A

Step 1: Understand the harmonic frequencies for a string fixed at both ends.
The frequency of the nth harmonic is given by the formula:
$$ f_n = n \cdot f_1 $$
where $f_1$ is the fundamental frequency.

Step 2: For the ninth harmonic (n = 9) and the seventh harmonic (n = 7), we can express their frequencies as:
- Ninth harmonic: $$ f_9 = 9 \cdot f_1 $$
- Seventh harmonic: $$ f_7 = 7 \cdot f_1 $$

Step 3: Compare the two frequencies:
We see that:
$$ f_9 > f_7 $$
because 9 is greater than 7.

Thus, the ninth harmonic frequency is higher than the seventh harmonic frequency.
Therefore, the correct answer is A.