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Andreas93 [3]
3 years ago
13

Find the three longest wavelengths (call them λ1, λ2, and λ3) that "fit" on the string, that is, those that satisfy the boundary

conditions at x=0 and x=l. these longest wavelengths have the lowest frequencies. express the three wavelengths in terms of l. list them in decreasing order of length, separated by commas.

Physics
1 answer:
zepelin [54]3 years ago
6 0
If you have a string that is fixed on both ends the amplitude of the oscillation must be zero at the beginning and the end of the string. Take a look at the pictures I have attached. It is clear that  our fundamental harmonic will have the wavelength of:
\lambda_1=\frac{L}{2}
All the higher harmonics are just multiples of the fundamental:
\lambda_n=n\lambda_1\\ \lambda_n=n\frac{L}{2}
Three longest wavelengths are:
n=3; \lambda_3=\frac{3L}{2}\\
n=2; \lambda_2=L\\
n=1; \lambda_=\frac{L}{2}\\


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