A wire of uniform linear mass density hangs from the ceiling. It takes 0.82 s for a wave pulse to travel the length of the wire. How long is the wire?
l=(T^2*g)/4 yapýcan
To determine the length of the wire, we can use the wave speed formula:
v = λ * f
where v is the wave speed, λ is the wavelength, and f is the frequency.
In this case, we have a wave pulse traveling along the wire, so the frequency is 1/T, where T is the time it takes for the wave pulse to travel the length of the wire.
Given that it takes 0.82 s for the wave pulse to travel the wire, the frequency is 1/0.82 s^{-1}.
Now, we need to determine the wave speed. The wave speed depends on the tension (T) and the linear mass density (μ) of the wire, according to the equation:
v = sqrt(T / μ)
Since the wire has a uniform linear mass density, we can express it as μ = m/L, where m is the mass of the wire and L is its length.
We can rearrange the equation to solve for the length (L):
L = m / (μ * v²)
However, we don't have the mass of the wire, so we need to eliminate it from the equation.
We know that the linear mass density (μ) is defined as μ = m/L. Thus, m = μ * L.
Now we can substitute this into the equation:
L = (μ * L) / (μ * v²)
Simplifying, we get:
L = L / v²
Now, we can solve for the length (L):
L = (T / (1/f)²) = T * f²
Given that the frequency is 1/T and that the time is 0.82 s, we can substitute these values:
L = T * (1/T)² = T / T² = 1 / T
Therefore, the length of the wire is 1 / T, or approximately 1.22 meters.
L = VT = 9.9*10^8ft/s * 0.82s = 8.12*10^8Ft. ?.
Seems unreal!
0.82 microseconds would make more sense.
If this is a sound wave:
L = 343m/s * 0.82s = 281.3m.