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).