write an equation that relates to frequency(f) applied to the string to the length(L) between the two fixed end points. This was from lab of standing waves.
To relate the frequency (f) applied to a string to the length (L) between the two fixed endpoints, we can use the wave equation:
v = f * λ
where:
- v represents the velocity of the wave,
- f represents the frequency of the wave,
- and λ represents the wavelength of the wave.
In the context of a string fixed at both ends, the velocity of the wave can be determined by the tension in the string (T) and the linear density of the string (μ):
v = √(T / μ)
where:
- √ represents the square root,
- T represents the tension in the string,
- and μ represents the linear density of the string.
The wavelength (λ) can be related to the length of the string (L) using the formula:
λ = 2L / n
where:
- 2L represents the length of the string,
- and n represents the number of nodes formed by the standing wave on the string.
Combining these equations, we can solve for the frequency (f):
f = (v * n) / (2L)
Therefore, the equation that relates the frequency (f) applied to the string to the length (L) between the two fixed endpoints is:
f = (√(T / μ) * n) / (2L)