PHYYYYYYSIIIIIIIIICS?
The mass of a string is 3.30 10-3 kg, and it is stretched so the tension in it is 160 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?
Please help xD
Update:Thanks you guys! That was my last problem on one of my webassigns!!! :)
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You need to calculate the speed of the wave, use the speed and the tension to calculate the mass/length (μ), then divide the mass by mass/length to get length.
The wave speed, frequency and wavelength are related by f = c/λ
Speed of the wave c = √(F/μ), which yields
c² = F/μ or μ = F/c²
L = m / μ
You do the math
v = wavelength * frequency = 0.6 * 260 = 156 m/s
v = â( F / μ ) ..... Marsene equation
156 = â(160 / μ)
μ = 6.57 x 10^-3 kg/m
μ = m / L .... mass per unit length of the string
6.57 x 10^-3 kg/m = 3.30 x 10^-3 kg / L
L = 0.5 m