The equation of a plane progressive wave is given by $y = 0.6 \sin 2\pi \left( t - \frac{x}{2} \right)$. On reflection from a denser medium,its amplitude becomes $2/3$ of the amplitude of the incident wave. The equation of the reflected wave is:

  • A
    $y = 0.6 \sin 2\pi \left( t + \frac{x}{2} \right)$
  • B
    $y = -0.4 \sin 2\pi \left( t + \frac{x}{2} \right)$
  • C
    $y = 0.4 \sin 2\pi \left( t + \frac{x}{2} \right)$
  • D
    $y = -0.4 \sin 2\pi \left( t - \frac{x}{2} \right)$

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The equation of a progressive wave is $Y = 3 \sin \left[ \pi \left( \frac{t}{3} - \frac{x}{5} \right) + \frac{\pi}{4} \right]$ where $x$ and $y$ are in meters and time $t$ is in seconds. Which of the following is correct?

The equation of a plane progressive wave is given by $y = 5 \cos \pi (200t - \frac{x}{150})$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is . . . . . . m/s.

What are called progressive waves? What is called a wave equation? Write the wave equation for a progressive harmonic transverse wave propagating and explain it by drawing graphs.

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The figure given below shows four progressive waves $A, B, C$ and $D$ with their phases expressed with respect to the wave $A$. It can be calculated from the figure that

In the given progressive wave $y = 5 \sin(100\pi t + 0.4\pi x)$,where $y$ and $x$ are in $m$ and $t$ is in $s$. Find the:
$(a)$ Amplitude
$(b)$ Wavelength
$(c)$ Frequency
$(d)$ Wave velocity
$(e)$ Particle velocity amplitude.

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