Waves Part 1

Given, The frequency of the sound wave, $f=245 \text{ Hz}$ The speed of the travelling wave, $v=300 \text{ m/s}$ As, total distance of to and fro motion is $6 \text{ cm}$. Hence, the amplitude of the wave, $A=\frac{6}{2}=3 \text{ cm}=0.03 \text{ m}$ As we know, Angular frequency is given as $\omega=2\pi f$ Substituting the value of $f$, we get $\omega=2\pi(245)$ $\omega=1.54 \times 10^{3} \text{ rad/s}$ Propagation constant is given as $k=\frac{\omega}{v}$ Substituting the value of $v$ and $\omega$, we get $k=\frac{1.54 \times 10^{3}}{300}\Rightarrow k=5.1\text{ m}^{-1}$ General mathematical expression for a travelling wave is given as $y=A\sin(kx-\omega t)$ Substituting the values in the above equation, we get $y=0.03\sin(5.1x-1.5\times10^{3}t)$