What is the period of the loaded tuning fork?

[blue.flake]

Two identical tuning forks vibrate at 256 Hz. One of them is then loaded with a drop of wax, after which 6 beats/s are heard. The period of the loaded tuning fork is?

So, as the uploaded pictures shows, I did solve the problem, but I'm not sure why the f1 frequency is bigger than f2. I mean how can I be sure which one should I subtract from the other?

edit: yeah i just noticed i messed up the unit for the period, I'm sorry..

 

[ObjectivelyRational]

A tuning fork will vibrate at a lower frequency when loaded.

 

[blue.flake]

thank you, but can you explain to me why exactly?

 

[ObjectivelyRational]

In simple terms, the fork's material has a solid material shape which if deformed, e.g. if a tine is struck, it will tend to "bounce back" to its original shape. This occurs with a restoring force due to the structure and shape of the fork. Each tine of the fork has weight. The relationship between the restoring force and the weight determines the frequency. Adding the wax does not change the way the fork's restoring energy works, it only adds mass to the system. From general knowledge of oscillators mass loaded vibrators such as spring systems or just by thinking about F=M*a (recall M increases but F stays the same) you can generalize that the extra mass will make the tine vibrate slower.

 

[blue.flake]

thank you so much ^_^