Beats in Sound Waves

Summary

The script explores the phenomenon of 'beats' in acoustics, where two sound waves of nearly equal frequencies and amplitudes create a fluctuating sound intensity. It explains how beats occur when two waves superimpose, resulting in a rhythmic pattern of sound intensity maxima and minima, with the beat frequency being the difference between the two original frequencies. The importance of nearly equal frequencies for distinct beats is highlighted, as well as the persistence of hearing, which requires the time interval between beats to exceed one-tenth of a second for them to be perceptible. A graphical method using two tuning forks illustrates the formation of beats.

Takeaways

• 😀 Beats occur when two sound waves of nearly equal frequencies and amplitudes superimpose.
• 🔊 The intensity of the resultant sound alternates between high and low as the waves interact.
• ⏲️ A beat is formed when the sound intensity reaches a maximum, then minimum, and maximum again over time.
• 🎶 The time interval between two successive beats is called the beat frequency.
• 🎼 For example, when sounds of 256 Hz and 260 Hz are combined, they produce a beat frequency of 4 Hz.
• 🔄 The frequency of the beats is the difference between the frequencies of the two combining sounds.
• 🔍 For distinct beats to be heard, the frequencies of the two sources must be nearly equal, typically with a difference of less than 10 Hz.
• 👂 The persistence of hearing causes the impression of sound to last about one-tenth of a second, affecting how beats are perceived.
• 📉 In graphical terms, compressions and rarefactions of the sound waves from two sources can be visualized to understand beat formation.
• 🔄 When compressions of one wave coincide with compressions of another, the resultant intensity is maximum; when they do not align, the intensity is minimum.

Q & A

What is the phenomenon called when two sound waves of nearly equal frequencies superimpose on each other?

The phenomenon is called 'beats.' It occurs when two sound waves of nearly equal frequencies and amplitudes traveling in the same direction superimpose, causing the intensity of the resultant sound to alternate between maximum and minimum.

What is meant by the 'intensity of sound' in the context of beats?

The 'intensity of sound' refers to the loudness or strength of the sound wave, which in the case of beats, varies with time due to the superposition of two nearly equal frequency sound waves.

How is the beat frequency related to the frequencies of the two sound waves involved?

The beat frequency is the number of times the intensity of the sound goes from maximum to minimum and back to maximum in one second. It is equal to the difference in frequencies of the two sound waves that are superimposing.

Why should the frequencies of the two sound sources be nearly equal for distinct beats to be heard?

For distinct beats to be heard, the frequencies of the two sound sources should be nearly equal because the difference in their frequencies must be small (less than ten). This ensures that the time interval between two successive beats is greater than one-tenth of a second, allowing our ears to distinguish between the beats.

What is the average frequency of the sound heard when two sound waves of 256 Hz and 260 Hz superimpose?

The average frequency of the sound heard when two sound waves of 256 Hz and 260 Hz superimpose is 258 Hz, which is the mean of the two combining frequencies.

What property of hearing is relevant to the perception of beats?

The property of 'persistence of hearing' is relevant to the perception of beats. It refers to the duration for which the impression of a sound persists in our mind, which is about one-tenth of a second, allowing us to mix up the impressions of two closely timed sounds.

What is the graphical method used to represent the formation of beats?

The graphical method involves representing the waves of compression and rarefaction from two sound sources as curves. By superimposing these curves according to the principle of superposition, one can visualize the resultant wave and the formation of beats.

How many vibrations does fork A complete in 1/4 of a second if its frequency is 4 Hz?

Fork A, with a frequency of 4 Hz, completes 1 vibration in 1/4 of a second (since 1 Hz = 1 vibration per second, 4 Hz = 4 vibrations per second).

How many vibrations does fork B complete in 1/2 of a second if its frequency is 8 Hz?

Fork B, with a frequency of 8 Hz, completes 4 vibrations in 1/2 of a second (since 8 Hz = 8 vibrations per second, half of that is 4 vibrations).

What happens to the resultant amplitude and intensity of sound when compression from one wave falls on compression from another wave?

When compression from one wave falls on compression from another wave, the resultant amplitude becomes maximum, and hence the intensity of the sound is also maximum.

What happens to the resultant amplitude and intensity of sound when rarefaction from one wave falls on compression from another wave?

When rarefaction from one wave falls on compression from another wave, the resultant amplitude becomes minimum, and hence the intensity of the sound is also minimum.