Answer :
The initial frequency of the violin string was approximately 443 Hz.
When a violin string is played without fingering, it produces its fundamental frequency, which is determined by factors such as its length, mass, and tension. In this scenario, the violin string is played simultaneously with a tuning fork of frequency 440 Hz, resulting in the generation of beats.
Beats occur when two slightly different frequencies interfere with each other, creating a periodic pattern of constructive and destructive interference.
Given that beats are heard at a rate of 3 per second, it implies that the frequency difference between the violin string and the tuning fork is 3 Hz. Since the beat frequency decreases when the tension in the string is increased slightly, it means that the frequency of the violin string was initially higher than the tuning fork's frequency.
Therefore, to determine the initial frequency of the violin string, we can add the beat frequency to the tuning fork's frequency.By adding 3 Hz to the tuning fork's frequency of 440 Hz, we obtain the initial frequency of the violin string, which is approximately 443 Hz.
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