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25 January, 15:34

Two identical strings, A and B, have nearly the samtension. When they both vibrate in their fundamental resonantmodes, ther is a beat of 3Hz. When string B is tightenedslightly, to increase the tension, the beat frequency becomes 6 Hz. This means.

A) that before and after tightening B has a higher frequencythan that of AB) That before and after tightening A has a higher frequencythan B. C) that before tightening B had a higher frequency than A, butafter tightening, A has a higher frequency than B. d) that before tightening A had a higher frequecy than B, butafter tightening. B has a higher frequency than A. E) none of the above.

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  1. 25 January, 15:39
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    A. Before and after tightening B has a higher frequency than that of A

    Explanation:

    Since, the beat frequency is 3 Hz before tightening. Therefore, the difference between the frequencies of strings, A and B is 3 Hz. As, we tighten the string B, its tension increases. From the following relation it is clear that the increase in tension increases the fundamental frequency.

    f₁ = (1/2L) √[T/μ]

    where,

    f₁ = fundamental frequency

    L = length of string

    T = Tension in string

    μ = linear mass density of string

    Therefore, frequency of B increases slightly. And the beat frequency or the difference between frequencies of A and B, becomes 6 Hz.

    Now, there can be two cases, which are:

    Either, the frequency of B was 3 Hz less than frequency of A earlier and after tightening frequency of B became 6 Hz greater than frequency of A.

    Or, the frequency of B was 3 Hz greater than the frequency of A, and after tightening it became 6 Hz greater than frequency of A.

    The second option seems more reasonable because it requires 3 Hz of increase in frequency of B, while the first option requires increase of 9 Hz in frequency of B. Since, the there is slight tightening. Therefore, the frequency will also increase by a slight value. Thus, the correct option is:

    A. Before and after tightening B has a higher frequency than that of A
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