Question:A sound wave of frequency $245 \mathrm{~Hz}$ travels with the speed of $300 \mathrm{~ms}^{-1}$ along the positive $x$-axis. Each point of the wave moves to and fro through a total distance of $6 \mathrm{~cm}$. What will be the mathematical expression of this travelling wave?
$\mathrm{Y}(\mathrm{x}, \mathrm{t})=0.03\left[\sin 5.1 \mathrm{x}-\left(0.2 \times 10^{3}\right) \mathrm{t}\right]$
$\mathrm{Y}(\mathrm{x}, \mathrm{t})=0.06\left[\sin 5.1 \mathrm{x}-\left(1.5 \times 10^{3}\right) \mathrm{t}\right]$
$\mathrm{Y}(\mathrm{x}, \mathrm{t})=0.06\left[\sin 0.8 \mathrm{x}-\left(0.5 \times 10^{3}\right) \mathrm{t}\right]$
$\mathrm{Y}(\mathrm{x}, \mathrm{t})=0.03\left[\sin 5.1 \mathrm{x}-\left(1.5 \times 10^{3}\right) \mathrm{t}\right]$
Correct Option: , 4
Solution:(4)
$\omega=2 \pi \mathrm{f}$
$=1.5 \times 10^{3}$
$\mathrm{A}=\frac{6}{2}=3 \mathrm{~cm}=0.03 \mathrm{~m}$
