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A fire-engine travelling at a speed of 30 m s⁻¹ emits a sound of frequency 2.3 kHz as it approaches an observer - Leaving Cert Physics - Question d - 2018

Question d

A fire-engine travelling at a speed of 30 m s⁻¹ emits a sound of frequency 2.3 kHz as it approaches an observer. Calculate the frequency observed. (speed of sound i... show full transcript

Worked Solution & Example Answer:A fire-engine travelling at a speed of 30 m s⁻¹ emits a sound of frequency 2.3 kHz as it approaches an observer - Leaving Cert Physics - Question d - 2018

Step 1

Calculate the observed frequency using the Doppler effect

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Answer

To determine the frequency observed, we can use the formula derived from the Doppler effect:

$f' = \frac{f_0 \cdot (c + u)}{c}$

Where:

$f'$ is the observed frequency,
$f_0$ is the emitted frequency (2.3 kHz),
$c$ is the speed of sound in air (340 m/s),
$u$ is the speed of the fire-engine (30 m/s).

Substituting the known values into the equation:

$f' = \frac{(2300) \cdot (340 + 30)}{340}$

Step 2

Calculate the numerical value

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Answer

Now carrying out the calculations:

$f' = \frac{2300 \cdot 370}{340}$

Calculating the numerator: $2300 \cdot 370 = 851000$

Now divide by 340:

$f' = \frac{851000}{340} \approx 2503.41$ Hz

Thus, the frequency observed is approximately 2523 Hz.

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