Q.Two sound waves having wavelengths 81 cm and 82.5 cm produce 8 beats per second. Calculate the speed of sound in air.

Beats are the periodic waxing and waning of sound loudness produced by the superposition of two nearly-equal-frequency sound waves.

When two sound waves of slightly different frequencies (f₁ and f₂, close to each other) but nearly equal amplitude travel in the same direction and superpose, the resultant amplitude at any point does not stay constant — it periodically rises to a maximum and falls to a minimum. This periodic variation in the intensity (loudness) of the resultant sound, heard as a regular waxing and waning, is called beats.

The number of beats produced per second (the beat frequency) equals the difference between the two individual frequencies:

fbeat = |f₁ − f₂|

Beats arise because the two waves alternately go into phase (constructive interference, giving loud sound) and out of phase (destructive interference, giving quiet/no sound) at a regular rate, since their phase difference keeps changing due to the small frequency difference.

Beats are a periodic interference effect between two close-frequency waves.

When two sound waves of slightly different frequencies $f_1$ and $f_2$ travel through the same medium simultaneously, they superpose (interfere). At some instants their crests align (constructive interference, loud sound) and at others crest meets trough (destructive interference, quiet), producing a periodic rise and fall in loudness — beats — with beat frequency $|f_1-f_2|$.

Beats are produced when two waves of nearly equal but slightly different frequencies superpose, causing periodic constructive/destructive interference — so it's the difference in FREQUENCY between the two waves that creates beats.

When two sound waves of frequencies f1 and f2 (close in value) overlap, their superposition produces a resultant wave whose amplitude rises and falls periodically. This is heard as a throbbing/pulsing loudness variation called 'beats,' occurring at a beat frequency = |f1 - f2|.

If the two waves had the same frequency, no beats would form (just a steady, possibly louder/softer, combined tone depending on phase); beats specifically require a frequency difference between the two source waves.

Beats are clearly heard when the two frequencies are nearly equal.

Beats are the periodic rise and fall of loudness produced when two waves of slightly different frequencies superpose; the beat frequency equals the difference of the two frequencies.

For the ear to follow this waxing and waning, the difference must be small (about ≤ 10 Hz), i.e. the frequencies must be nearly equal. If they differ greatly, the beats are too rapid to be perceived.

Beats are produced by interference of two sound waves of slightly different frequency.

When two waves of nearly equal frequencies travel in the same direction and superpose, they interfere constructively and destructively alternately, producing a periodic variation in intensity called beats. This is an example of interference of waves (in time), not reflection, refraction or resonance.

Beat frequency = |f1 − f2| = 4 Hz, so the time between successive intensity maxima is 1/4 s.

Beat frequency $f_{beat} = |f_1 - f_2| = |454 - 450| = 4$ Hz. The time interval between two successive maxima (loudness peaks) equals the beat period:

$T_{beat} = \frac{1}{f_{beat}} = \frac{1}{4}\ \text{s}$

Beat frequency = number of beats ÷ time taken = 2 beats / 0.20 s = 10 Hz.

When two sound sources of slightly different frequency are sounded together, the resultant intensity waxes and wanes periodically — this phenomenon is called beats. The beat frequency equals the difference between the two source frequencies, and is measured as the number of beats produced per second:

$f_{beat} = \frac{\text{number of beats}}{\text{time}}$

Here, 2 beats occur in $0.20$ s:

$f_{beat} = \frac{2}{0.20} = 10\text{ Hz}$

The beat frequency is simply the magnitude of the difference between the two individual frequencies: f_beat = |f1 - f2|.

When two sound waves of nearly equal but slightly different frequencies f1 and f2 travel together, their superposition produces a periodic waxing and waning of loudness called beats. The number of such loud-soft cycles heard per second (the beat frequency) equals the difference between the two frequencies.

Beats are the periodic loudness variation produced when two waves of nearly equal frequency interfere; beat frequency = |f1 - f2|.

When two sound waves of slightly different frequencies f1 and f2 (with f1 close to f2) travel through the same medium and superpose, at some instants they arrive in phase and reinforce each other (loud sound), and shortly after they arrive out of phase and cancel each other (faint/no sound) — because the phase difference between them keeps changing steadily with time. This periodic waxing and waning of the resultant sound intensity is called beats. The number of times the loudness becomes maximum per second is the beat frequency, and it equals the difference of the two individual frequencies: f_beat = |f1 - f2|. Beats are commonly used by musicians to tune instruments to the same pitch — as the two frequencies get closer, the beat frequency (heard as a slow throbbing) decreases toward zero.