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Wavelength, lambda = 86.0 cm

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Answer

860 m/s\text{860 m/s}

Step-by-step solution

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Here's how to solve the problem:

Given:
Wavelength, λ=86.0 cm\lambda = 86.0 \text{ cm}
Period, T=1 msT = 1 \text{ ms} (assuming "1ms" is the period, and " = 200m/s" is extraneous information or a typo)

Required:
Speed of the sound wave (vv)

  1. Convert the wavelength from centimeters (cm) to meters (m).

    λ=86.0 cm=86.0×10−2 m=0.86 m\lambda = 86.0 \text{ cm} = 86.0 \times 10^{-2} \text{ m} = 0.86 \text{ m}

  2. Convert the period from milliseconds (ms) to seconds (s).

    T=1 ms=1×10−3 sT = 1 \text{ ms} = 1 \times 10^{-3} \text{ s}

  3. Calculate the speed of the sound wave using the formula v=λTv = \frac{\lambda}{T}.

    Substitute the converted values:

    v=0.86 m1×10−3 sv = \frac{0.86 \text{ m}}{1 \times 10^{-3} \text{ s}} v=0.86×103 m/sv = 0.86 \times 10^3 \text{ m/s} v=860 m/sv = 860 \text{ m/s}

    The speed of the sound wave is 860 m/s\text{860 m/s}.

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