Question

Given the equation of the wave:

y(x, t)=1.0mCos(2πm-1 x - 𝜋3𝑠 𝑡)

What is: a.) wavelength, b.) frequency, c.) angular frequency, d.) period, and e.) velocity

Answer 1

a)

$$\lambda=\dfrac{2\pi}{k}=\dfrac{2\pi}{2\pi\ m^{-1}}=1.0\ m.$$

b)

$$f=\dfrac{\omega}{2\pi}=\dfrac{\dfrac{\pi}{3} \dfrac{rad}{s}}{2\pi}=0.166\ Hz.$$

c)

$$\omega=\dfrac{\pi}{3}\ \dfrac{rad}{s}.$$

d)

$$T=\dfrac{1}{f}=\dfrac{1}{0.166\ Hz}=6.0\ s.$$

e)

$$v=f\lambda=0.166\ Hz\cdot1.0\ m=0.166\ \dfrac{m}{s}.$$