Question

Equation for a wave on a string is given by $y=0.03\sin (7.86x-2t)$ where $y$ and $x$ are in metres and $t$ is in seconds. At $t=0$, find the value of displacement (approximately) for a particle on string at $x=0.1\text{m}$.

• A. $2.1\text{cm}$
• B. $4\text{cm}$
• C. $3\text{cm}$
• D. $7.86\text{cm}$

Answer 1

The correct option is A $2.1\text{cm}$

Given, The equation of a wave on a string
$y=0.03\sin (7.86x-2t)$
Substituting $t=0$ and $x=0.1$ in above equation we get,
$y=0.03\sin \left(0.786\right)$
Angle in radian can be converted to degrees by multiplying with $\frac{180}{\pi }$
$\Rightarrow y=0.03\sin (0.786\times \frac{180}{\pi })$
$\Rightarrow y=0.03\sin {45}^{\circ }$, approx
$\therefore y=0.021\text{m}=2.1\text{cm}$