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Fig 5.1 shows an oscilloscope trace of a sound wave. An oscilloscope can be used to determine the frequency of a sound wave. (i) Calculate the period of the sound wave. (ii) Calculate the frequency of the sound wave.

Physics

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Here's the solution to the problem:

a) (i)

  1. Determine the number of horizontal squares for one complete wave cycle.

    From the oscilloscope trace, one complete wave cycle (e.g., from one peak to the next peak, or one full 'S' shape) spans 4 horizontal squares.

  2. Use the oscilloscope settings to find the time represented by these squares.

    The x-direction setting states that 1 square = 0.25 ms0.25\, \text{ms}.

  3. Calculate the period (T) of the sound wave.

    T=number of squares per cycle×time per squareT = \text{number of squares per cycle} \times \text{time per square} T=4 squares×0.25 ms/squareT = 4\, \text{squares} \times 0.25\, \text{ms/square} T=1.0 msT = 1.0\, \text{ms}

    Convert milliseconds to seconds:

    T=1.0×10−3 s=0.001 sT = 1.0 \times 10^{-3}\, \text{s} = 0.001\, \text{s}

    The period of the sound wave is 0.001 s\boxed{\text{0.001 s}}.

    a) (ii)

  4. State the formula for frequency (f) in terms of period (T).

    f=1Tf = \frac{1}{T}

  5. Substitute the calculated period into the formula and calculate the frequency.

    f=10.001 sf = \frac{1}{0.001\, \text{s}} f=1000 Hzf = 1000\, \text{Hz}

    The frequency of the sound wave is 1000 Hz\boxed{\text{1000 Hz}}.

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