A hospital uses an ultrasonic scanner to locate tumours in a...

A hospital uses an ultrasonic scanner to locate tumours in a tissue. The operating freqency of the scanner is $3.2 \mathrm{MHz}$. The speed of sound in a tissue is $1.6 \mathrm{~km} \mathrm{~s}^{-1}$. The wavelength of sound in the tissue is (a) $0.25 \mathrm{~mm}$ (b) $0.5 \mathrm{~mm}$ (c) $0.75 \mathrm{~mm}$ (d) $1 \mathrm{~mm}$

A hospital uses an ultrasonic scanner to locate tumours in a tissue. The operating freqency of the scanner is $3.2 \mathrm{MHz}$. The speed of sound in a tissue is $1.6 \mathrm{~km} \mathrm{~s}^{-1}$. The wavelength of sound in the tissue is
(a) $0.25 \mathrm{~mm}$
(b) $0.5 \mathrm{~mm}$
(c) $0.75 \mathrm{~mm}$
(d) $1 \mathrm{~mm}$

Key Concepts

Wavelength

Wavelength is the distance between successive points of equivalent phase in a wave (for example, between consecutive crests). Using the wave equation, wavelength can be computed by dividing the speed of the wave by its frequency, providing insight into the resolution and detail of the imaging results.

Speed of Sound

The speed of sound in a medium represents how fast sound waves travel through that medium. It depends on the medium's properties, such as density and elasticity. In biological tissues, the speed of sound is a crucial parameter for determining wave characteristics like wavelength.

Ultrasonic Imaging

Ultrasonic imaging employs high-frequency sound waves to create images of internal body structures. The performance of these systems is directly linked to the properties of the waves used, including frequency, speed, and wavelength, which together determine the imaging resolution and penetration capabilities.

Wave Equation

The wave equation, expressed as v = f?, is fundamental in wave physics. It relates the speed (v) of a wave to its frequency (f) and its wavelength (?). This formula allows one to calculate any one of these parameters if the other two are known, making it essential for understanding wave behavior in different media.

Frequency

Frequency measures the number of cycles a wave completes per second and is typically measured in hertz (Hz). In the context of ultrasonic applications, a higher frequency generally provides better resolution in imaging, although it may sacrifice penetration depth.

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