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In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6Hz. When tension in B is slightly decreased, the beat frequency increases to 7Hz. If the frequency of A is 530Hz, the original frequency of B will be
  • a)
    524Hz
  • b)
    536Hz
  • c)
    537Hz
  • d)
    523Hz
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a guitar, two strings A and B made of same material are slightly o...
Solution:


Given, strings A and B produce beats of frequency 6Hz when out of tune. Let the frequency of string B be 'f'.


Step 1: Finding the Original Frequency of B

When the tension in string B is decreased, the beat frequency increases to 7Hz. Let the new frequency of string B be 'f'.


The beat frequency is given by the difference in frequencies of the two strings:


7 Hz = |530 Hz - f|


As the beat frequency is positive, we can write:


f = 530 Hz - 7 Hz = 523 Hz


Therefore, the original frequency of string B was 523 Hz.


Step 2: Finding the Change in Frequency of B

When the tension in string B is decreased, the beat frequency increases from 6Hz to 7Hz.


The change in beat frequency is given by:


Δf = |f1 - f2| = |6 Hz - 7 Hz| = 1 Hz


As the beat frequency increases when the tension in string B is decreased, we can conclude that the frequency of string B was higher than the original frequency of 523 Hz.


Step 3: Finding the New Frequency of B

Let the new frequency of string B be 'f'.


When the tension in string B is decreased, the frequency of string B decreases.


Therefore, we can write:


f = 523 Hz - Δf = 523 Hz - 1 Hz = 522 Hz


Therefore, the new frequency of string B is 522 Hz.


Step 4: Verifying the Result

We can verify the result by calculating the beat frequency between strings A and B:


Beat frequency = |530 Hz - 522 Hz| = 8 Hz


As the beat frequency is not equal to 6 Hz, we can conclude that the result is incorrect.


Step 5: Correcting the Result

From the given information, we know that the beat frequency between strings A and B is 6 Hz.


Therefore, we can write:


6 Hz = |530 Hz - f|


As the beat frequency is positive, we can write:


f = 530 Hz - 6 Hz = 524 Hz


Therefore, the original frequency of string B was 524 Hz (Option A).
Free Test
Community Answer
In a guitar, two strings A and B made of same material are slightly o...
Frequency of string,
Frequency ∝ √ Tension
Difference of fA and fB is 6 Hz.
If tension decreases, fB decreases and becomes fB
Now, difference of fA and fB′ = 7Hz (increases) So,fA > fB
fA − fB = 6Hz
⇒ fA = 530Hz
⇒fB = 524Hz (original)
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In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6Hz. When tension in B is slightly decreased, the beat frequency increases to 7Hz. If the frequency of A is 530Hz, the original frequency of B will bea)524Hzb)536Hzc)537Hzd)523HzCorrect answer is option 'A'. Can you explain this answer?
Question Description
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