The mass of a string is 8.40 10-3 kg, and it is stretched so the tension in it is 225 N. A transverse wave traveling on this string has a frequency of 260 Hz and a wavelength of 0.60 m. What is the length of the string?
m
To find the length of the string, we can use the formula for the speed of a wave on a string:
v = √(F/μ)
where:
v = speed of the wave
F = tension in the string
μ = mass per unit length of the string
First, let's calculate the mass per unit length of the string (μ):
μ = mass / length
Given that the mass of the string is 8.40 x 10^-3 kg, and we need to find its length, we rearrange the formula to solve for length:
length = mass / μ
To find μ, we need to calculate the mass per unit length of the string.
Given:
Mass of the string (m) = 8.40 x 10^-3 kg
Tension in the string (F) = 225 N
Frequency of the wave (f) = 260 Hz
Wavelength of the wave (λ) = 0.60 m
Now, let's calculate μ:
μ = m / length
Since we need to find the length of the string, rearrange the formula to solve for length:
length = m / μ
To solve for μ, we need to find the speed of the wave (v) first.
The speed of the wave (v) can be calculated using the formula:
v = f * λ
Given:
f = 260 Hz (frequency)
λ = 0.60 m (wavelength)
v = 260 * 0.60
Now that we have the speed of the wave (v), we can find μ:
μ = F / v²
Given:
F = 225 N (tension in the string)
v = calculated speed of the wave (in m/s)
μ = 225 / (calculated v)²
Once you have calculated μ, you can use it to find the length of the string using the formula:
length = mass / μ
Substitute the values you calculated to find the length of the string.