The frequency and wavelength of a transverse wave on a string are 340 Hz and 0.70 m, respectively. The tension in the string is 110 N. What is the linear density of the string?
To find the linear density of the string, we first need to understand the relationship between frequency, wavelength, tension, and linear density in wave propagation.
In transverse waves on a string, the speed of the wave is determined by the tension in the string and the linear density. The formula relating these variables is:
v = √(T/μ)
where:
v represents the velocity of the wave,
T is the tension in the string, and
μ is the linear density.
We also know that the velocity of a wave is given by the formula:
v = f * λ
where:
v represents the velocity of the wave,
f is the frequency of the wave, and
λ is the wavelength of the wave.
Combining these equations, we can equate the two equations for velocity:
f * λ = √(T/μ)
We can rearrange this equation to solve for μ (the linear density):
μ = T / (f² * λ²)
Now, we can substitute the given values into this formula to calculate the linear density:
μ = 110 N / (340 Hz² * 0.70 m²)
μ ≈ 0.000381 kg/m
Therefore, the linear density of the string is approximately 0.000381 kg/m.