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Frequency of diagnostic ultrasound is

.$$\begin{gathered} f=4.5\text{0MHz} \\ =4.50脳{10}^{\text{6}}\text{Hz} \end{gathered}$$

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

The expression for the velocity is given by,

${\mathit{v}}_{\mathbf{a}\mathbf{i}\mathbf{r}}\mathbf{=}{\mathit{位}}_{\mathbf{鈥�}\mathbf{a}}\mathbf{脳}\mathit{f}$

Here, v is the velocity of the sound in air,f is the frequency and ${位}_{鈥�a}$is the wavelength.

Velocity of sound in air is $v_{air}=3\text{43m/s}$and frequency of diagnostic ultrasound is

. $f=4.50脳1{\text{0}}^{\text{6}}\text{Hz}$

Therefore, the wavelength can be calculated as,

$v_{air}={位}_{鈥�a}脳f$

Substitute$343鈥�m/sfor{V}_{air,}4.50脳{10}^{\text{6}}\text{Hzforf}$ into the above equation,

$$\begin{gathered} 343={位}_{鈥�a}脳4.50脳{10}^{\text{6}} \\ {位}_{鈥�a}=\frac{343}{4.50脳{10}^6} \\ {位}_{鈥�a}=76.22脳{\text{10}}^{\text{- 6}}\text{m} \\ {位}_{鈥�a}=76.22渭m \end{gathered}$$

Hence, the wavelength of ultrasound in air is${位}_{鈥�a}=76.22渭m$ .

Velocity of sound in tissue is $v_t=150\text{0m/s}$and frequency of diagnostic ultrasound is

. $f=4.50脳{10}^{\text{6}}\text{Hz}$

Therefore, wavelength can be calculated as,

$$\begin{gathered} v_t={位}_{鈥�t}脳f \\ 鈬�{位}_{鈥�t}=\frac{v_t}{f} \end{gathered}$$

Substitute $150{\text{0m/sforv}}_{t}4.50脳{10}^{\text{6}}\text{Hzforv}t$into the above equation,

$$\begin{gathered} {位}_{鈥�t}=\frac{1500}{4.50脳{10}^6} \\ =333.33脳{10}^{-6}\text{m} \\ =0.\text{333mm} \end{gathered}$$

Hence, the ultrasonic wavelength on tissue is $位=$0.333mm