What is the wavelength of ultrasound therapy at 3 MHz in an average tissue of Human Body?

Question

Accepted Answer

The correct option is (4):
The foundation for answering this question lies in the fundamental physics of wave propagation, specifically the relationship between the velocity, frequency, and wavelength of sound waves. This relationship is mathematically expressed as $v = f \cdot \lambda$, where $v$ is velocity, $f$ is frequency, and $\lambda$ is wavelength. In the context of therapeutic ultrasound, the speed of sound ($v$) in average soft human tissue is consistently cited as approximately 1500 meters per second (m/s). Given the frequency ($f$) of 3 MHz (or $3,000,000$ Hertz), we can rearrange the formula to solve for the wavelength: $\lambda = v / f$. Plugging in the standard clinical values, $\lambda = 1500 \text{ m/s} / 3,000,000 \text{ Hz}$, which equals $0.0005$ meters, or $0.5$ millimeters (mm). This short wavelength for 3 MHz ultrasound is directly linked to its clinical purpose of treating *superficial* tissues, as the energy is rapidly absorbed closer to the surface, typically at depths between 0.8 cm and 1.6 cm.

The incorrect option is (1):
The wavelength of 2 mm is incorrect for 3 MHz ultrasound. This value would imply a sound velocity of $6000 \text{ m/s}$ ($2 \text{ mm} \times 3 \text{ MHz}$), which is four times the accepted speed of sound in average soft tissue. Such a high velocity is not observed in human tissues; the velocity of sound is relatively constant in soft biological tissues. Therefore, 2 mm is not the correct wavelength for a 3 MHz frequency used in therapy.

The incorrect option is (2):
The value 1.5 mm is the standard and correct wavelength, not for 3 MHz, but for the *lower* frequency therapeutic ultrasound, which is 1 MHz. If you apply the calculation, $\lambda = 1500 \text{ m/s} / 1,000,000 \text{ Hz}$, the result is exactly $1.5$ mm. Therapists select the 1 MHz frequency when they need to treat deeper tissue structures, as its longer wavelength allows for less rapid attenuation (absorption) of energy in superficial layers, enabling penetration up to approximately 5 cm. This option is a common distractor and is specifically linked to the 1 MHz setting, not 3 MHz.

The incorrect option is (3):
A wavelength of 1 mm is incorrect and does not accurately correspond to the 3 MHz therapeutic ultrasound frequency. If we use the average sound velocity of $1500 \text{ m/s}$, a 1 mm wavelength would correspond to a frequency of 1.5 MHz ($1500 \text{ m/s} / 0.001 \text{ m}$). The inverse relationship between frequency and wavelength dictates that a higher frequency like 3 MHz must have a wavelength significantly shorter than that of the lower 1.5 MHz frequency, confirming that 1 mm is too long to be the correct answer.