Question

Given the wave equation y(x, t) = 2.0 Sin(3.0x – 4.0t + π

2

)m, where x is

in meter and t is in second. Find the:

a. Amplitude

b. Frequency

c. Wavelength

d. Speed

e. Initial height at x=1.0m

Answer 1

Given:

$$y(x, t) = 2.0 \sin(3.0x – 4.0t + π/2)$$

The general form of a wave is given by

$$y(x, t) = A \sin \left(kx – \omega t +\phi_0\right)$$

In our case:

a. Amplitude

$$A=2.0\rm \: m$$

b. Frequency

$$f=\omega/(2\pi)=0.64\:\rm Hz$$

c. Wavelength

$$\lambda=2\pi/k=2.1\:\rm m$$

d. Speed

$$v=f\lambda=0.64*2.1=1.3\:\rm m/s$$

e. Initial height at x=1.0 m

$$y(1.0, 0) = 2.0 \sin(3.0*1.0 – 4.0*0 + π/2)\\=-1.3\:\rm m$$