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The formula for the fundamental frequency of a stretched string is given by:
sqrt [ T/ (m/L)]/ 2*L , where T is the tension in the string, m is the mass per length and L is the length of the string.
We have been told that all the strings are of the same length, they have the same mass per length and the same tension is applied to all of them. So if we substitute the values in the formula for fundamental frequency we see that it is the same for all of them. Nothing differentiates it except the factors that have already been mentioned.
To get different fundamental frequencies either the length, the tension or the mass/ length of the strings has to be altered.
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