Download Problems Group A

Dipl.Phys. Alexandra Perschke
alexandra.perschke@uni-due.de
http://www.uni-due.de/ofm/physics09
ISE Physics
Problems 3rd exercises Group A (10th may)
Problem 1 (sinusoidal waves)
A sinusoidal wave with an amplitude of 1 cm and a frequency of 80 Hz travels at 160m/s in the
positive x-direction. At t=0 s, the point x=1m is on the crest of the wave.
a) Determine A, v, λ , k, f, ω , T, and φ 0 for this wave.
b) Write down the equation for the wave’s displacement as it travels.
c) Draw a snapshot graph of the wave at t=0 s
Problem 2 (phase difference)
A 110 Hz sound wave travels with a wave speed of 340 m/s.
• What is the phase difference between two points 80 cm apart along the direction the wave is
travelling?
• How far apart are two points whose phase differs by 90°?
Problem 3 (standing waves)
Cold spots in a microwave oven are found to be 6 cm apart. What is the frequency of the microwaves?
A standing wave is created by microwaves reflecting from walls. v=c.
Problem 4 (standing waves)
Helium-neon lasers emit the red laser light commonly used in classroom demonstrations and
supermarket checkout scanners. A helium neon laser operates precisely at a wavelength of
632,9924nm when the spacing between the mirrors is 310.372mm.
• In which mode does the laser operate?
• What is the next longest wavelength that could form a standing wave in this cavity?
Problem 5 (Doppler Effect)
A bat locates insects by emitting ultrasonic chirps and then listening for echoes from the bugs.
Suppose a bat chirp has a frequency of 25 kHz. How fast would the bat have to fly and in what
direction for you to just barely be able to hear the chirp at 20 kHz?
Problem 6 (Doppler Effect)
A police siren has a frequency of 500 Hz as the police car approaches you, 420 Hz after it has passed
you and is receding. How fast are the police travelling? The speed of sound is 340m/s.
What frequency does the siren has when the car is at rest? (stationary source and stationary observer)
Problem 7: Snell’s law
A laser beam is aimed at a 1 cm thick glass plate at an incident angle of 60°. The index of refraction of
air is 1, the index of glass 1,5.
• Draw the ray diagram.
•
•
What are the angles of the laser beam inside and outside the glass plate?
By what distance is the beam displaced?
Problem 8: Snell’s law
A fish and a sailor look at each other through a 5cm thick glass porthole in a submarine. There
happens to be a small air bubble right in the center of the glass. How far behind the surface of the glass
does the air bubble appear the fish? And to the sailor? The index of refraction of air is 1, the index of
glass 1,55 and the index of water 1,33. Represent the air bubble as a point source.
Problem 9: Total internal reflection
A light bulb is set in the bottom of a 3m deep swimming pool. What is the diameter of the circle of
light seen on the water’s surface from above? Represent the bulb as a point source. The index of
refraction of water is 1,33.
Problem 10: Thin lenses
A 4 cm diameter flower is 2 m from the 50-cm focal length of a camera. How far should the film be
placed behind the lens to record a well focused image? What is the diameter of the image?
Problem 11: Thin lenses
A 2 cm tall object is 15 cm in front of a converging lens that has a 20 cm focal lens. Do the ray tracing
and calculate the image position and height.
Problem 12: Thin lenses
A 2 cm tall object is 15 cm in front of a diverging lens that has a -20 cm focal lens. Do the ray tracing
and calculate the image position and height.
Problem 13: Optical instruments - the telescope
A simple telescope consists of an objective with the focal length f1 = 100 cm and an eyepiece with f2 =
5 cm. You try to observe the moon, which naturally appears under an angle of
θ0 = 0,009 rad.
• What is the diameter of the image generated by the objective?
• Under which angle θe does the final image appear infinitively far away?
• Determine the magnifying power of the telescope.
Astronomical telescope [P.A.Tipler – physics, 4. ed. (1999)].