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A siren on an ambulance emits sound at a constant frequency of 750 Hz. The ambulance is travelling at a constant speed of 25-0 ms⁻¹ towards a stationary observer. The speed of sound in air is 340 ms⁻¹. The frequency of the sound heard by the observer is

Physics

ScanSolve AI Answer

Answer

E\text{E}

Step-by-step solution

5 steps
  1. Identify the given values.

    The frequency of the sound emitted by the siren (source frequency) is fs=750 Hzf_s = 750 \text{ Hz}.
    The speed of the ambulance (speed of source) is vs=25.0 m/sv_s = 25.0 \text{ m/s}.
    The speed of sound in air is v=340 m/sv = 340 \text{ m/s}.
    The observer is stationary, so the speed of the observer is vo=0 m/sv_o = 0 \text{ m/s}.
    The ambulance is moving towards the stationary observer.

  2. Apply the Doppler effect formula.

    For a source moving towards a stationary observer, the observed frequency fof_o is given by the formula:

    fo=fs(vv−vs)f_o = f_s \left( \frac{v}{v - v_s} \right)
  3. Substitute the given values into the formula.

    fo=750 Hz(340 m/s340 m/s−25.0 m/s)f_o = 750 \text{ Hz} \left( \frac{340 \text{ m/s}}{340 \text{ m/s} - 25.0 \text{ m/s}} \right)
  4. Calculate the observed frequency.

    First, calculate the denominator:

    340 m/s−25.0 m/s=315 m/s340 \text{ m/s} - 25.0 \text{ m/s} = 315 \text{ m/s}

    Now, substitute this back into the equation:

    fo=750 Hz(340315)f_o = 750 \text{ Hz} \left( \frac{340}{315} \right) fo=750 Hz×1.079365...f_o = 750 \text{ Hz} \times 1.079365... fo≈809.52 Hzf_o \approx 809.52 \text{ Hz}
  5. Compare the result with the given options.

    The calculated frequency is approximately 809.52 Hz809.52 \text{ Hz}. Looking at the options:
    A: 695 Hz
    B: 699 Hz
    C: 750 Hz
    D: 805 Hz
    E: 810 Hz

    The closest option to 809.52 Hz809.52 \text{ Hz} is 810 Hz810 \text{ Hz}.

    The final answer is E\text{E}.

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