A wave travels along a string with a speed of 5 m/s. At a particular point on the string, the wave has a frequency of 200 Hz and a wavelength of 0.02 m.
a) Calculate the period of the wave. b) Determine the amplitude of the wave. c) Find the angular frequency of the wave. d) Calculate the wave number of the wave. e) Determine the displacement of a particle on the string at a time t = 0.01 s.
Assume the wave is sinusoidal and travels along the string in the positive x-direction.
a) To calculate the period of the wave, we can use the equation:
T = 1/f
Given the frequency f = 200 Hz, we can substitute this into the equation:
T = 1/200
T = 0.005 s
So, the period of the wave is 0.005 seconds.
b) The amplitude of the wave represents the maximum displacement of the particles from their equilibrium position. Unfortunately, the problem did not provide the amplitude directly. Therefore, we cannot determine it using the given information.
c) The angular frequency (ω) of a wave is given by:
ω = 2πf
Given the frequency f = 200 Hz, we can substitute this into the equation:
ω = 2π(200)
ω ≈ 1257 rad/s
So, the angular frequency of the wave is approximately 1257 radians/second.
d) The wave number (k) of a wave is related to its wavelength (λ) by:
k = 2π/λ
Given the wavelength λ = 0.02 m, we can substitute this into the equation:
k = 2π/(0.02)
k = 314.16 rad/m
So, the wave number of the wave is approximately 314.16 radians per meter.
e) The displacement of a particle on the string at a given time (t) can be determined using the equation:
y(x, t) = A * sin(kx - ωt + φ)
where:
Since we have not been given the amplitude or phase constant, we cannot calculate the displacement of a particle on the string at t = 0.01 s using the given information.