Question

The equation of the wave starting from $x=2att=1s$ travelling along negative X-axis is given by

• A. $y=0.1\sin \left(4\pi \right(t-1)+8(x-2\left)\right)$
• B. $y=0.1\sin \left(\right(t-1)-(x-2\left)\right)$
• C. $y=0.1\sin \left(4\pi \right(t-1)-8(x-2\left)\right)$
• D. none of these

Answer 1

The correct option is A $y=0.1\sin \left(4\pi \right(t-1)+8(x-2\left)\right)$

From the given conditions wave starts at $x=2$

$\therefore$ Equation must be of the form $y=a\sin (\omega (t\pm b)\pm k(x-2))$ also wave starts at $t=1$

$\therefore$ Equation must be of the form $y=a\sin (\omega (t-1)\pm k(x-2))$ also wave travels along negative x-axis

$\therefore$ Equation must be of the form $y=a\sin (\omega (t-1)+k(x-2))$

$\therefore$ with $\omega =4\pi$ and $k=8,a=0.1$, option A satisfies all given conditions

Option A is the answer

($\omega$, k, a can be any real values)