The wave speed on a stretched string is directly proportional to the tension in the string. The fundamental frequency for standing waves on a stretched string is inversely proportional to the wave speed on the string. Therefore, increasing the tension in the string increases the wave speed and decreases the frequency.
The wave speed on a stretched string is directly proportional to the tension in the string.
So, if the tension in the string is increased, the wave speed will also increase.
The fundamental frequency for standing waves on a stretched string is inversely proportional to the wave speed on the string. Therefore, when the musician increases the tension in the string, it makes the frequency decrease.
To summarize:
The wave speed on a stretched string is directly proportional to the tension in the string.
The fundamental frequency for standing waves on a stretched string is inversely proportional to the wave speed on the string.
Increasing the tension in the string increases the wave speed and decreases the frequency