|MadSci Network: Physics|
I shall start by answering your questions directly and go on to give certain details that might interest you later. Your question has been italicized in the following text.
I was sitting listening to music one morning, and I noticed that the tempo was a lot faster than it had been the night before. Is there any scientific basis to suggest that time is moving faster when I first wake up than when I went to sleep?
No. Time does not normally move faster or slower. The reason why I used "normally" there is that time would move slower in circumstances where one reaches speeds comparable to the speed of light (300,000 km/sec - 10 million times faster than a car). Obviously you were not travelling in these astonomical speeds at night :) and even if you would, you wouldnt notice the difference since your music player was moving with you. Thus for all normal physical circumstances one can assume that time does not move faster or slower. Thus this is not your problem. If you want to read more on this stuff, you can pick up any good book on modern physics that talks about relativistic phenomena (Einstein's theory).
Is it just my perception of the music in the morning opposed to when I listened to it at night, or is time traveling faster then it was the last time I heard the music?
The reason why you felt so could be:
[note added by MadSci Admin: Perception can also be altered by ones state of mind due to tiredness. So having a good (or bad) night's rest can alter your perception relative to the night before.]
Coming to the physics behind it: the speed at which you receive the
music would not change as long as both you and the source (the music
speakers) are static. If you are constantly going away from the source,
you would receive slower beats and if moving towards, would
receive faster beats. This is known as the Doppler Effect which
you can read about in Resnick and Halliday or any high school physics
If the source and you are not moving relative to each other, what does have an effect because of day and night (owing to the change in temperature) is the intensity of sound. Intensity of sound is the energy transferred by sound on an average to its surroundings. Intensity directly has an effect on the loudness of sound . If the temperature is lesser, it leads to denser air, which in turn leads to higher intensity and thus higher loudness of sound. This is one of the reasons why sounds are heard louder at night. Its easy to get the formula for intensity of sound. I guess it is:
I=(1/2) * rho * w^2 * A^2
rho=density of air
w = cyclic frequency
A = amplitude
If you have any doubts on the concepts involved, you can get in touch
with me via Madsci again.
Try the links in the MadSci Library for more information on Physics.