If tension is maintained on a stretched string of length 0.6m, such that its fundamental frequency of 220Hz is excited, determine the velocity of the transv...
If tension is maintained on a stretched string of length 0.6m, such that its fundamental frequency of 220Hz is excited, determine the velocity of the transverse wave in the string.
Answer Details
The velocity of a wave traveling along a stretched string can be calculated using the formula:
v = fλ
where v is the velocity, f is the frequency of the wave, and λ is the wavelength.
For a stretched string, the fundamental frequency is given by:
f1 = (1/2L)√(T/μ)
where L is the length of the string, T is the tension in the string, and μ is the linear density of the string.
We can rearrange this equation to solve for the linear density:
μ = (T/4)(L/f1)^2
Now we can substitute this expression for μ into the wavelength equation:
λ = 2L/n
where n is the harmonic number (in this case, n = 1 for the fundamental frequency).
Substituting for μ and λ in the velocity equation, we get:
v = f1(2L/1) = 2f1L
So we just need to plug in the given values:
L = 0.6 m
f1 = 220 Hz
v = 2(220 Hz)(0.6 m) = 264 m/s
Therefore, the velocity of the transverse wave in the string is 264 m/s.
is the correct answer.