Physics · Waves · NEET
Two different things happen at once. The pitch you hear (the note) is the AVERAGE: (f1 + f2) / 2. The waxing and waning of loudness that you count is the DIFFERENCE: |f1 - f2|. In NEET problems the word 'beats' or 'beats per second' always means the difference. Do not average - subtract.
Beat frequency is a count of loud-soft cycles per second, so it must be a positive number. It does not matter which fork is faster; a 5 Hz and 3 Hz fork give |5 - 3| = 2 beats, same as |3 - 5| = 2. The modulus just keeps the answer positive.
Both are possible from the formula alone: 256 + 5 = 261 or 256 - 5 = 251. The beat count cannot decide by itself. You need one more clue - loading the fork with wax (lowers its frequency) or changing string tension - and see if beats go up or down. That extra test is exactly what the NEET guitar-string problem uses.
For a string, frequency increases with tension (f is proportional to root T). So decreasing tension lowers that string's frequency. If lowering it makes beats INCREASE, the two frequencies were moving further apart, meaning that string was already the lower one. If beats DECREASE, it was the higher one. This one line of reasoning solves most string-beat PYQs.
The ear can follow the loud-soft rise and fall only up to about 6 to 7 beats per second. Beyond roughly 10 Hz difference, the waxing and waning becomes too fast to sense and you just hear two separate notes or a rough sound. That is why beats work only for 'close but not equal' frequencies.
Three sound waves of equal amplitude have frequencies (n-1), n and (n+1) Hz. They superimpose to give beats. The number of beats produced per second is:
In a guitar, two strings A and B of the same material are slightly out of tune and produce beats of frequency 6 Hz. When the tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
f_beat = |f1 - f2|, the positive difference of the two frequencies. If two forks are 512 Hz and 508 Hz, you hear 4 beats per second.
One beat is one full cycle of the sound growing loud and then soft again. Counting how many of these happen in one second gives the beat frequency in Hz.
Because |f - f_known| = n means f = f_known + n or f_known - n. The beat count alone cannot say which. A second observation (adding wax or changing tension and noting whether beats rise or fall) removes the ambiguity.
Wax adds mass, so it LOWERS the fork's frequency. This is a common NEET clue: if beats change after adding wax, you can tell whether the fork's frequency was above or below the reference.
About 6 to 7 beats per second. Beyond roughly 10 Hz difference the ear cannot follow the loudness change, so no distinct beats are heard - only a rough or dissonant sound.
