Ultrasound pulses with a frequency of 1.000 MHz are transmitted into water, where the speed of sound is 1500 m /s. The spatial length of each pulse is 12 mm.
a. How many complete cycles are contained in one pulse?
b. What range of frequencies must be superimposed to create each pulse?
.a) Number of cycle complete in one pulse is 8
.b) Range of frequencies 0.938 MHz f 1.063 MHz
.a) The number of complete cycles in one pulse can be obtained by dividing the spatial length of the pulse by the wavelength of the ultrasound pulse, where the wavelength can be calculated as follows
Number of cycle complete in one pulse
first, we need to find the pulse duration , and that can be done by finding the period of the wave and multiply it by the number of complete cycles in one pulse. The period is
thus, the duration of the pulse (the wave packet ) is
now can be calculated as
Finally, the range of frequencies that must be superimposed to create the given pulse is
Consider the electron wave function
where x is in cm.
a. Determine the normalization constant c.
b. Draw a graph of c1x2 over the interval -2 cm x 2 cm. Provide numerical scales on both axes.
c. Draw a graph of 0 c1x2 0 2 over the interval -2 cm x 2 cm. Provide numerical scales.
d. If 104 electrons are detected, how many will be in the interval 0.00 cm x 0.50 cm?
a. Starting with the expression for a wave packet, find an expression for the product for a photon.
b. Interpret your expression. What does it tell you?
c. The Bohr model of atomic quantization says that an atom in an excited state can jump to a lower-energy state by emitting a photon. The Bohr model says nothing about how long this process takes. You'll learn in Chapter 41 that the time any particular atom spends in the excited state before cmitting a photon is unprcdictablc, but the average lifetime of many atoms can be determined. You can think of as being the uncertainty in your knowledge of how long the atom spends in the excited state. A typical value is ns. Consider an atom that emits a photon with a wavelength as it jumps down from an excited state. What is the uncertainty in the energy of the photon? Give your answer in eV.
d. What is the fractional uncertainty in the photon's energy?
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