Question

A travelling wave in a string is given by y=0.03sin (2.2x-3.5t) where y and x are in meters and t is in seconds find the amplitude,wavelength, frequency , speed of the wave

Answer 1

The equation of a travelling wave in general form is the following

$$y = A\sin \left(\dfrac{2\pi}{\lambda}x-2\pi f t \right)$$

where $A$ is the amplitude, $\lambda$ is the wavelength, $f$ is the frequency, and the speed of the wave is given as follows:

$$v = \lambda f$$

Comparing the general expression with the given one, find the paremeters. Amplitude: $A = 0.03m$, wavelenght: $\lambda = \dfrac{2\pi}{2.2}m\approx 2.86m$, frequency: $f = \dfrac{3.5}{2\pi}Hz \approx 0.557Hz$, speed: $v =2.86m\cdot 0.557Hz \approx 1.59m/s$.

Answer. Amplitude: $A = 0.03m$, wavelenght: $\lambda = 2.86m$, frequency: $f = 0.557Hz$, speed: $v = 1.59m/s$.