INTRODUCTION TO ACOUSTICS WAVE

Time and Frequency

Any periodic motion has a frequency. For example, we might say there are 60 cycles per second. This means that if we observe a time interval of one second, we would see 60 cycles occurring. However, it is not always practical to watch exactly one second and count the number of cycles.

Instead, we can measure the time duration of a single cycle and then calculate the frequency. Conversely, if the frequency is already known, we can determine the time period for one cycle. Time and frequency are reciprocals of one another. For instance, if 60 cycles happen in one second, dividing 1 by 60 gives the time period for one cycle. Likewise, to find the frequency from the time period of one cycle, divide 1 by that time period.

If 60 cycles occur in one second, the time period for one cycle is 0.0167 seconds. This relationship can be verified using the formula $f\times \tau =1$, or $60\times 0.0167=1$. It is important to note that for any frequency above 1 Hz, the time period for one cycle will be less than one second. Additionally, if frequency is expressed in cycles per second, then time must be measured in seconds.

Frequency

Frequency is defined as the number of cycles that occur within a given time period, typically one second. Until a few years ago, frequency was referred to as cycles per second (cps). The term cps was later changed to hertz (Hz) in honor of the person who developed the theory of frequency. Machine speed is often measured in revolutions per minute (RPM), but the frequencies generated by those machines are measured in hertz. Based on the discussion above, the formulas relating frequency and time can be derived.

For simple, these formulas can be concluded with a triangle like picture.

In this context, $f$ represents frequency—that is, the number of cycles that can occur within one second. The symbol $\tau$ denotes the time period required for one complete cycle, while the number 1 refers to one second.

Acoustic Waves

Acoustic waves are pressure disturbances that travel through a compressible fluid, such as air, and are perceived by the human ear as sound. Under normal conditions, these pressure fluctuations are very small in comparison to the surrounding atmospheric pressure, yet they can be measured using sensitive microphones. Acoustic waves typically spread out uniformly in all directions unless they encounter a change in impedance. Like other mechanical waves, acoustic waves undergo reflection, scattering, diffraction, refraction, and interference.

Sound Intensity

When analyzing enclosures, it will be useful to define the sound intensity and sound power of a source. The sound intensity, I, at a point is the time average of the instantaneous rate at which work is done by a sound wave as it travels. It is defined as

Where P is the sound power, A(r) is the area of a sphere of radius r. For spherical sound power sources the sound intensity are

Acoustic Impedance

Acoustic impedance plays a significant role in how sound waves propagate. By selecting materials with the appropriate impedance, engineers can control the transmission of sound along a specific path. A sound wave will continue moving without interruption as long as the acoustic impedance remains unchanged. When materials with similar impedance characteristics are chosen, engineers can promote wave transmission—this principle is applied in ultrasonic testing. Conversely, sound can be suppressed by selecting materials with vastly different impedances. For example, when a wave traveling through air (which has relatively low impedance) hits a wall (which has very high impedance), most of the wave reflects back, and only a small portion continues forward. Acoustic impedance is not solely a material property; it also changes due to variations in cross-sectional area, bends, junctions, and openings. Acoustical impedance is formally defined as the ratio of complex acoustic pressure to complex particle velocity.

Where $p$ represents sound wave pressure and $u$ represents the velocity of the sound wave.

The noise level of a household water pump can be measured easily. However, to make things clearer, we need to define what noise actually is. Noise refers to a sound that causes psychological disturbance. It can disrupt a person's daily activities, whether at work, while studying, or during sleep. Even more seriously, prolonged exposure to noise can lead to deafness.

Water pumps are still widely used in households, especially in areas that rely on groundwater. The operation of these pumps generally produces noise, which can disturb sleep when the pump runs at night.

To reduce this noise, either active or passive methods can be applied. The active method uses sound waves that are out of phase with the existing noise waves. The passive method uses acoustic materials.

The first step in controlling noise levels is to identify the sound sources producing the noise. The next step is to measure the sound pressure level (SPL) at the source. Finally, an appropriate noise control method can be implemented.

Measuring the noise level of a water pump can be done easily using a sound level meter, which is relatively affordable on the market. Alternatively, an Android smartphone with a sound level meter application can be used. These applications are generally still free.

The noise measurement is carried out by first dividing the pump's dimensions into several parts, such as the top, right side, left side, and so on. Each part is then divided into a number of measurement points. At each point, the SPL can be measured three or more times, as shown in the figure.

 

After the data obtained further spool water pump is made in the form of noise contour. Noise contours that have been completed can be seen in the following figure

 

From this noise contours then we can start designing a method for efficient and effective reduction shall we do to the water pump.

Post will later be followed by a simple experiment everyday materials that can be used to reduce the noise of the water pump.

thanks hopefully useful