Answer to Question #81164 in Mechanics | Relativity for Fiikky Lhee

Question

A travelling wave is represented by the equation : x = 3sin 2π(10t- 0.2y)
Where x and y are in m, calculate
- the Amplitude
-the frequency
- the wave length
- the speed
- the maximum oscillating particle velocity

Answer 1

Here, we consider an equation x = a Sin 2π (t/T-y/A) ………………….(1)
Where, a = amplitude, T= Time period, A = wave length.
Now compare given equation with equation (1) , we get
Amplitude = a = 3
Time period =T = 0.1 Sec.
Angular velocity = ω = 2π/T = 2π/0.1 = 62.83 rad/sec.
Frequency = n = 1/T = 10 Hz
Wavelength = A = 1/0.2=5 m.
Speed = v = n x A = 10 x 5 = 50 m/sec.
Maximum oscillating particle velocity = ω x a = 62.83 x 3 = 188.5 m/sec.

Answer: Amplitude = 3 , Frequency = 10 Hz, Wavelength =5 m. , Speed = 50 m/sec. , Maximum oscillating particle velocity = 188.5 m/sec.