A stretched string fixed at each end has a mass of 41.0 g and a length of 8.80 m. The tension in the string is 41.0 N.
Nodes
Antinodes
b.What is the vibration frequency for this harmonic?
To determine the vibration frequency for this harmonic, we can use the formula for the frequency of a standing wave on a string:
f = (v / λ)
where:
f is the frequency of the wave,
v is the velocity of the wave, and
λ is the wavelength of the wave.
In this case, since the string is fixed at each end, the wavelength of the wave corresponds to the length of the string (L). The velocity (v) can be determined using the tension (T) in the string and the linear mass density (μ) of the string.
The linear mass density (μ) is calculated by dividing the mass of the string (m) by its length (L):
μ = m / L
To find the velocity (v), we use the equation:
v = √(T / μ)
where:
√ represents the square root.
Plugging in the given values:
Mass of string (m) = 41.0 g = 0.041 kg
Length of string (L) = 8.80 m
Tension in the string (T) = 41.0 N
First, we calculate the linear mass density (μ):
μ = m / L = 0.041 kg / 8.80 m ≈ 0.00466 kg/m
Next, we calculate the velocity (v):
v = √(T / μ) = √(41.0 N / 0.00466 kg/m) ≈ 201.1 m/s
Finally, we can calculate the frequency (f) using the formula:
f = v / λ = v / L
f = 201.1 m/s / 8.80 m ≈ 22.8 Hz
Therefore, the vibration frequency for this harmonic is approximately 22.8 Hz.