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Amplitude refers to the height of the wave and is a crucial factor when it comes to understanding the energy and intensity of a sound wave. In the context of sound waves, amplitude measures how much the air particles are displaced by the wave. A higher amplitude means louder sound. In our exercise, each wave has an amplitude of 12 nanometers (nm).

When two sound waves travel in the same direction and interfere, the resulting amplitude can be computed using the formula:

• For waves with amplitude \(A = 12 \text{ nm}\) and a phase difference \(\phi = \pi/3\),
• Resultant amplitude formula: \(A_r = 2A\cos\left(\frac{\phi}{2}\right)\)

Substituting the given values, the resultant amplitude turns out to be \(12\sqrt{3} \text{ nm}\).

In contrast, if the sound waves proceed in opposite directions, they form a standing wave. The amplitude in this case is the simplest, calculated simply as twice that of one wave: \(A_r = 24 \text{ nm}\). This arises from the addition of vibrational energy. The concepts of amplitude thus play a critical role in dictating the effect of interference in sound waves.

Wavelength is the distance between two consecutive points that are in phase on a wave, like two crests or troughs. It determines characteristics such as pitch in sound waves. Longer wavelengths correspond to deeper (lower pitch) sounds, while shorter wavelengths correlate with higher pitches.

In our given exercise, the wavelength of each sound wave is given as 35 centimeters (cm). This parameter remains constant and unaffected, whether the waves travel in the same or opposite directions. This is because interference affects the shape and amplitude rather than the actual distance between repeating points on the wave.

To summarize:

• Interference of waves in the same direction doesn’t alter their wavelength.
• Formation of standing waves due to opposite direction interference preserves the original wavelength, \(\lambda = 35 \text{ cm}\).

Understanding how wavelength interacts with other properties of a wave helps in decrypting how waves behave in various circumstances.

Phase difference refers to the difference in phase angle between two waves, which can significantly affect their resultant interference. When waves are in phase (phase difference zero), their effects reinforce each other, resulting in a larger resultant wave.

In our scenario, the phase difference is \(\pi/3 \text{ rad}\). This particular phase difference affects the waves traveling in the same direction using the cosine factor in the amplitude formula:

• Phase difference \(\phi = \pi/3\) reduces the degree of constructive interference, as shown by \(\cos(\pi/6) = \frac{\sqrt{3}}{2}\).

The concept of phase difference is also integral in understanding how standing waves form:

• If the phase difference is such that it leads to complete cancellation, destructive interference occurs, significantly reducing the resultant amplitude.
• For our opposite traveling waves with the same wavelength, however, standing waves feature the fundamental phase characteristics of destructive and constructive interplay at nodes and antinodes.

Comprehending phase difference is crucial for understanding not only how sound waves behave in interference but also how various phase shifts can impact real-world audio applications and wave technologies.