What Frequency is Needed for Effective Ultrasonic Cleaning?

[ghad58@yahoo.]

Homework Statement

Particles approximately 3.0 X 10-2 cm in diameter are to be scrubbed loose from machine parts in an aqueous ultrasonic cleaning bath. Above what frequency should the bath be operated to produce wavelengths of this size and smaller?

Homework Equations

speed of sound in water = 1500 m/s
frequency = (speed of sound)/wavelength

The Attempt at a Solution

1500x10^4/3 = 5x10^6 Hz
does this sound right?

 

[Nasa01]

Hi

Yes, your calculations seem correct. But let me give you a tip, always do your calculations in SI units. You have the velocity in SI unit, why not change the diameter to SI instead of the other way around?

In this case you are alright since frequency is dimensionless. However, in a case where the result is not dimensionless you will save time and minimized conversion errors risks having used SI units to begin with.

Cheers!

 

[thomate1]

I would like to provide a more detailed and comprehensive response to this question. Firstly, the concept of wavelength and intensity are fundamental to the study of waves, including sound waves. Wavelength is defined as the distance between two consecutive points on a wave that are in phase, meaning they have the same amplitude and are moving in the same direction. Intensity, on the other hand, is a measure of the energy carried by a wave per unit area.

In the given scenario, we are dealing with ultrasonic waves in an aqueous medium. Ultrasonic waves have frequencies higher than the audible range of humans, typically above 20 kHz. These waves are commonly used in cleaning processes as they have a high intensity and can produce cavitation, which helps in removing particles from surfaces.

To determine the appropriate frequency for the ultrasonic bath in order to produce wavelengths of 3.0 X 10^-2 cm and smaller, we can use the formula frequency = speed of sound/wavelength. The speed of sound in water is approximately 1500 m/s, which can be converted to 1500x10^4 cm/s. Plugging in the given wavelength of 3.0 X 10^-2 cm, we get a frequency of approximately 5x10^6 Hz, which is equivalent to 5 MHz.

In conclusion, to produce wavelengths of 3.0 X 10^-2 cm and smaller, the ultrasonic bath should be operated at a frequency of 5 MHz or higher. It is important to note that the intensity of the waves also plays a crucial role in the effectiveness of the cleaning process, and it should be carefully controlled to prevent damage to the machine parts. Additionally, the size and shape of the particles and the composition of the cleaning solution can also affect the efficiency of the ultrasonic cleaning process. Therefore, it is essential to consider all these factors when determining the appropriate frequency for the ultrasonic bath.