274454
Which of the following equations correctly represents a travelling wave having wavelength $\lambda =4.0\text{cm}$, frequency $\text{v}=100\text{Hz}$ and travelling in positive $\text{x}$-axis direction?
(d) We have
$k=\frac{2\pi }{\lambda }=\frac{2\pi }{4}=0.5\pi \text{c}{{\text{m}}^{-1}}$
$\omega =2\pi \text{f}=2\pi \times 100=200\pi {{\text{s}}^{-1}}$
NCERT Page-373 / N-284
WAVES (NCERT)
274455
A travelling harmonic wave is represented by the equation $y\left( x,\text{t} \right)={{10}^{-3}}\text{sin}\left( 50\text{t}+2x \right)$, where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?
1 The wave is propagating along the negative$x$-axis with speed $25\text{m}{{\text{s}}^{-1}}$.
2 The wave is propagating along the positive$\text{x}$-axis with speed $100\text{m}{{\text{s}}^{-1}}$.
3 The wave is propagating along the positive$x$-axis with speed $25\text{m}{{\text{s}}^{-1}}$.
4 The wave is propagating along the negative$x$-axis with speed $100\text{m}{{\text{s}}^{-1}}$.
Explanation:
(a) Comparing the given equation
$y={{10}^{-3}}\text{sin}\left( 50t+2x \right)$ with standard equation,
$\text{y}=\text{asin}\left( \omega \text{t}-\text{kx} \right)$
$\Rightarrow $ wave is moving along -ve x-axis with speed
$\text{v}=\frac{\omega }{\text{K}}\Rightarrow \text{v}=\frac{50}{2}=25\text{m}/\text{sec}$.
NCERT Page-373 / N-284
WAVES (NCERT)
274436
A progressive wave travelling along the positive $x$-direction is represented by $y\left( x,t \right)=A\text{sin}\left( kx-\omega t+\phi \right)$. Its snapshot at $t=0$ is given in the figure.
For this wave, the phase $\phi $ is:
1 $-\frac{\pi }{2}$
2 $\pi $
3 0
4 $\frac{\pi }{2}$
Explanation:
(b) At $t=0,x=0,y=0$
$\phi =\pi \text{rad}$
NCERT Page-370 / N-282
WAVES (NCERT)
274437
The equation $y=A\text{si}{{\text{n}}^{2}}\left( kx-\omega t \right)$ represents a wave with
1 amplitude $\text{A}$, frequency $\omega /2\pi $
2 amplitude $A/2$, frequency $\omega /\pi $
3 amplitude $2\text{A}$, frequency $\omega /4\pi $
NEET Test Series from KOTA - 10 Papers In MS WORD
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WAVES (NCERT)
274454
Which of the following equations correctly represents a travelling wave having wavelength $\lambda =4.0\text{cm}$, frequency $\text{v}=100\text{Hz}$ and travelling in positive $\text{x}$-axis direction?
(d) We have
$k=\frac{2\pi }{\lambda }=\frac{2\pi }{4}=0.5\pi \text{c}{{\text{m}}^{-1}}$
$\omega =2\pi \text{f}=2\pi \times 100=200\pi {{\text{s}}^{-1}}$
NCERT Page-373 / N-284
WAVES (NCERT)
274455
A travelling harmonic wave is represented by the equation $y\left( x,\text{t} \right)={{10}^{-3}}\text{sin}\left( 50\text{t}+2x \right)$, where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?
1 The wave is propagating along the negative$x$-axis with speed $25\text{m}{{\text{s}}^{-1}}$.
2 The wave is propagating along the positive$\text{x}$-axis with speed $100\text{m}{{\text{s}}^{-1}}$.
3 The wave is propagating along the positive$x$-axis with speed $25\text{m}{{\text{s}}^{-1}}$.
4 The wave is propagating along the negative$x$-axis with speed $100\text{m}{{\text{s}}^{-1}}$.
Explanation:
(a) Comparing the given equation
$y={{10}^{-3}}\text{sin}\left( 50t+2x \right)$ with standard equation,
$\text{y}=\text{asin}\left( \omega \text{t}-\text{kx} \right)$
$\Rightarrow $ wave is moving along -ve x-axis with speed
$\text{v}=\frac{\omega }{\text{K}}\Rightarrow \text{v}=\frac{50}{2}=25\text{m}/\text{sec}$.
NCERT Page-373 / N-284
WAVES (NCERT)
274436
A progressive wave travelling along the positive $x$-direction is represented by $y\left( x,t \right)=A\text{sin}\left( kx-\omega t+\phi \right)$. Its snapshot at $t=0$ is given in the figure.
For this wave, the phase $\phi $ is:
1 $-\frac{\pi }{2}$
2 $\pi $
3 0
4 $\frac{\pi }{2}$
Explanation:
(b) At $t=0,x=0,y=0$
$\phi =\pi \text{rad}$
NCERT Page-370 / N-282
WAVES (NCERT)
274437
The equation $y=A\text{si}{{\text{n}}^{2}}\left( kx-\omega t \right)$ represents a wave with
1 amplitude $\text{A}$, frequency $\omega /2\pi $
2 amplitude $A/2$, frequency $\omega /\pi $
3 amplitude $2\text{A}$, frequency $\omega /4\pi $
274454
Which of the following equations correctly represents a travelling wave having wavelength $\lambda =4.0\text{cm}$, frequency $\text{v}=100\text{Hz}$ and travelling in positive $\text{x}$-axis direction?
(d) We have
$k=\frac{2\pi }{\lambda }=\frac{2\pi }{4}=0.5\pi \text{c}{{\text{m}}^{-1}}$
$\omega =2\pi \text{f}=2\pi \times 100=200\pi {{\text{s}}^{-1}}$
NCERT Page-373 / N-284
WAVES (NCERT)
274455
A travelling harmonic wave is represented by the equation $y\left( x,\text{t} \right)={{10}^{-3}}\text{sin}\left( 50\text{t}+2x \right)$, where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?
1 The wave is propagating along the negative$x$-axis with speed $25\text{m}{{\text{s}}^{-1}}$.
2 The wave is propagating along the positive$\text{x}$-axis with speed $100\text{m}{{\text{s}}^{-1}}$.
3 The wave is propagating along the positive$x$-axis with speed $25\text{m}{{\text{s}}^{-1}}$.
4 The wave is propagating along the negative$x$-axis with speed $100\text{m}{{\text{s}}^{-1}}$.
Explanation:
(a) Comparing the given equation
$y={{10}^{-3}}\text{sin}\left( 50t+2x \right)$ with standard equation,
$\text{y}=\text{asin}\left( \omega \text{t}-\text{kx} \right)$
$\Rightarrow $ wave is moving along -ve x-axis with speed
$\text{v}=\frac{\omega }{\text{K}}\Rightarrow \text{v}=\frac{50}{2}=25\text{m}/\text{sec}$.
NCERT Page-373 / N-284
WAVES (NCERT)
274436
A progressive wave travelling along the positive $x$-direction is represented by $y\left( x,t \right)=A\text{sin}\left( kx-\omega t+\phi \right)$. Its snapshot at $t=0$ is given in the figure.
For this wave, the phase $\phi $ is:
1 $-\frac{\pi }{2}$
2 $\pi $
3 0
4 $\frac{\pi }{2}$
Explanation:
(b) At $t=0,x=0,y=0$
$\phi =\pi \text{rad}$
NCERT Page-370 / N-282
WAVES (NCERT)
274437
The equation $y=A\text{si}{{\text{n}}^{2}}\left( kx-\omega t \right)$ represents a wave with
1 amplitude $\text{A}$, frequency $\omega /2\pi $
2 amplitude $A/2$, frequency $\omega /\pi $
3 amplitude $2\text{A}$, frequency $\omega /4\pi $
274454
Which of the following equations correctly represents a travelling wave having wavelength $\lambda =4.0\text{cm}$, frequency $\text{v}=100\text{Hz}$ and travelling in positive $\text{x}$-axis direction?
(d) We have
$k=\frac{2\pi }{\lambda }=\frac{2\pi }{4}=0.5\pi \text{c}{{\text{m}}^{-1}}$
$\omega =2\pi \text{f}=2\pi \times 100=200\pi {{\text{s}}^{-1}}$
NCERT Page-373 / N-284
WAVES (NCERT)
274455
A travelling harmonic wave is represented by the equation $y\left( x,\text{t} \right)={{10}^{-3}}\text{sin}\left( 50\text{t}+2x \right)$, where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?
1 The wave is propagating along the negative$x$-axis with speed $25\text{m}{{\text{s}}^{-1}}$.
2 The wave is propagating along the positive$\text{x}$-axis with speed $100\text{m}{{\text{s}}^{-1}}$.
3 The wave is propagating along the positive$x$-axis with speed $25\text{m}{{\text{s}}^{-1}}$.
4 The wave is propagating along the negative$x$-axis with speed $100\text{m}{{\text{s}}^{-1}}$.
Explanation:
(a) Comparing the given equation
$y={{10}^{-3}}\text{sin}\left( 50t+2x \right)$ with standard equation,
$\text{y}=\text{asin}\left( \omega \text{t}-\text{kx} \right)$
$\Rightarrow $ wave is moving along -ve x-axis with speed
$\text{v}=\frac{\omega }{\text{K}}\Rightarrow \text{v}=\frac{50}{2}=25\text{m}/\text{sec}$.
NCERT Page-373 / N-284
WAVES (NCERT)
274436
A progressive wave travelling along the positive $x$-direction is represented by $y\left( x,t \right)=A\text{sin}\left( kx-\omega t+\phi \right)$. Its snapshot at $t=0$ is given in the figure.
For this wave, the phase $\phi $ is:
1 $-\frac{\pi }{2}$
2 $\pi $
3 0
4 $\frac{\pi }{2}$
Explanation:
(b) At $t=0,x=0,y=0$
$\phi =\pi \text{rad}$
NCERT Page-370 / N-282
WAVES (NCERT)
274437
The equation $y=A\text{si}{{\text{n}}^{2}}\left( kx-\omega t \right)$ represents a wave with
1 amplitude $\text{A}$, frequency $\omega /2\pi $
2 amplitude $A/2$, frequency $\omega /\pi $
3 amplitude $2\text{A}$, frequency $\omega /4\pi $
