Question involving beats and finding an unknown frequency.

insertnamehere

Hello.
I think I have the answer to the following question, but I'm not sure if I got the concept.
You have a standard tuning fork whose frequency is 262 Hz and a second tuning fork with an unknown frequency. When you tap both of them on the heel of one of your sneakers, you hear beats with a frequency of 4 per second. Thoughtfully chewing you gum, your gum, you wonder whether the unknown frequency is 258Hz or 266Hz. How can you decide?

Of course, the beat frequency is the absolute value of the difference between the two frequencies, but in order to decide whether the unknown would be four more or four less than the standard, I get lost here. A hint would be really appreciated. Help!!
-thank you very much for your time.

Tide

HINT: Attach a small piece of your chewing gum to one of the tuning forks thereby lowering its natural frequency. Then repeat the experiment. What can you infer?

insertnamehere

So, by lowering that tuning fork's natural frequency and repeating the experiment, I will have to see which tuning fork will continue to give me the beat frequency of 4 beats/second? I'm not sure if I got the concept right....

Tide

Suppose you lower the frequency of the standard (262 Hz). The beat frequency you would then hear will either be greater than 4 beats per second or less than 4 beats per second - i.e. it would either increase or decrease the frequency separation. What would you infer in either of these cases?

insertnamehere

ok, so does that mean that it doesn't matter which frequency the unknown tuning fork was?

Tide

No. It is a means by which you can determine whether the unknown frequency of the second tuning fork is greater than or less than that of the standard tuning fork.

Ask yourself:

(a) If the beat frequency increases what does that tell you about the unknown frequency?

(b) If the beat frequency decreases what does that tell you about the unknown frequency?