Longitudinal Wave Physics Example 3

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Example 3

medium
An ultrasound device emits sound at 2×106 Hz2 \times 10^6 \text{ Hz} in human tissue (v=1540 m/sv = 1540 \text{ m/s}). What is the wavelength? Why is this frequency useful for medical imaging?

Solution

  1. 1
    Wavelength: λ=vf=15402×106=7.7×10−4 m=0.77 mm\lambda = \frac{v}{f} = \frac{1540}{2 \times 10^6} = 7.7 \times 10^{-4} \text{ m} = 0.77 \text{ mm}.
  2. 2
    The short wavelength allows the ultrasound to resolve small structures in the body, producing detailed images.

Answer

λ=0.77 mm\lambda = 0.77 \text{ mm}
High-frequency ultrasound produces very short wavelengths in tissue, enabling detailed imaging. Lower frequencies penetrate deeper but with less resolution, so the frequency is chosen based on the clinical need.

About Longitudinal Wave

A wave in which the particles of the medium oscillate parallel to the direction of wave propagation, creating alternating regions of compression (high pressure) and.

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More Longitudinal Wave Examples

Example 1 easy

A longitudinal wave in a spring has compressions [formula] apart. The wave frequency is [formula]. W

Example 2 medium

Sound travels at [formula] in air and [formula] in steel. A [formula] sound wave enters a steel rail

Example 4 hard

An earthquake produces both P-waves ([formula], longitudinal) and S-waves ([formula], transverse). A

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