The mass of a string is 6.0 x 10^-3 kg, and it is stretched so the tension in it is 195 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?
Isn't wavespeed= sqrt(Tension/(mass/length))
you know wavespeed (wave equation, given f and lambda). You know tension, so solve for mass/length. You know mass, so solve for length.
Yes, you're correct! To find the length of the string, we can use the wave equation:
wave speed (v) = frequency (f) x wavelength (λ)
In this problem, we are given the frequency (f = 260 Hz) and the wavelength (λ = 0.60 m), so we can calculate the wave speed (v).
Next, we can use the formula you mentioned:
wave speed (v) = √(Tension / (mass/length))
We are given the tension (T = 195 N) and the mass (m = 6.0 x 10^-3 kg) of the string. We need to solve for the mass/length term. Rearranging the equation:
mass/length = Tension / (wave speed)^2
Now we can substitute the known values:
mass/length = 195 N / (wave speed)^2
And since we know the values of wave speed (v), frequency (f), and wavelength (λ), we can substitute these into the wave speed formula:
v = f * λ
Solving for wave speed:
v = 260 Hz * 0.60 m
Finally, plug in the value of wave speed into the equation for mass/length:
mass/length = 195 N / (v)^2
Once you have the value of mass/length, you can solve for the length (L) by rearranging the formula:
mass/length = mass / L
Therefore,
L = mass / (mass/length)
Plug in the given mass value and the calculated mass/length value to find the length of the string.