In a longitudinal wave, the more particles that are compressed together determines the ___ of the wave.

A. Amplitude

B. Frequency

C. Wavelength

D. Velocity

To determine the correct answer, we need to understand the properties of a longitudinal wave and how they relate to each other.

A longitudinal wave is a type of wave where the particles of the medium vibrate parallel to the direction of wave propagation. Examples of longitudinal waves include sound waves and seismic waves.

Now, let's analyze the options:

A. Amplitude: The amplitude of a wave refers to the maximum displacement of particles from their equilibrium position. It is a measure of the wave's intensity or energy. In the case of a longitudinal wave, the amplitude corresponds to the maximum compression or rarefaction of the particles. So, increasing the compression of particles or bringing them closer together could increase the amplitude of the wave, but it is not always the determining factor.

B. Frequency: The frequency of a wave measures the number of complete wave cycles that pass a given point in one second. It is usually measured in hertz (Hz). The frequency of a longitudinal wave is determined by the rate at which the particles vibrate, but it is not affected by their compression.

C. Wavelength: The wavelength of a wave is the distance between two consecutive points that are in phase with each other, for example, two adjacent compressions or rarefactions in a longitudinal wave. The wavelength remains constant for a given medium and is not determined by the compression of particles.

D. Velocity: The velocity of a wave refers to the speed at which the wave propagates through a medium. It is determined by the properties of the medium, such as its density and elasticity. The compression of particles can affect the velocity of a longitudinal wave because it relates to the density of the medium, but it does not solely determine it.

Based on these explanations, we can conclude that the correct answer is A. Amplitude. The more particles there are compressed together in a longitudinal wave, the greater the amplitude of the wave.