Tumor in Liver!

Classical Mechanics Level 4

A narrow beam of ultrasonic waves reflects from a liver tumor at some depth inside the liver as shown in figure. The speed of the ultrasonic wave is 25% less in the liver than in the surrounding medium. What is the depth of the tumor? Give your answer in cm \text{cm} .


The answer is 8.

Nishant Rai by Nishant Rai , 25, India

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2 solutions

Nishant Rai
May 29, 2015

Since speed of ultrasonic wave is 25% lesser in liver, v = 3 C 4 v = \frac{3C}{4}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Please mention that the incident ray is in a medium of refractive index of 1 Else it is confusing. Good practical problem.

Ashwin Gopal - 6 years ago
Nathanael Case
May 29, 2015

Snell's law can be derived from the assumption that the frequency is unchanged, thus is can be applied to sound waves.

Using Snell's law you get sin ⁡ ( arctan ⁡ ( 6 x ) ) sin ⁡ ( 53 deg ⁡ ) = V l i v e r V s u r r o u n d i n g = 0.75 ⇒ x ≈ 8 \frac{\sin(\arctan(\frac{6}{x}))}{\sin(53\deg)}=\frac{V_{liver}}{V_{surrounding}}=0.75\Rightarrow x\approx 8 cm

1 Helpful 0 Interesting 0 Brilliant 0 Confused

@Nishant Rai

There is a small typo in the problem: it says "25 less" instead of "25% less"

Nathanael Case - 6 years ago

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thanks for pointing, corrected!

@Nathanael Case

Nishant Rai - 6 years ago

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