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What frequency would be detected by an observer when a source emitting a sound of frequency 512 Hz approaches at a velocity of 28 m s⁻¹? - Leaving Cert Physics - Question d - 2015

Question d

What frequency would be detected by an observer when a source emitting a sound of frequency 512 Hz approaches at a velocity of 28 m s⁻¹?

Worked Solution & Example Answer:What frequency would be detected by an observer when a source emitting a sound of frequency 512 Hz approaches at a velocity of 28 m s⁻¹? - Leaving Cert Physics - Question d - 2015

Step 1

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Answer

To determine the frequency detected by the observer, we can apply the Doppler Effect formula for a source approaching the observer:

$f' = \frac{f_c}{c - u}$

Where:

$f'$ is the observed frequency,
$f_c$ is the source frequency (512 Hz),
$c$ is the speed of sound in air (approximately 343 m/s at room temperature), and
$u$ is the speed of the source (28 m/s).

Step 2

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Answer

Substituting the values into the formula gives:

$f' = \frac{512 \text{ Hz} \cdot 343 \text{ m/s}}{343 \text{ m/s} - 28 \text{ m/s}}$

Calculating the denominator:

$343 - 28 = 315 \text{ m/s}$

Now substituting this value into the formula:

$f' = \frac{512 \cdot 343}{315} \approx 557.95 \text{ Hz}$

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