To calculate the velocity of the wave in the rope, we can use the equation:
v = √(T/μ)
where v is the velocity of the wave, T is the tension in the rope, and μ is the linear mass density of the rope.
The linear mass density (μ) is given by:
μ = m/L
where m is the mass of the rope and L is the length of the rope.
Given: Mass of the rope (m) = 20 kg Length of the rope (L) = 250 m Tension in the rope (T) = 3000 N
First, let's calculate the linear mass density (μ):
μ = m/L = 20 kg / 250 m = 0.08 kg/m
Now we can calculate the velocity of the wave (v):
v = √(T/μ) = √(3000 N / 0.08 kg/m) ≈ √37500 m^2/s^2 ≈ 193.65 m/s
Therefore, the velocity of the wave when the rope is under a tension of 3000 N is approximately 193.65 m/s.
To calculate the frequency (f) of the wave, we can use the equation:
v = λf
where v is the velocity of the wave, λ is the wavelength, and f is the frequency.
Given: Wavelength (λ) = 0.5 m Velocity of the wave (v) = 193.65 m/s
Rearranging the equation, we have:
f = v / λ = 193.65 m/s / 0.5 m ≈ 387.3 Hz
Therefore, the frequency of the wave is approximately 387.3 Hz.