Problems Practice Problems The threshold photoelectric effect in

Problems • Practice Problems • The threshold photoelectric effect in tungsten is produced by light of wavelength 260 nm. Give the energy of a photon of this light in joules. • A mercury lamp emits radiation with a wavelength of 4. 36 x 10 -7 m. What is the frequency of the light? • The brilliant read colors seen in fireworks are due to the emission of light with wavelengths around 659 nm. Calculate the frequency of red light of this wavelength. • The blue color fireworks are produced when a compound emits light with a wavelength of 450 nm. What is the energy of the light emitted?

• The threshold photoelectric effect in tungsten is produced by light of wavelength 260 nm. Give the energy of a photon of this light in joules. • E = hf E = hc/ • E = (6. 63 x 10 -34 x 3 x 108)/(260 x 10 -9) • E = 7. 65 x 10 -19 J

• A mercury lamp emits radiation with a wavelength of 4. 36 x 10 -7 m. What is the frequency of the light? • f = c/ f = (3 x 108)/(4. 36 x 10 -7) f = 6. 88 x 1014 Hz

The brilliant read colors seen in fireworks are due to the emission of light with wavelengths around 659 nm. Calculate the frequency of red light of this wavelength. • f = c/ f = (3 x 108)/(659 x 10 -9) f = 4. 55 x 1014 Hz

The blue color fireworks are produced when a compound emits light with a wavelength of 450 nm. What is the energy of the light emitted? • E = hf E = hc/ • E = (6. 63 x 10 -34 x 3 x 108)/(450 x 10 -9) • E = 4. 42 x 10 -19 J

waves_02 6 SUPERPOSITION OF WAVES • Two waves passing through the same region will superimpose - e. g. the displacements simply add • Two pulses travelling in opposite directions will pass through each other unaffected • While passing, the displacement is simply the sum of the individual displacements Animations courtesy of Dr. Dan Russell, Kettering University CP 514

7 waves_02: MINDMAP SUMMARY – SUPERPOSITION PRINCIPLE Travelling waves, superposition principle, interference, constructive interference, destructive interference, intermediate interference, nodes, antinodes, phase difference, in phase, out of phase, path difference, two point interference, standing waves on strings, standing waves in air columns, thin film interference Superposition (at time to) Wave 1 + Wave 2 14 15 Constructive interference: = m (2 ) Destructive interference: = (m + 1/2) = (m + ½) (2 ) m = 0, 1, 2, 3, . . .

SUPERPOSITION INTERFERENCE 8 In phase constructive interference Out of phase destructive interference CP 510

9 Problem 1 Two sine waves travelling in the same direction Constructive and Destructive Interference Two sine waves travelling in opposite directions standing wave

10 Interference of two overlapping travelling waves depends on: * relative phases of the two waves * relative amplitudes of the two waves fully constructive interference: if each wave reaches a max at the same time, waves are in phase (phase difference between waves two waves = 0) greatest possible amplitude ( ymax 1 + ymax 2) fully destructive interference: one wave reaches a max and the other a min at the same time, waves are out phase (phase difference between two waves = rad), lowest possible amplitude |ymax 1 - ymax 2| 0 < phase difference < rad or < phase difference < 2 intermediate interference:

SUPERPOSITION INTERFERENCE A phase difference of 2 rad corresponds to a shift of one wavelength between two waves. For m = 0, 1, 2, 3 fully constructive interference phase difference = m fully destructive interference phase difference = (m + ½) 11

12 SUPERPOSITION INTERFERENCE A B Which graph corresponds to constructive, destructive and intermediate interference ? C

SUPERPOSITION INTERFERENCE What do these pictures tell you ? 16 17 18 19 20 21 13

Problem solving strategy: I S E E Identity: What is the question asking (target variables) ? What type of problem, relevant concepts, approach ? Set up: Execute: Evaluate: Diagrams Equations Data (units) Physical principals PRACTICE ONLY MAKES PERMANENT Answer question Rearrange equations then substitute numbers Check your answer – look at limiting cases sensible ? units ? significant figures ? 14

SUPERPOSITION INTERFERENCE 15 CP 523

Problem 2 16 Two small loudspeakers emit pure sinusoidal waves that are in phase. (a) What frequencies does a loud sound occur at a point P? (b) What frequencies will the sound be very soft? (vsound = 344 m. s-1). CP 523

Solution 2 Construction interference 1. 27 k. Hz, 2. 55 k. Hz, 3. 82 k. Hz, … , 19. 1 k. Hz Destructive interference 0. 63 k. Hz, 1. 91 k. Hz, 3. 19 k. Hz, … , 19. 7 k. Hz

Problem 3 Two speakers placed 3. 00 m apart are driven by the same oscillator. A listener is originally at Point O, which is located 8. 00 m from the center of the line connecting the two speakers. The listener then walks to point P, which is a perpendicular distance 0. 350 m from O, before reaching the first minimum in sound intensity. What is the frequency of the oscillator? Take speed of sound in air to be 343 m. s-1.