Finding unknown frequency from beats?

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In summary, when a known frequency of 358Hz is struck alongside an unknown tuning fork, a beat frequency of 4Hz is heard. To find the unknown resonant frequency, the difference in frequency must be 2Hz, therefore the unknown frequency must be 362Hz.
  • #1
Idrees
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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
 
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  • #2


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)
 
  • #3


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
 
  • #4


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.
 
  • #5


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
 
  • #6


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.
 
  • #7


Idrees said:

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.
 

FAQ: Finding unknown frequency from beats?

1. What is the concept of "Finding unknown frequency from beats"?

The concept of "Finding unknown frequency from beats" involves using the phenomenon of beats to determine the unknown frequency of a sound wave. When two sound waves with slightly different frequencies are played together, they create a periodic variation in the amplitude of the resulting sound, known as beats. By measuring the frequency of the beats, the unknown frequency of one of the waves can be calculated.

2. How do beats help in finding the unknown frequency?

Beats help in finding the unknown frequency by providing a means to compare the unknown frequency with a known frequency. As mentioned earlier, when two sound waves with different frequencies are played together, they create beats. The frequency of these beats is equal to the difference between the two sound wave frequencies. By measuring the frequency of the beats, the unknown frequency can be determined.

3. What are the steps involved in finding the unknown frequency from beats?

The following are the steps involved in finding the unknown frequency from beats:

  • Step 1: Measure the frequency of the first sound wave with a known frequency.
  • Step 2: Play the first sound wave along with the second sound wave with an unknown frequency.
  • Step 3: Listen for the beats and count the number of beats in a given time period.
  • Step 4: Calculate the frequency of the beats by dividing the number of beats by the time period.
  • Step 5: Determine the unknown frequency by adding or subtracting the frequency of the beats from the known frequency.

4. What are some practical applications of finding unknown frequency from beats?

The concept of finding unknown frequency from beats has various practical applications, such as:

  • Tuning musical instruments: Beats can help in tuning instruments by comparing the unknown frequency of the instrument with a known frequency.
  • Measuring sound waves: Beats can be used to measure the frequency of sound waves in experiments or in industrial settings.
  • Detecting Doppler shifts: Beats can be used to detect Doppler shifts in sound waves, which can provide information about the speed and direction of a moving object.
  • Frequency modulation: Beats can be used to modulate the frequency of a carrier wave in frequency modulation techniques.

5. Are there any limitations to finding unknown frequency from beats?

Yes, there are some limitations to finding unknown frequency from beats, such as:

  • The accuracy of the measurement depends on the precision of the instruments used and the ability of the listener to detect the beats.
  • The method may not work for frequencies that are too close or too far apart.
  • External noise or interference can affect the accuracy of the measurement.
  • The method is limited to finding the frequency of one unknown wave at a time.

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