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25 November, 14:30

A piano tuner hears a beat every 2.20 s when listening to a 258.0 Hz tuning fork and a single piano string. What are the two possible frequencies (in Hz) of the string? (Give your answers to at least one decimal place.) 1. f =. Hz (smaller value) 2. f = Hz (larger value)

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  1. 25 November, 15:39
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    Smaller value = 257.55 Hz.

    Larger value = 254.455 Hz.

    Explanation:

    Beat : Beat is a phenomenon obtained when two notes of nearly equal frequency are sounded together. Thereafter, there is a rise and fall of intensity of sound. It is as a result of constructive interference.

    ±f₍b₎ = f₁ + f₂

    where f₍b) = Beat frequency, f₁ = frequency of the turning fork, f₂ = frequency of the string.

    T₍b₎ = beat time = 2.2 s.

    Recall That,

    f = 1/T

    f₍b) = 1/2.2 = 0.455 Hz

    The beat is formed

    Either

    T₍beat) = f₁ + f₂ =

    0.455 = 258 + f₂

    ∴ f₂ = 258 - 0.455 = 257.55 Hz.

    or

    -T₍beat) = f₁ + f₂

    f₂ = f₁ + T₍beat)

    f₂ = 254 + 0.455 = 254.455 Hz.
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