10. How far does a transverse pulse travel in 1.23 ms on a string with a density of 5.47 × 10−3 kg/m under tension of 47.8 ????? How far wil

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10. How far does a transverse pulse travel in 1.23 ms on a string with a density of 5.47 × 10−3 kg/m under tension of 47.8 ????? How far will this pulse travel in the same time if the tension is doubled?

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Thu Thủy 4 years 2021-08-10T12:27:26+00:00 1 Answers 40 views 0

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  1. Nem
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    2021-08-10T12:28:54+00:00
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    Answer: Tension = 47.8N, Δx = 11.5×10^{-6} m.

                  Tension = 95.6N, Δx = 15.4×10^{-5} m

    Explanation: A speed of wave on a string under a tension force can be calculated as:

    |v| = \sqrt{\frac{F_{T}}{\mu} }

    F_{T} is tension force (N)

    μ is linear density (kg/m)

    Determining velocity:

    |v| = \sqrt{\frac{47.8}{5.47.10^{-3}} }

    |v| = \sqrt{0.00874 }

    |v| = 0.0935 m/s

    The displacement a pulse traveled in 1.23ms:

    \Delta x = |v|.t

    \Delta x = 9.35.10^{-2}*1.23.10^{-3}

    Δx = 11.5×10^{-6}

    With tension of 47.8N, a pulse will travel Δx = 11.5×10^{-6}  m.

    Doubling Tension:

    |v| = \sqrt{\frac{2*47.8}{5.47.10^{-3}} }

    |v| = \sqrt{2.0.00874 }

    |v| = \sqrt{0.01568}

    |v| = 0.1252 m/s

    Displacement for same time:

    \Delta x = |v|.t

    \Delta x = 12.52.10^{-2}*1.23.10^{-3}

    \Delta x = 15.4×10^{-5}

    With doubled tension, it travels \Delta x = 15.4×10^{-5} m

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