sample problems on waves

Sample Problems for WavesDiffraction, Interference, Doppler Effect, Standing Waves, Resolution, and Polarization

Tuesday, July 24, 2012

Sample 1

Waves leaving two sources arrive at point P. Point P is 12 m from the first source and 16.5 m from the second. The waves have a wavelength of 3 m. What is observed at P?


Sample 2

A sound wave of frequency 300 Hz is emitted towards an approaching car. The wave is reflected from the car and is then received back at the emitter at a frequency of 315 Hz. What is the velocity of teh car? (Take the speed of sound to be 340 m s-1.


Sample 3

A train with a 500 Hz siren on is moving at a constant speed of 8.0 m s-1 in a straight line. An observer is in front of the train and off its line of motion. What frequencies does the observer hear?(Take the speed of sound to be 340 m s-1.)


Sample 4

Hydrogen atoms in a distant galaxy emit light of wavelength 658 nm. The light received on earth is measured to have a wavelength of 689 nm. State whether the galaxy is approaching the earth or moving away, and calculate the speed of the galaxy.


Sample 5

A standing wave is set up on a string kept under tension T. What must be done to the tension in order to double the fundamental frequency of the wave?


Sample 6

What is the ratio of the frequencies of the fundamental to the second harmonic for a standing wave set up on a string, both ends of which are kept fixed?


Sample 7

A tube has one end open and the other closed. What is the ratio of the wavelengths of the fundamental to the second harmonic?


Sample 8

A standing wave is set up in a tube with both ends open. The frequency of the fundamental is 300 Hz. What is the length of the tube?(Take the speed of sound to be 340 m s-1.


Sample 9

A single slit of width 1.50 µm is illuminated with light of wavelength 500.0 nm. Find the angular width of the central maximum.


Sample 10The intensity pattern for single-slit diffraction is shown in the Figure. (The vertical units are arbitrary.) (a) Find the width of the slit in terms of the wavelength used.(b) On a copy of teh diagram, draw the intensity pattern for two such slits placed parallel to each other and separated by a distance equal to 10 wavelengths. How many interference maxima fall within the central diffracton maximum?


Sample 11

The camera of a spy satellite orbiting at 200 km has a diameter of 35 cm. What is the smallest distance this camera can resolve on the surface of the earth? (Assume a wavelength of 500 nm.)


Sample 12

The headlights of a car are 2 m apart. The pupil of the human eye has a diameter of about 2 mm. Suppose that light of wavelength 500 nm is being used. What is the maximum distance at which the two headlights ae seen as distinct?


Sample 13

The pupil of the human eye has a diameter of about 2 mm and the distance between the pupil and the back of the eye (the retina) where the image is formed is about 20 mm. Suppose the eye uses light of wavelength 500 nm. Use this information to estimate the distance between the receptors in the eye.


Sample 14

Could a telescope with an objective lens of diameter 20 cm resolve two objects a distance of 10 km away separated by 1 cm? (Assume we are using a wavelength of 600 nm.)


Sample 15

The Jodrell Bank radio telescope has a diameter of 76 m. Assume that it receives electromagnetic waves of wavelength 21 cm.(a) Calculate the smallest angular separation that can be resolved by this telescope.(b) Determine whether this telescope can resolve the two stars of a binary star system that are separated by a distance of 3.6 x 1011 m and are 8.8 x 1016 m from the earth. (Assume a wavelength of 21 cm.)


Sample 16

A spacecraft is returning to earth after a long mission far from earth. At what distance from earth will an astronaut in the spacecraft first see the earth on the moon as distinct objects with a naked eye? Take the separation of the earth and the moon to be 3.8 x 108 m, and assume a pupil diameter of 4.5 mm and light of wavelength 5.5 x 10-7 m.


Sample 17

Vertically polarized light of intensity Io is incident on a polarizer that has its transmission axis at θ = 30° to the vertical. The transmitted light is then incident on a second polarizer whose axis is θ = 60° to the vertical. Calculate the factor by which the transmitted intensity is reduced.


Sample 18

Calculate the Brewster angle for light incident on the surface of water. The refractive index of water is 1.33.


Sample 19

Unpolarized light of intensity Io is incident on a polarizer. The transmitted light is incident on a second polarizer whose transmission axis is at 60° to that of the first. Calculate, in terms of Io, the intensity of light transmitted through the second polarizer.


Sample 20

Unpolarized light is incident on two polarizers whose transmission axes are parallel to each other. Calculate the angle by which one of them must be rotated so that the transmitted intensity is half of the intensity incident on the second polarizer.
