Physics · Waves · NEET
Two sound waves of slightly different frequency (say 11 Hz and 9 Hz) travel to your ear at the same time. By the principle of superposition their displacements add up. Because the frequencies differ a little, one wave slowly gets ahead of the other. At some moments both are 'in step' (crest meets crest) and add up to a loud sound. A moment later they are 'out of step' (crest meets trough) and cancel to a soft or silent sound. This slow loud-soft-loud cycle is a beat. So beats are just interference in time between two close frequencies.
If the two frequencies are close, the two waves drift out of step slowly, so the loud-soft change happens slowly enough for your ear to follow it as a throbbing (typically up to about 10 beats per second). If the frequencies differ a lot, the beat frequency becomes very high and your ear can no longer separate the loud and soft moments. It then just sounds like two different tones, not beats. That is why the definition says 'nearly equal frequencies.'
It is the DIFFERENCE, not the sum. Beat frequency f_beat = |f1 - f2|. The resultant tone you hear has a frequency near the average (f1 + f2)/2, but the throbbing (waxing and waning) happens at the difference. A common mistake is to add the frequencies; you must subtract. Example: 256 Hz and 260 Hz give 4 beats per second, not 516.
Ordinary interference (like two speakers in a room) is interference in SPACE: at some points it is always loud and at other points always soft, and the two waves usually have the same frequency. Beats are interference in TIME at one point (your ear): the loudness there changes moment to moment because the two frequencies are slightly different. So beats are a special time-domain case of superposition.
One beat is one full cycle of the sound going from loud to soft and back to loud. So if you count how many times the sound rises to a maximum loudness in one second, that count is the beat frequency. For NEET, remember: number of loud moments (maxima) per second = f_beat = |f1 - f2|.
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 modulus (positive) of the difference of the two source frequencies. It gives the number of times per second the sound rises to maximum loudness.
About 10 beats per second. Beyond this the loud and soft moments blur together and the ear no longer perceives distinct beats; it hears two separate tones instead.
The pitch you hear is close to the average of the two frequencies, (f1 + f2)/2, while the loudness rises and falls at the beat frequency |f1 - f2|.
Yes. Musicians tune instruments by listening for beats against a reference tone and adjusting until the beats vanish (zero beat = equal frequency). Piano and guitar tuning both use this.
No, beats can occur with any waves of nearly equal frequency, but for NEET they are almost always discussed with sound waves (tuning forks, strings, organ pipes) because we can hear them directly.
