A tuning fork C produces 8 beats per second with another tuning fork D of frequency 340 Hz. When the prongs of tuning fork C are filed a little, the number of beats produced per second decreases to 4. Find the frequency of the tuning fork C before filing its prongs. (Ans: 
= 332 Hz)
Answers
given :
nD = tuning fork D frequency = 340 Hz
nC = tuning fork C frequency=8 – 4 = 4 beats per second.
First nC ± nD = 8 (before filing)
nC ± nD = 4 (after filing)
From given condition nC ± nD = 8
∴ nC ± 340 = 8
∴ nC = 340 + 8 = 348 Hz
or nC = 340 – 8 = 332 Hz
when tuning fork C is filed then nC ± nD = 4
∴ nC ± 340 = 4
∴ nC = 340 + 4 = 344 Hz
or nC = 340 – 4 = 336 Hz
The frequency of tuning fork increases on filing. Hence nC ≠ 344 Hz.
If original frequency of tuning fork C is taken 332 Hz, then on filing both the value 344 Hz, and 336 Hz are greater. Also it produces 4 beats per second with tunning fork D.
∴ frequency of tuning fork C = 332 Hz
∴ nC = 332 Hz.
Answer:
given :
nD = tuning fork D frequency = 340 Hz
nC = tuning fork C frequency=8 – 4 = 4 beats per second.
First nC ± nD = 8 (before filing)
nC ± nD = 4 (after filing)
From given condition nC ± nD = 8
∴ nC ± 340 = 8
∴ nC = 340 + 8 = 348 Hz
or nC = 340 – 8 = 332 Hz
when tuning fork C is filed then nC ± nD = 4
∴ nC ± 340 = 4
∴ nC = 340 + 4 = 344 Hz
or nC = 340 – 4 = 336 Hz
The frequency of tuning fork increases on filing. Hence nC ≠ 344 Hz.
If original frequency of tuning fork C is taken 332 Hz, then on filing both the value 344 Hz, and 336 Hz are greater. Also it produces 4 beats per second with tunning fork D.
∴ frequency of tuning fork C = 332 Hz