A travelling wave in a string is given by y= 0.03 Sin(2.2x – 3.5t) where y and x are in metres, and t is in seconds. Find the amplitude, the wavelength, the frequency, the period and the speed of the wave. (
To find the amplitude, we look at the coefficient in front of the sine function, which is 0.03. Therefore, the amplitude is 0.03 metres.
The wave is in the form y = A sin(kx - ωt), where A is the amplitude, k is the wave number, and ω is the angular frequency. In this case, k = 2.2 and ω = 3.5.
The wave number (k) is related to the wavelength (λ) by the formula k = 2π / λ. Solving for λ, we get λ = 2π / k = 2π / 2.2 ≈ 2.85 metres. Therefore, the wavelength is 2.85 metres.
The angular frequency (ω) is related to the frequency (f) by the formula ω = 2πf. Solving for f, we get f = ω / 2π = 3.5 / 2π ≈ 0.558 Hz. Therefore, the frequency is 0.558 Hz.
The period (T) is the reciprocal of the frequency, so T = 1 / f ≈ 1.79 seconds. Therefore, the period is 1.79 seconds.
The speed of the wave is given by the formula v = λf = 2.85 * 0.558 ≈ 1.59 m/s. Therefore, the speed of the wave is 1.59 m/s.