Question
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. (
Answers
GPT 3.5
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.
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.