(D) Given equations are $y_1 = a \sin \omega t$ and $y_2 = a \cos \omega t$.We can rewrite $y_2$ as $y_2 = a \sin(\omega t + \pi / 2)$.The phase of th

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behind the second by $\pi / 2$.

(D) Given equations are $y_1 = a \sin \omega t$ and $y_2 = a \cos \omega t$.We can rewrite $y_2$ as $y_2 = a \sin(\omega t + \pi / 2)$.The phase of the first wave is $\phi_1 = \omega t$.The phase of the second wave is $\phi_2 = \omega t + \pi / 2$.The phase difference is $\Delta \phi = \phi_1 - \phi_2 = \omega t - (\omega t + \pi / 2) = -\pi / 2$.Since the phase difference is negative,the first wave lags behind the second wave by a phase of $\pi / 2$.

Class 11 Physics Waves and Sound Wave Equation and Characteristics of Waves

Easy

Two waves are represented by the equations $y_1 = a \sin \omega t$ and $y_2 = a \cos \omega t$. The first wave is .....

A
ahead of the second by $\pi$.
B
behind the second by $\pi$.
C
ahead of the second by $\pi / 2$.
D
behind the second by $\pi / 2$.

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Waves and Sound

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Wave Equation and Characteristics of Waves

The wave described by $y = 0.25 \sin(10\pi x - 2\pi t)$,where $x$ and $y$ are in $meters$ and $t$ in $seconds$,is a wave travelling along:

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$A$ wave in a string has an amplitude of $2\, cm$. The wave travels in the $+ve$ direction of $x-$axis with a speed of $128\, m/s$ and it is noted that $5$ complete waves fit in $4\, m$ length of the string. The equation describing the wave is

MediumAIPMT 2009

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$A$ simple harmonic progressive wave is represented by $y=A \sin (100 \pi t+3 x)$. The distance between two points on the wave at a phase difference of $\frac{\pi}{3}$ radian is

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The wave function of a pulse is given by $y = \frac{5}{(4x + 6t)^2}$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The velocity of the pulse is ......... $m/s$.

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$A$ transverse wave $Y=2 \sin (0.01 x+30 t)$ moves on a stretched string from one end to another end in $0.5 \ s$. If $x$ and $y$ are in $cm$ and $t$ in $s$,then the length of the string is: (in $m$)

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Two waves are represented by the equations $y_1 = a \sin \omega t$ and $y_2 = a \cos \omega t$. The first wave is .....

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The wave described by $y = 0.25 \sin(10\pi x - 2\pi t)$,where $x$ and $y$ are in $meters$ and $t$ in $seconds$,is a wave travelling along:

$A$ wave in a string has an amplitude of $2\, cm$. The wave travels in the $+ve$ direction of $x-$axis with a speed of $128\, m/s$ and it is noted that $5$ complete waves fit in $4\, m$ length of the string. The equation describing the wave is

$A$ simple harmonic progressive wave is represented by $y=A \sin (100 \pi t+3 x)$. The distance between two points on the wave at a phase difference of $\frac{\pi}{3}$ radian is

The wave function of a pulse is given by $y = \frac{5}{(4x + 6t)^2}$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The velocity of the pulse is ......... $m/s$.

$A$ transverse wave $Y=2 \sin (0.01 x+30 t)$ moves on a stretched string from one end to another end in $0.5 \ s$. If $x$ and $y$ are in $cm$ and $t$ in $s$,then the length of the string is: (in $m$)

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