Ultrasound Waves Are Used to Measure Blood Flow Speeds

Model Answer

Benha University 18/6/2011

Faculty of science Third year special

Physics Department Time: 3 hours

Solid state-experimental Physics

Dr. Eslam Sheha

· Compare between electron and optical microscope

· Ultrasound waves are used to measure blood flow speeds. Suppose a device emits sound at 500 kHz, and the speed of sound in human tissue is taken to be 1540 m/s. What is the expected beat frequency if blood is flowing naturally in large leg arteries at 2.0 cm/s directly away from the sound source?

2 cm/s = .02 m/s
This is another reflection problem. There are two steps to solving it, first, the object (blood in this case) is a moving "observer" and the frequency it is reflecting is Doppler shifted, and then it becomes a moving source. In both cases the shift is toward lower frequencies.
So the frequency of the reflected sound is:
¦' = (1 - v0/v)¦ moving observer (We choose - to make the frequency lower)
¦' = (1 - (.02 m/s)/(1540 m/s))( 500000Hz ) = 499993.51 Hz
And then there is also a moving source shift from the object:
¦' = ¦/(1 + vs/v) moving source (We choose the + again, to make the frequency lower, as the object is going away from us)
¦' = (499993.51 Hz)/(1 ± (.02 m/s)/(1540 m/s)) = 499987 Hz
And finally, the beat frequency is:
fbeat = |f1 - f2| = |500000Hz - 499987 Hz| = 13 Hz

· State the physical set up of NMR experiment

The core of the experimental apparatus is shown in Figure 3. The RF oscillator generates a tuneable, sine-wave signal near 15MHz, approximately the precession frequency for protons in the field of the permanent magnet. The pulse programmer creates a pulse stream that switches, or gates, the output of the oscillator, so that it produces short bursts of radio frequency signals whenever the pulses are ”on” and no output when they are ”off”. It also sends a synchronization pulse to the external trigger of the oscilloscope. It can produce single pulses (type A) and pulse trains (type A followed by one or several pulses of type B). The RF bursts are amplified and sent to the transmitter coils in the sample probe. These coils are wound in a Helmholtz configuration to optimize the homogeneity of the applied magnetic field H1. This field is applied along the x-axis. The permanent magnet produces a homogeneous field of about 3.5 kG along the z-axis. The receiver coil, oriented along the y-axis, picks up an emf generated by the precessing magnetization of the protons in the sample. During the RF bursts, the pulse programmer sends a blanking signal to the receiver, switching it off while pulses are applied to the sample. (There is some cross-talk between the transmitter and receiver coils.) Between the pulse bursts the RF signal from the receiver coil is amplified and measured two different ways. The RF amplitude detector rectifies the signal so that its output is proportional to the amplitude of the RF signal from the receiver. The RF oscillations decay with time, forming the the free induction decay envelope. When you observe the signal from Detector Out, you only see the envelope, but not the oscillations themselves.

Information

1-Position of the peak

2- Number of the peaks

3- Integrating of the peaks

· Correct the following expression relates the external magnetic field to the frequency of resonance (NMR):

· State the physical set up of X-ray experiment

X-rays are produced whenever high-speed electrons collide with a metal target. A source of electrons – hot W filament, a high accelerating voltage between the cathode (W) and the anode and a metal target, Cu, Al, Mo, Mg. The anode is a water-cooled block of Cu containing desired target metal.

· The Bragg scattering angle for n=1 from the (110) planes in iron(bcc) is 22 degrees for a x-ray wavelength of 1.54 Angstroms. Determine the length of the edge of the cube for iron.

According to Bragg law

2dhklsin(Q)=nl Hence, dhkl=2.056

And the edge of the cube a0

Hence, a0 = 1.454 Angstroms