A person stands at rest in front of a large smooth wall. Between him and the wall he golds a tuning fork with a frequency of 400Hz. The person moves the fork toward the wall at a speed of 1 m/s.  How many beats per second will the person hear between sound waves reaching him directly from the fork, and those reaching him from the sound reflecting off the wall.  Thank you for the help.

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A person stands at rest in front of a large smooth wall. Between him and the wall he golds a tuning fork with a frequency of 400Hz. The person moves the fork toward the wall at a speed of 1 m/s. 

How many beats per second will the person hear between sound waves reaching him directly from the fork, and those reaching him from the sound reflecting off the wall. 

Thank you for the help. 

Expert Solution
Step 1: The Doppler effect formula and given informations

The number of beats per second is the difference in frequencies between the sound waves directly from the fork and those reflected off the wall.

The Doppler effect formula for sound when the source is moving towards a stationary observer is:

f apostrophe equals fraction numerator f left parenthesis v plus v subscript o right parenthesis over denominator left parenthesis v plus v subscript s right parenthesis end fraction

Where:
f is the frequency of the source (400 Hz)
v is the speed of sound in air (approximately 343 m/s at room temperature)
v subscript o is the speed of the observer (0 m/s since the person is at rest)
v subscript s is the speed of the source (1 m/s, towards the wall)
f to the power of prime is the observed frequency.

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