Final answer:
For a 0.850m-long string with a linear mass density of 7.50 g/m and tension of 5.00 N, the frequency of the fundamental standing wave is 5.88 Hz.
Step-by-step explanation:
The frequency of the fundamental standing wave for a 0.850m-long string can be found using the equation:
f = (v/λ)
Where:
- f is the frequency of the wave
- v is the speed of the wave
- λ is the wavelength of the wave
We can calculate the speed of the wave using the equation:
v = √(FT/μ)
Where:
- FT is the tension in the string
- μ is the linear mass density of the string
Substituting the given values:
v = √(5.00N / 0.075 kg/m) = 10.00 m/s
Next, we can calculate the wavelength of the wave using the equation:
λ = 2L/n
Where:
- L is the length of the string
- n is the mode of oscillation (in this case, the fundamental mode with n=1)
Substituting the given values:
λ = 2(0.850m) / 1 = 1.700m
Finally, substitute the calculated values back into the first equation to find the frequency:
f = (10.00 m/s) / (1.700m) = 5.88 Hz