A travelling harmonic wave is represented by the equation $y(x, t) = 10^{-3}\,sin\,(50t + 2x)$, where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?
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A transverse wave is represented by $y=2 \sin$ $(\omega t - kx ) cm$. The value of wavelength (in $cm$ ) for which the wave velocity becomes equal to the maximum particle velocity, will be.
A transverse wave propagating along $x-$ axis is represented by $y (x,t)= 8.0 sin$ $\left( {0.5\pi x - 4\pi t - \frac{\pi }{4}} \right)$ where $x$ is in metres and $t$ is in seconds. The speed of the wave is ..... $m/s$
A source of sound emits sound waves at frequency $f_0$. It is moving towards an observer with fixed speed $v_s$ ($v_s < v$, where $v$ is the speed of sound in air). If the observer were to move towards the source with speed $v_0$, one of the following two graphs ($A$ and $B$) will given the correct variation of the frequency $f$ heard by the observer as $v_0$ is changed The variation of $f$ with $v_0$ is given correctly by
A wave represented by the equation $y_1 = a\,cos(Kx-\omega t)$ is superimposed with another wave to form a stationary wave such that the point $x = 0$ is a node. The equation for the other wave is
When a wave travels in a medium, the particle displacements are given by $y = a\, sin\, 2\pi\, (bt -cx)$ where $a, b,$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if
A source producing sound of frequency $170 Hz$ is approaching a stationary observer with a velocity $17 \,ms^{-1}$. The apparent change in the wavelength of sound heard by the observer is (speed of sound in air $= 340 \,ms^{-1}$) ..... $m$
Which of the following is not true for this progressive wave $y = 4\sin 2\pi \left( {\frac{t}{{0.02}} - \frac{x}{{100}}} \right)$ where $y$ and $x$ are in $cm$ & $t$ in $sec$
The displacement due to a wave moving in the positive $x-$direction is given by $y = \frac{1}{{(1 + {x^2})}}$ at time $t = 0$ and by $y = \frac{1}{{[1 + {{(x - 1)}^2}]}}$ at $t = 2$ seconds, where $x$ and $y$ are in metres. The velocity of the wave in $m/s$ is