Finding unknown frequency from beats???

[Idrees]

1. The problem statement, all variables and given/known data

i have to find the unknown resonant frequency of a tuning fork??

2. Relevant equations

when this unknown is struck along a known freq of 360 hertz = you hear beat frequency of 2 hertz.. and when its struck alongside a known freq of 358 = you hear beat frequncy of 4 hertz what is the frequency of the unknown tuning fork?????

3. The attempt at a solution

i have no clue please help me

[Ouabache]

what is the relationship between any two fork frequencies sounded together and the beat frequency generated? (hint: look in your text and your lab documents)

[Idrees]

Ouabache= the relation is when two similar frequencies are heard= a beat is generated

and freq of beat= freq1 -freq 2 therefore... my textbook doesnt have any sample questions thats y please help me with more direct answer.. or atleast one or two steps

one attempt i made was let unknown freq be x
thus x + 360 hz = beat freq of 2 hz
x+ 358 hz = beat freq of 4 hz

but i dont know if i can solve x unknown frequency now

[Stonebridge]

The beat frequency depends on the difference, not the sum; as you correctly said initially.
You know the difference is 2 but you don't know which one is the higher.
So, the clue to that is to look at the one where the difference was 4.

[Idrees]

if the difference is 4 hertz that means

the unknown frequency will be 362 hertz

because the formula is freq of beat = f2 - f1
thus difference of 4 hertz means 362- 358

is this correct please give me more hints im stuck here

[Stonebridge]

That's correct.
It is 2 more than 360 and 4 more than 358.
so 2=362-360 (beat frequ of 2)
and
4=362-358 (beat frequ of 4)
362 is the only frequency that satisfies both equations.

[Ouabache]

1. The problem statement, all variables and given/known data

i have to find the unknown resonant frequency of a tuning fork??

2. Relevant equations

when this unknown is struck along a known freq of 360 hertz = you hear beat frequency of 2 hertz.. and when its struck alongside a known freq of 358 = you hear beat frequncy of 4 hertz what is the frequency of the unknown tuning fork?????


An intuitive way to solve this...
When you strike a known fork against the unknown and you don't hear any beats at all, then their difference in frequency is zero |f2-f1|=0 or f1 = f2

When you were given the 2nd bit of information, where the known fork = 358Hz, the beat frequency "increased" to 4Hz, but you want the beats to decrease to zero..
So you know immediately, that the unknown frequency must be > 360Hz ..
For |360-f1| = 2Hz, f1 = 362Hz.