Question

A travelling wave is represented by the function:

y(x,t) = 0.009 m sin (1.2m^-1x – 5.0s^-1t)

Find the following:

a. Amplitude

b. Wave number

c. Wavelength

d. Angular frequency

e. Frequency

f. wave speed

Answer 1

a)

$$A= 0.009\ m.$$

b)

$$k=1.2\ m^{-1}.$$

c)

$$\lambda=\dfrac{2\pi}{k}=\dfrac{2\pi}{1.2\ m^{-1}}=5.23\ m.$$

d)

$$\omega=5.0\ \dfrac{rad}{s}.$$

e)

$$f=\dfrac{\omega}{2\pi}=\dfrac{5.0\ \dfrac{rad}{s}}{2\pi}=0.79\ Hz.$$

f)

$$v=f\lambda= 0.79\ Hz\cdot5.23\ m=4.13\ \dfrac{m}{s}.$$