A car traveling at 22.1 m/s honks its horn as it directly approaches the side of a large building. The horn produces a long sustained note of frequency f0 = 235 Hz. The sound is reflected
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To find the frequency that the observer hears, we need to consider the Doppler effect. The Doppler effect is the change in frequency or pitch of a sound wave when the source and the observer are in relative motion.
In this scenario, we have a moving car and a stationary observer. The car is emitting a sound wave (the horn) towards the observer, and the sound wave gets reflected off the building and reaches the observer. The car is traveling towards the observer, so the frequency of the sound wave will be different from the frequency emitted by the horn due to the Doppler effect.
The formula to calculate the observed frequency (fo) is:
fo = (v + vo) / (v - vs) * f0
Where:
- fo is the observed frequency
- v is the speed of sound in air (approximately 343 m/s at room temperature)
- vo is the velocity of the observer relative to the medium (positive if moving towards the source)
- vs is the velocity of the source relative to the medium (positive if moving towards the observer)
- f0 is the frequency emitted by the source (the horn)
In this case, the car is approaching the building, so the velocity of the source (vs) is positive, while the velocity of the observer (vo) is zero since the observer is stationary.
Let's substitute the values into the formula:
fo = (343 + 0) / (343 - 22.1) * 235
Simplifying this expression, we get:
fo ≈ 238.69 Hz
Therefore, the observer will hear a frequency of approximately 238.69 Hz.