Final answer:
The physics student hears beats due to the Doppler effect as they walk towards a closed end with a vibrating tuning fork. By using the beat frequency and the known speed of sound, the speed at which the student is walking can be calculated.
Step-by-step explanation:
A physics student is walking down a hall with a vibrating 372.0 Hz tuning fork and hears 3.0 beats per second as the sound reflects from a closed end. This scenario involves the Doppler effect and the concept of beats in acoustics. To solve the problem, we use the equation for the observed frequency due to the Doppler effect:
f' = f(v + vo) / (v - vs)
where f is the original vibrating frequency of the tuning fork, v is the speed of sound, vo is the observer's speed towards the source, and vs is the source's speed towards the observer (vs is 0 since the wall is stationary). Since the observer is moving towards the reflecting wall, the beat frequency is the difference between the original and the observed frequencies:
Beat frequency = |f' - f|
We're told that the beat frequency is 3.0 Hz. Therefore, using 343 m/s (the approximate speed of sound in air at room temperature) as the speed of sound and solving for vo (since vs is zero), the student must be moving at a particular speed to hear the beats at 3.0 Hz. You can rearrange the equation to solve for vo.
The student hears the increased frequency when approaching the wall due to the Doppler effect, causing the beat phenomenon observed.