A tuning fork is known to vibrate with frequency 262 Hz. When it is sounded along with a mandolin string, four beats are heard every second.

Question

A tuning fork is known to vibrate with frequency 262 Hz. When it is sounded along with a mandolin string, four beats are heard every second. Next, a bit of tape is put onto each tine of the tuning fork, and the tuning fork now produces five beats per second with the same mandolin string. What is the frequency of the string?

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Delwyn 6 months 2021-07-20T21:05:28+00:00 2 Answers 17 views 0

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    0
    2021-07-20T21:07:06+00:00

    Answer:

    The frequency of the string is 266 Hz

    Explanation:

    The frequency of the instrument is equal:

    f_{inst} =f_{beat} +f_{fork}

    Where

    fbeat = beat frequency = 4 Hz

    ffork = frequency of the fork = 262 Hz

    Replacing:

    f_{inst} =4+262=266Hz

    0
    2021-07-20T21:07:09+00:00

    Answer: 266 Hz

    Explanation:

    Firstly, it should be noted that the beats being heard are the beat frequencies

    And the formula for that is

    Beat frequency = Frequency of instrument – Frequency of the fork

    Also, the less the beats are, the closer an instrument can be close to being in tune

    For example, if you tape the ends of the fork, you are more or less, dampening the frequency of the fork

    Now, we know that the frequency of the mandolin is either 258 or 266 Hz. However when you drop the pitch, you get another beat frequency (aka farther out of tune)

    Thus, it can only be the higher number which is 266 Hz

    Therefore, the frequency of the strings is 266 Hz

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