Beats occur when two sound waves of slightly different frequencies interfere with each other. The superposition of these waves creates a resultant wave with an amplitude that fluctuates over time, producing a periodic variation in loudness known as the beat frequency, which is equal to the absolute difference between the two source frequencies.

The human auditory system can perceive the periodic variation in amplitude known as beats. When the difference between two sound frequencies is small, typically below 7 Hz, the ear perceives a distinct pulsating sensation. As the beat frequency increases beyond this range, the pulsations blend into a continuous tone, making individual beats difficult to distinguish.

The speed of a wave on a string is determined solely by the physical properties of the string, specifically its tension and linear mass density. The number of loops (mode of vibration) and the plucking point determine the harmonic content and amplitude, but they do not change the intrinsic speed of the wave propagation.

A stationary wave is formed by the superposition of two waves traveling in opposite directions. Nodes are points of zero displacement, while antinodes are points of maximum displacement. The distance between two consecutive nodes is half the wavelength (λ/2), and the distance between two consecutive antinodes is also λ/2. This pattern is a fundamental characteristic of standing waves in strings or pipes.

A zone of silence occurs when two sound waves meet in such a way that their crests and troughs align perfectly, resulting in destructive interference. In this state, the amplitude of the combined wave is reduced to zero, effectively canceling out the sound at that specific location.

Beats occur due to the interference of two sound waves with slightly different frequencies. As the waves overlap, they alternate between constructive interference (resulting in increased loudness) and destructive interference (resulting in decreased loudness). The frequency of these loudness fluctuations, known as the beat frequency, is equal to the absolute difference between the frequencies of the two original sound sources.

The speed v is 20 mm/s and frequency f is 10 Hz. The wavelength λ = v/f = 20/10 = 2 mm. In a standing wave, the distance between adjacent nodes is λ/2. Thus, 2 mm / 2 = 1.0 mm. This calculation confirms the distance between nodes in the resulting interference pattern.

Stationary waves are formed by the superposition of two identical waves traveling in opposite directions. Unlike progressive waves, which transport energy through a medium, stationary waves do not result in a net transfer of energy across the medium. The energy remains localized within the standing wave pattern.

The wave speed in a string is defined by the formula v = sqrt(T/μ), where T is tension and μ is linear mass density. The number of loops (harmonic mode) and the plucking point determine the frequency and the specific standing wave pattern formed, but they do not change the speed at which the individual traveling waves move along the string.

In a string fixed at both ends, the fundamental frequency (first harmonic) is denoted as f1. The first overtone corresponds to the second harmonic, which is 2 * f1. Given that the first overtone is 320 Hz, we set 2 * f1 = 320 Hz. Solving for f1 yields 160 Hz. This relationship is standard for standing waves on strings.