You have a string with a mass of 0.0123 kg. 0.0123 kg. You stretch the string with a force of 8.37 N, 8.37 N, giving it a length of 1.81 m. 1.81 m. Then, you vibrate the string transversely at precisely the frequency that corresponds to its fourth normal mode; that is, at its fourth harmonic. What is the wavelength?4λ4 of the standing wave you create in the string? What is the frequency f4?

Question

Physics

Dean Thompson

26 March, 00:18

You have a string with a mass of 0.0123 kg. 0.0123 kg. You stretch the string with a force of 8.37 N, 8.37 N, giving it a length of 1.81 m. 1.81 m. Then, you vibrate the string transversely at precisely the frequency that corresponds to its fourth normal mode; that is, at its fourth harmonic. What is the wavelength?4λ4 of the standing wave you create in the string? What is the frequency f4?

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Answers (1)

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Naima Briggs · Answer 1

v = 35.09m/s

f = 38.77Hz

Explanation:

Length 'L' = 1.81 m

Now, First off the fourth harmonic of a string with two nodes is given by:

L=2λ

1.81=2λ

λ = 1.81/2 = >0.905 m

Wave speed on a strecthed string is:

v=√ (Ft / (m/l))

v = √ (8.37) / (0.0123/1.81)

v = 35.09m/s

Next is to determine frequency i, e

v=λf or f = v/λ

f = 35.09/0.905

f = 38.77Hz