Final answer:
The observed frequency of the note being sung by your friend is 439.2 Hz as they approach you at a speed of 24.3 m/s.
Step-by-step explanation:
To determine the speed at which the friend is approaching, we need to consider the Doppler effect. The Doppler effect refers to the change in frequency of a sound wave as the source of the sound wave and the observer are in relative motion.
In this case, the friend is moving toward you at a speed of 24.3 m/s, while emitting a sound wave with a frequency of 411 Hz. The speed of sound is 347 m/s.
The formula to calculate the observed frequency is:
observed frequency = emitted frequency × (speed of sound + speed of observer) / (speed of sound + speed of source)
Plugging in the values, we have:
observed frequency = 411 Hz × (347 m/s + 24.3 m/s) / (347 m/s + 0 m/s)
observed frequency = 411 Hz × 371.3 m/s / 347 m/s
observed frequency = 439.2 Hz
Therefore, the observed frequency of the note being sung by your friend is 439.2 Hz.