How does increasing the tension of a string affect various properties?

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Increasing the tension of a string raises the fundamental frequency of vibrations, leading to a higher pitch. The wavelength of the standing wave decreases as tension increases, while the speed of standing waves on the string increases due to the greater tension. The speed of sound waves produced by the string also increases, but the frequency of the sound waves remains directly proportional to the fundamental frequency. Understanding these relationships is crucial for grasping wave mechanics in strings and sound production. This discussion highlights the interconnectedness of tension, frequency, wavelength, and wave speed in string dynamics.
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This isn't really a homework question, just a question i got wrong on test and want to understand:
If the tension of a string increases how would the following be affected (Increase, decrease, stay the same, not enough info)?
1. The fundamental frequency of vibrations on a string?
2. The wavelength of the standing wave on a string?
3. The wavelength of the sound waves produced by the string?
4. The frequency of the sound waves produced by the string?
5. The speed of the standing waves on a string?
6. The speed of the sound waves produced by the string?

If someone could "enlighten" me that would be much appreciated, and please tell me why the answers to these questions are what they are. :)
 
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