Finding unknown frequency from beats?

[Idrees]

Finding unknown frequency from beats?

Homework Statement

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

Homework 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?

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 doesn't have any sample questions that's 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 don't 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 I am 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]

Homework Statement

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

Homework 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.