Diagnostic ultrasound of frequency 3.45 MHz is 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 1500 m/s, what is the wavelength of this wave in tissue? (Take the speed of sound in air to be 343 m/s.)

4.35*10⁻⁴ m

Explanation:

(a)

From wave,

v = λf ... Equation 1

Where v = speed of sound in air, λ = wavelength of sound, f = frequency of sound.

Make λ the subject of formula in equation 1

λ = v/f ... Equation 2

Given: v = 343, f = 3.45 MHz = 3.45*10⁶ Hz

Substitute into equation 2

λ = 343 / (3.45*10⁶)

λ = 99.42*10⁻⁶ m

λ = 9.942*10⁻⁵ m

(b)

using,

v' = λ'f ... Equation 3

Where v' = speed of sound in tissue, λ' = wavelength of sound in tissue.

make λ' the subject of the equation

λ' = v'/f ... Equation 4

Given: v' = 1500 m/s, f = 3.45 MHz = 3.45*10⁶ Hz

Substitute into equation 4

λ' = 1500 / (3.45*10⁶)

λ' = 434.783*10⁻⁶

λ' ≈ 4.35*10⁻⁴ m.