Final answer:
The first overtone of string B, which is the second harmonic, has the same frequency as the fundamental frequency of string A.
Step-by-step explanation:
The tension, length, diameter, and density of a string influence its vibrational properties and, consequently, the frequencies of its fundamental frequency and overtones. In physics, the fundamental frequency, which is the lowest frequency of vibration, has the longest wavelength for a given mode. Overtones, or harmonics, are integer multiples of this fundamental frequency.
For string B, which has double the tension, length, diameter, and density compared to string A, it follows from the physics of waves on strings that the velocity of the wave on the string, and thus the frequency, will be affected. Specifically, the frequency of a vibrating string is proportional to the square root of the tension and inversely proportional to the square root of the length and linear density. Since string B has double the tension, its frequency will be higher by a factor of the square root of two. With all other factors also doubled, the net result is that the frequency of string B's fundamental is the same as that of string A's first overtone.
In essence, for two strings under different conditions, the one with the higher tension and other factors will have a higher pitch, due to higher wave velocity on the string. The answer to the question, "Which overtone of string B has the same frequency as the fundamental frequency of string A?" is the first overtone of string B, which corresponds to the second harmonic, and is twice the fundamental frequency, making it equivalent to string A's fundamental frequency.