Q: A patient’s artery has a cross-sectional area of $$2.0\ \text{cm}^2$$ and blood flows at $$0.20\ \text{m/s}. $$What is the volume flow rate?

$$4.0 \times 10$$^{-6}$$\ \text{m}^3/\text{s}$$

Question 1

Two identical ropes are set up as shown in the image, each with a different mass hanging from the end, forming standing waves of identical frequencies. If the tension in each rope is provided by the hanging mass, what is the ratio of the masses $$m_A : m_B$$? (Hint: recall $$v = \sqrt{\frac{T}{\mu}})$$

Accepted Answer

$$9 : 4$$

Question 2

A uniform block floats in water with $$\frac{1}{3} of $$its volume above the surface. What is the mass density of the block in terms of the mass density of water $$\rho_w$$?

Accepted Answer

$$\frac{2\rho_w}{3}$$

Question 3

A Doppler ultrasound device emits waves at $$f_s = 5.0\ 	ext{MHz} to $$measure blood flow. The speed of sound in tissue is $$1540\ 	ext{m/s}$$, and red blood cells move toward the transducer at $$v_b = 0.30\ 	ext{m/s}. $$What is the frequency of the reflected wave detected by the transducer? (Assume a head-on approach.)

Accepted Answer

$$5.00195\ 	ext{MHz}$$

Question 4

Water flows steadily through a pipe as shown, with the cross-sectional area at A twice as large as at B. At which point is the volume flow rate greater, and by how much?

Accepted Answer

Tie

Question 5

A string of length $$L$$ and mass per unit length $$\mu is $$under tension $$T. $$What is the fundamental frequency of standing waves on the string?

Accepted Answer

$$f_1$$ = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$$

Question 6

A block floats in oil with $$\frac{1}{4} of $$its volume above the surface. If the density of oil is $$800\ 	ext{kg/m}^3$$, what is the density of the block?

Accepted Answer

$$600\ 	ext{kg/m}^3$$

Question 7

A patient’s artery has a cross-sectional area of $$2.0\ 	ext{cm}^2$$ and blood flows at $$0.20\ 	ext{m/s}. $$What is the volume flow rate?

Accepted Answer

$$4.0 	imes 10$$^{-6}$$\ 	ext{m}^3/	ext{s}$$

Question 8

If the frequency of a wave on a string is doubled while the tension and mass per unit length remain constant, what happens to the wavelength?

Accepted Answer

It is halved

Question 9

A submarine uses sonar to detect a school of fish. If the emitted frequency is $$30\ 	ext{kHz}$$ and the reflected frequency is $$30.2\ 	ext{kHz}$$, what can be inferred about the motion of the fish?

Accepted Answer

The fish are moving toward the submarine

Question 10

A pipe narrows from a cross-sectional area of $$0.10\ 	ext{m}^2 to$$ $$0.05\ 	ext{m}^2. If $$the velocity of water at the wide section is $$2\ 	ext{m/s}$$, what is the velocity at the narrow section?

Accepted Answer

$$4\ 	ext{m/s}$$

Question 11

A Doppler ultrasound is used to measure the speed of blood flow. If the detected frequency is higher than the emitted frequency, what does this indicate about the direction of blood flow?

Accepted Answer

Blood is moving toward the transducer

Question 12

A string under tension $$T$$ has a mass per unit length $$\mu. If $$the tension is quadrupled, what happens to the speed of waves on the string?

Accepted Answer

It is doubled

Question 13

A block floats in a liquid with $$60\% of $$its volume submerged. If the density of the liquid is $$900\ 	ext{kg/m}^3$$, what is the density of the block?

Accepted Answer

$$540\ 	ext{kg/m}^3$$

Question 14

A patient’s artery narrows, causing the blood velocity to increase. According to the continuity equation, what happens to the pressure in the narrow region?

Accepted Answer

It decreases

Question 15

A string of length $$1.0\ 	ext{m}$$ and mass per unit length $$0.01\ 	ext{kg/m} is $$under a tension of $$100\ 	ext{N}. $$What is the speed of waves on the string?

Accepted Answer

$$100\ 	ext{m/s}$$

Discussion 13

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