Final answer:
The calculation using the Doppler Effect formula and given frequencies, along with the speed of sound, suggests that the trumpeter is approaching at a speed of 3.07 m/s. However, this speed does not match any of the given answer choices, suggesting a potential error in the question or the options.
Step-by-step explanation:
The question involves applying the Doppler Effect to determine the speed of a moving source of sound towards a stationary observer. The Doppler Effect occurs when there is a change in frequency of a wave in relation to an observer who is moving relative to the wave source.
In this case, the frequency of the note produced by the trumpet is 880 Hz, but the frequency observed by the spectator is 888 Hz. We can use the Doppler Effect formula for a source moving towards the observer:
f' = f × (v + vs) / v
where f' is the observed frequency (888 Hz), f is the emitted frequency (880 Hz), v is the speed of sound (338 m/s), and vs is the speed of the source (musician).
Solving for vs, we get:
vs = v × (f'/f - 1)
Plugging in the values:
vs = 338 m/s × (888 Hz / 880 Hz - 1)
vs = 338 m/s × (0.0091)
vs = 3.07 m/s
This value does not match any of the provided options, implying a possible error in the question or the answer choices. If we consider alternative possibilities, such as rounding or a typo, none of the available choices (a. 7.5 m/s, b. 15.0 m/s, c. 22.5 m/s, or d. 30.0 m/s) match the calculated speed.
Therefore, with the values given, the musician's speed cannot be accurately determined from the provided options.