Final answer:
The observed frequency of the loud singing by your friend, who is approaching you at 35.0 m/s on a day when the outside temperature is 29°C, would be approximately 439.75 Hz due to the Doppler effect.
Step-by-step explanation:
The subject of this question is Physics, specifically exploring the concept of the Doppler effect and how it affects the frequency of sound waves as a source moves towards an observer. To determine the frequency appearing to you as your friend sings a note at 400 Hz while racing towards you on your driveway at 35.0 m/s, we use the formula for the Doppler effect when the source is moving towards the observer:
f' = f (v + vo) / v
Where:
- f' is the observed frequency
- f is the source frequency (400 Hz)
- v is the speed of sound
- vo is the speed of the source towards the observer (35.0 m/s)
First, we need to calculate the speed of sound at 29°C using the formula:
v = v0 + (0.6 × Tc)
v0 is the speed of sound at 0°C, approximately 331 m/s. Tc is the temperature in Celsius.
So, v = 331 + (0.6 × 29) = 331 + 17.4 = 348.4 m/s. Now we can calculate the observed frequency:
f' = 400 (348.4 + 35.0) / 348.4 = 400 (383.4 / 348.4) = 439.75 Hz (approximately)
Therefore, the frequency appearing to you as your friend approaches would be approximately 439.75 Hz.