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Fundamentals Of Physics
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Short Answer

Question: Diagnostic ultrasound of frequency is 4.50 MHz used to examine tumors in soft tissue. (a) What is the wavelength in air of such a sound wave? (b) If the speed of sound in tissue is , what is the wavelength of this wave in tissue?

Answer

  1. The wavelength of ultrasound in air is λa=76.2μm.
  2. The wavelength of ultrasound in tissue is λt=0.333nm.

See the step by step solution

Step by Step Solution

Step 1: Given data

Frequency of diagnostic ultrasound is

.f=4.50MHz =4.50×106Hz

Step 2: Determining the concept

By using the relation between velocity and frequency, calculate the wavelength in air and tissue.

The expression for the velocity is given by,

vair=λa×f

Here, v is the velocity of the sound in air, f is the frequency and λais the wavelength.

Step 3: (a) Determining the wavelength in air of such a sound wave

Velocity of sound in air is vair=343m/s and frequency of diagnostic ultrasound is

. f=4.50×106Hz

Therefore, the wavelength can be calculated as,

vair=λa×f

Substitute343m/s for Vair , 4.50×106Hz for f into the above equation,

343=λa×4.50×106λa=3434.50×106λa=76.22×10 - 6mλa=76.22μm

Hence, the wavelength of ultrasound in air isλa=76.22μm .

Step 4: (b) Determine the wavelength of the wave in tissue

Velocity of sound in tissue is vt=1500m/s and frequency of diagnostic ultrasound is

. f=4.50×106Hz

Therefore, wavelength can be calculated as,

vt=λt×fλt=vtf

Substitute 1500m/s for vt 4.50×106Hz for vtinto the above equation,

λt=15004.50×106=333.33×10-6m=0.333mm

Hence, the ultrasonic wavelength on tissue is λ=0.333mm

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