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16 December, 06:12

A violinist is tuning the A string on her violin by listening for beats when this note is played simultaneously with a tuning fork of frequency 440 Hz. She hears a beat frequency of 4 Hz. She notices that, when she increases the tension in the string slightly, the beat frequency decreases. What was the frequency of the mistuned A string?

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  1. 16 December, 06:34
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    f_2 = 436 Hz

    Explanation:

    Given:

    - Frequency of the note played f_1 = 440 Hz

    - Number of beats heard per second b = 4 Hz

    Find:

    What was the frequency of the mis-tuned A string?

    Solution:

    - The beat is the difference in frequency of the notes played and is given by the expression:

    | f_1 - f_2 | = beats

    - we heard 4 beats, so

    | f_1 - f_2 | = 4

    - Plug in the value: | 440 - f_2 | = 4

    Hence, f_2 = 436 Hz
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