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Theory
The pitch will increase if the object approaches, decrease if the object recedes.
It is a bit difficult to answer that question without knowing what vibrating object you are talking about. For example, if you double the frequency of a vibrating tuning fork, you get a higher pitch. If you double the frequency of a vibrating electron, you get a different and more energetic type of electromagnetic radiation, for example you could shift from visible light to ultraviolet light.
The tension effects how much the string is capable of vibrating. Different vibrations create different length sound waves so the sound will change at different tensions.
Pitch is determined by sound wave frequency; how fast something is vibrating. High-pitched sounds are higher frequency meaning they are vibrating faster. Low pitch means they are vibrating slower.
Moving your finger along the string will alter the length and the pitch of the sound produced.
Theory
The pitch will increase if the object approaches, decrease if the object recedes.
It is a bit difficult to answer that question without knowing what vibrating object you are talking about. For example, if you double the frequency of a vibrating tuning fork, you get a higher pitch. If you double the frequency of a vibrating electron, you get a different and more energetic type of electromagnetic radiation, for example you could shift from visible light to ultraviolet light.
I'm assuming that it then has a higher frequency, making the pitch higher than before.
pitch increased
The tension effects how much the string is capable of vibrating. Different vibrations create different length sound waves so the sound will change at different tensions.
In general, a low pitch is created by sound waves vibrating and having to travel down a lengthy object, while a high pitch only has to travel down a shorter distance
Pitch is determined by sound wave frequency; how fast something is vibrating. High-pitched sounds are higher frequency meaning they are vibrating faster. Low pitch means they are vibrating slower.
Do you mean "The Doppler Effect"?
a high pitch
When a loud object such as a train passes you, there is what is officially known as the Doppler Effect, by which the sound has a higher pitch as the object approaches, and a lower pitch as it passes. The speed of the object, whether approaching or receding, affects the wavelength of the sound.