A string of linear density μ and length L is under a constant tension T = mg. One end of the string is attached to a tunable harmonic oscillator. A resonant standing wave is observed A) at any frequency. B) when the frequency where n = 1, 2, 3, ... C) when the frequency where n = 1, 2, 3, ... D) when the frequency where n = 1, 2, 3, ...and v_s is the speed of sound. E) unable to tell.

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Quizplus · Accepted Answer

A resonant standing wave occurs when the length of the string L is equal to an integer multiple of half of the wavelength of the wave on the string. The wavelength of the wave on the string is given by λ = 2L/n, where n is an integer (mode number). The speed of the wave can be calculated as v = √(T/μ), where μ is the linear density of the string. Substituting the values given, we get v = √(mg/μ). The frequency of the wave is given by f = v/λ = (n/2L)√(mg/μ). Substituting the given value of frequency, we get n = f(2L/√(mg/μ)). Since n has to be an integer, the frequency can only be 11ec81ae_0018_2e7c_8138_97f67443ec45_TB7291_11 where n = 1, 2, 3, ... (Option B).

A String of Linear Density μ and Length L Is