A string exhibits three resonant frequencies at 90 Hz , 150 Hz ,...

The given resonant frequencies are $90 \text{ Hz}$, $150 \text{ Hz}$, and $210 \text{ Hz}$.

The fundamental frequency $f_0$ is the highest common factor of the given resonant frequencies.

$f_0 = \text{HCF}(90, 150, 210) = 30 \text{ Hz}$

Expressing the given frequencies in terms of $f_0$:

$90 \text{ Hz} = 3 \times 30 \text{ Hz} = 3f_0$

$150 \text{ Hz} = 5 \times 30 \text{ Hz} = 5f_0$

$210 \text{ Hz} = 7 \times 30 \text{ Hz} = 7f_0$

Therefore, the given frequencies correspond to the 3rd, 5th, and 7th harmonics.