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3 years ago

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Diagnostic ultrasound of frequency 3.82 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 1650 m/s, what is the wavelength of this wave in tissue? (Take the speed of sound in air to be 343 m/s.)

1 answer:

maxonik [38]3 years ago

7 0

Explanation:

It is given that,

Frequency of diagnostic ultrasound, f = 3.82 MHz = 3820 Hz

The speed of the sound in air, v = 343 m/s

(a) We need to find the wavelength in air of such a sound wave. Let it is given by λ₁

i.e. $\lambda=\dfrac{v}{\nu}$

$\lambda_1=\dfrac{343\ m/s}{3820\ Hz}$

$\lambda_1=0.089\ m$

(b) If the speed of sound in tissue is 1650 m/s .

$\lambda_2=\dfrac{v}{\nu}$

$\lambda_2=\dfrac{1650\ m/s}{3820\ Hz}$

$\lambda_2=0.43\ m$

Hence, this is the required solution.

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Answer:

A) $Z = 0.577 C +112.931$

$Z = 0.577*(100) +112.931=170.631 Z$

B) $C=\frac{Z-112.931}{0.577}= \frac{100-112.931}{0.577}=-22.41 C$

C) $K = C +273.15$

$K = -22.41 +273.15 =250.739 K$

Explanation:

For this case we want to create a function like this:

$Z = a C + b$

Where Z represent the degrees for the Z scale C the Celsius grades and tha valus a and b parameters for the model.

The boiling point of nitrogen is -195,8 °C

The melting point of iron is 1538 °C

We know the following equivalences:

-195.8 °C = 0 °Z

1538 °C = 1000 °Z

Let's say that one point its (1538C, 1000 Z) and other one is (-195.8 C, 0Z)

So then we can calculate the slope for the linear model like this:

$a = \frac{z_2 -z_1}{c_2 -c_1}= \frac{1000 Z- 0Z}{1538C -(-195.8 C)}=\frac{1000 Z}{1733.8 C}=0.577 \frac{Z}{C}$

And now for the slope we can use one point let's use for example (-195.8C, 0Z), and we have this:

$0 = 0.577 (-195.8) + b$

And if we solve for b we got:

$b = 0.577*195.8 =112.931 Z$

So then our lineal model would be:

$Z = 0.577 C +112.931$

Part A

The boiling point of water is 100C so we just need to replace in the model and see what we got:

$Z = 0.577*(100) +112.931=170.631 Z$

Part B

For this case we have Z =100 and we want to solve for C, so we can do this:

$Z-112.931 = 0.577 C$

$C=\frac{Z-112.931}{0.577}= \frac{100-112.931}{0.577}=-22.41 C$

Part C

For this case we know that $K = C +273.15$

And we can use the result from part B to solve for K like this:

$K = -22.41 +273.15 =250.739 K$

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