega t)$
2 $x=A \sin (k y-\omega t)$
3 $y=A \sin k y \cos \omega t$
4 $y=A \cos k y \sin \omega t$
Explanation:
B The equation for the wave travelling along the $\mathrm{y}$-axis, $\mathrm{x}=\mathrm{Asin}(\mathrm{ky}-\omega \mathrm{t})$ When a transverse wave is moving in a $\mathrm{Y}$ - direction, then the displacement of the wave will be in the $\mathrm{x}$ direction, So, in transverse wave, the displacement of a particle will be perpendicular to the direction of the wave motion.
UP CPMT-2005
WAVES
172294
Stationary wave is represented by $Y=A$ sin $(100 \mathrm{t}) \cos (0.01 x)$ where $Y$ and $A$ are in $\mathbf{m m}, t$ in sec. and $x$ in $m$. The velocity of stationary wave is
1 $1 \mathrm{~m} / \mathrm{s}$
2 $10^{3} \mathrm{~m} / \mathrm{s}$
3 $10^{4} \mathrm{~m} / \mathrm{s}$
4 Not derivable
Explanation:
C Stationary wave is represented by $y=A \sin (100 t) \cos (0.01 x)$ Velocity of wave $(v)=\frac{\text { Coefficient of } t}{\text { Coefficient of } x}$ $=\frac{100}{0.01}$ $=10^{4} \mathrm{~m} / \mathrm{sec}$
MP PET-2008
WAVES
172296
Progressive waves are represented by the equation $\mathbf{y}_{1}=\mathbf{a} \sin (\omega t-x) \text { and }$ $\mathbf{y}_{2}=b \cos (\omega t-x)$ The phase difference between waves is
1 $0^{\circ}$
2 $45^{\circ}$
3 $90^{\circ}$
4 $180^{\circ}$
Explanation:
C Progressive waves which travels continuously in a medium in the same direction. Without a change in its amplitudes is called a travelling wave $\sin \left(\theta+\frac{\pi}{2}\right)=\cos \theta$ $\mathrm{y}_{2}=\mathrm{b} \cos (\omega \mathrm{t}-\mathrm{x})=\mathrm{b} \sin \left(\omega \mathrm{t}-\mathrm{x}+\frac{\pi}{2}\right)$ Difference between the two waves $\frac{\pi}{2}=90^{\circ}$.
172282
Among the following equations, which one represents the spherical progressive wave?
1 $y=r \sin \omega t$
2 $y=\frac{a}{r} \sin (\omega t-k x)$
3 $y=\frac{a}{\sqrt{r}} \sin (\omega t-k x)$
4 $y=\sqrt{\frac{a}{r}} \sin (\omega t-k x)$
Explanation:
B $y=\frac{a}{r} \sin (\omega t-k x)$ In case of spherical progressive wave, the amplitude of a wave is inversely proportional to the distance of the source from the point of consideration i.e. Amplitude $\propto \frac{1}{\mathrm{r}}$. Hence, $\quad y=\frac{a}{r} \sin (\omega t-k x) \quad$ represents equation of spherical progressive wave.
UP CPMT-2012
WAVES
172286
Which of the following equations represents a wave travelling along $y$-axis?
1 $y=A \sin (k x-\omega t)$
2 $x=A \sin (k y-\omega t)$
3 $y=A \sin k y \cos \omega t$
4 $y=A \cos k y \sin \omega t$
Explanation:
B The equation for the wave travelling along the $\mathrm{y}$-axis, $\mathrm{x}=\mathrm{Asin}(\mathrm{ky}-\omega \mathrm{t})$ When a transverse wave is moving in a $\mathrm{Y}$ - direction, then the displacement of the wave will be in the $\mathrm{x}$ direction, So, in transverse wave, the displacement of a particle will be perpendicular to the direction of the wave motion.
UP CPMT-2005
WAVES
172294
Stationary wave is represented by $Y=A$ sin $(100 \mathrm{t}) \cos (0.01 x)$ where $Y$ and $A$ are in $\mathbf{m m}, t$ in sec. and $x$ in $m$. The velocity of stationary wave is
1 $1 \mathrm{~m} / \mathrm{s}$
2 $10^{3} \mathrm{~m} / \mathrm{s}$
3 $10^{4} \mathrm{~m} / \mathrm{s}$
4 Not derivable
Explanation:
C Stationary wave is represented by $y=A \sin (100 t) \cos (0.01 x)$ Velocity of wave $(v)=\frac{\text { Coefficient of } t}{\text { Coefficient of } x}$ $=\frac{100}{0.01}$ $=10^{4} \mathrm{~m} / \mathrm{sec}$
MP PET-2008
WAVES
172296
Progressive waves are represented by the equation $\mathbf{y}_{1}=\mathbf{a} \sin (\omega t-x) \text { and }$ $\mathbf{y}_{2}=b \cos (\omega t-x)$ The phase difference between waves is
1 $0^{\circ}$
2 $45^{\circ}$
3 $90^{\circ}$
4 $180^{\circ}$
Explanation:
C Progressive waves which travels continuously in a medium in the same direction. Without a change in its amplitudes is called a travelling wave $\sin \left(\theta+\frac{\pi}{2}\right)=\cos \theta$ $\mathrm{y}_{2}=\mathrm{b} \cos (\omega \mathrm{t}-\mathrm{x})=\mathrm{b} \sin \left(\omega \mathrm{t}-\mathrm{x}+\frac{\pi}{2}\right)$ Difference between the two waves $\frac{\pi}{2}=90^{\circ}$.
172282
Among the following equations, which one represents the spherical progressive wave?
1 $y=r \sin \omega t$
2 $y=\frac{a}{r} \sin (\omega t-k x)$
3 $y=\frac{a}{\sqrt{r}} \sin (\omega t-k x)$
4 $y=\sqrt{\frac{a}{r}} \sin (\omega t-k x)$
Explanation:
B $y=\frac{a}{r} \sin (\omega t-k x)$ In case of spherical progressive wave, the amplitude of a wave is inversely proportional to the distance of the source from the point of consideration i.e. Amplitude $\propto \frac{1}{\mathrm{r}}$. Hence, $\quad y=\frac{a}{r} \sin (\omega t-k x) \quad$ represents equation of spherical progressive wave.
UP CPMT-2012
WAVES
172286
Which of the following equations represents a wave travelling along $y$-axis?
1 $y=A \sin (k x-\omega t)$
2 $x=A \sin (k y-\omega t)$
3 $y=A \sin k y \cos \omega t$
4 $y=A \cos k y \sin \omega t$
Explanation:
B The equation for the wave travelling along the $\mathrm{y}$-axis, $\mathrm{x}=\mathrm{Asin}(\mathrm{ky}-\omega \mathrm{t})$ When a transverse wave is moving in a $\mathrm{Y}$ - direction, then the displacement of the wave will be in the $\mathrm{x}$ direction, So, in transverse wave, the displacement of a particle will be perpendicular to the direction of the wave motion.
UP CPMT-2005
WAVES
172294
Stationary wave is represented by $Y=A$ sin $(100 \mathrm{t}) \cos (0.01 x)$ where $Y$ and $A$ are in $\mathbf{m m}, t$ in sec. and $x$ in $m$. The velocity of stationary wave is
1 $1 \mathrm{~m} / \mathrm{s}$
2 $10^{3} \mathrm{~m} / \mathrm{s}$
3 $10^{4} \mathrm{~m} / \mathrm{s}$
4 Not derivable
Explanation:
C Stationary wave is represented by $y=A \sin (100 t) \cos (0.01 x)$ Velocity of wave $(v)=\frac{\text { Coefficient of } t}{\text { Coefficient of } x}$ $=\frac{100}{0.01}$ $=10^{4} \mathrm{~m} / \mathrm{sec}$
MP PET-2008
WAVES
172296
Progressive waves are represented by the equation $\mathbf{y}_{1}=\mathbf{a} \sin (\omega t-x) \text { and }$ $\mathbf{y}_{2}=b \cos (\omega t-x)$ The phase difference between waves is
1 $0^{\circ}$
2 $45^{\circ}$
3 $90^{\circ}$
4 $180^{\circ}$
Explanation:
C Progressive waves which travels continuously in a medium in the same direction. Without a change in its amplitudes is called a travelling wave $\sin \left(\theta+\frac{\pi}{2}\right)=\cos \theta$ $\mathrm{y}_{2}=\mathrm{b} \cos (\omega \mathrm{t}-\mathrm{x})=\mathrm{b} \sin \left(\omega \mathrm{t}-\mathrm{x}+\frac{\pi}{2}\right)$ Difference between the two waves $\frac{\pi}{2}=90^{\circ}$.
172282
Among the following equations, which one represents the spherical progressive wave?
1 $y=r \sin \omega t$
2 $y=\frac{a}{r} \sin (\omega t-k x)$
3 $y=\frac{a}{\sqrt{r}} \sin (\omega t-k x)$
4 $y=\sqrt{\frac{a}{r}} \sin (\omega t-k x)$
Explanation:
B $y=\frac{a}{r} \sin (\omega t-k x)$ In case of spherical progressive wave, the amplitude of a wave is inversely proportional to the distance of the source from the point of consideration i.e. Amplitude $\propto \frac{1}{\mathrm{r}}$. Hence, $\quad y=\frac{a}{r} \sin (\omega t-k x) \quad$ represents equation of spherical progressive wave.
UP CPMT-2012
WAVES
172286
Which of the following equations represents a wave travelling along $y$-axis?
1 $y=A \sin (k x-\omega t)$
2 $x=A \sin (k y-\omega t)$
3 $y=A \sin k y \cos \omega t$
4 $y=A \cos k y \sin \omega t$
Explanation:
B The equation for the wave travelling along the $\mathrm{y}$-axis, $\mathrm{x}=\mathrm{Asin}(\mathrm{ky}-\omega \mathrm{t})$ When a transverse wave is moving in a $\mathrm{Y}$ - direction, then the displacement of the wave will be in the $\mathrm{x}$ direction, So, in transverse wave, the displacement of a particle will be perpendicular to the direction of the wave motion.
UP CPMT-2005
WAVES
172294
Stationary wave is represented by $Y=A$ sin $(100 \mathrm{t}) \cos (0.01 x)$ where $Y$ and $A$ are in $\mathbf{m m}, t$ in sec. and $x$ in $m$. The velocity of stationary wave is
1 $1 \mathrm{~m} / \mathrm{s}$
2 $10^{3} \mathrm{~m} / \mathrm{s}$
3 $10^{4} \mathrm{~m} / \mathrm{s}$
4 Not derivable
Explanation:
C Stationary wave is represented by $y=A \sin (100 t) \cos (0.01 x)$ Velocity of wave $(v)=\frac{\text { Coefficient of } t}{\text { Coefficient of } x}$ $=\frac{100}{0.01}$ $=10^{4} \mathrm{~m} / \mathrm{sec}$
MP PET-2008
WAVES
172296
Progressive waves are represented by the equation $\mathbf{y}_{1}=\mathbf{a} \sin (\omega t-x) \text { and }$ $\mathbf{y}_{2}=b \cos (\omega t-x)$ The phase difference between waves is
1 $0^{\circ}$
2 $45^{\circ}$
3 $90^{\circ}$
4 $180^{\circ}$
Explanation:
C Progressive waves which travels continuously in a medium in the same direction. Without a change in its amplitudes is called a travelling wave $\sin \left(\theta+\frac{\pi}{2}\right)=\cos \theta$ $\mathrm{y}_{2}=\mathrm{b} \cos (\omega \mathrm{t}-\mathrm{x})=\mathrm{b} \sin \left(\omega \mathrm{t}-\mathrm{x}+\frac{\pi}{2}\right)$ Difference between the two waves $\frac{\pi}{2}=90^{\circ}$.
