Optics Answers

 Many bats use the Doppler Effect for detecting obstacles and prey. One species sends out high

 frequency sound waves and locates the objects in front of it from an analysis of the reflected waves. If the bat flies at a steady speed of 4ms^-1, and emits waves of frequency 90.0 kHz, what is the frequency of the wave detected by the bat after reflection from a stationary obstacle directly ahead of the bat? Derive any equation for the Doppler Effect used in the calculation.

 State what could be deduced about the obstacle if a bat detected a reflected wave of frequency less than that emitted.

Describe a simple laboratory demonstrating the Doppler effect of sound waves.

A car sounding an alarm at a frequency of 512Hz is approaching a listener at a speed of 8ms-1, The

         reflected sound from the listener awakes a passenger of the car who was sleeping.

         (a.) Determine the apparent frequency of the horn as perceived by the listener and that of the

         reflected sound as perceived by the awakened passenger under the following cases:

         (i.) the listener is stationary, (ii.) the listener is approaching the car at 2ms-1, (iii.) the listener is

         moving away from the approaching car at 3ms-1.

         (b.) Explain why in all the above cases, the listener has the impression that the frequency of the

         sound heard is varying. 

 An engine travelling at a constant speed towards a tunnel emits a short burst of sound of

frequency 400Hz which is reflected from the tunnel entrance. The engine driver hears an echo of

 frequency 500 Hz two seconds after the sound is emitted. Assuming the speed of sound is

         340ms^-1, calculate the speed of the engine, and its distance from the tunnel when the driver hears

the echo.

         (a.) A source which is emitting sound waves of frequency fo is travelling at a speed u towards an

         observer who is traveHing with a speed v in the same direction. Derive an expression for the

 frequency f heard by the observer.

 A police radar set emits a parallel beam of electromagnetic radiation at wavelength λo and velocity c, which falls on a motor car moving directly towards the set with a velocity u.λo from the car, to reach the car.

 (a Derive an expression for the wavelength λ of the radiation reflected from the car

(b) If Zo = 0 im, c = 3.0 × 108ms'1 and u = 33ms'1, calculate the change in wavelength of tho

    radiation received at the set after reflection from the car. 

 What is Doppler Effect?

       A police radar set emits a parallel beam of electromagnetic radiation at wavelength λo and velocity c, Which falls on a motor car moving directly towards the set with a velocity u.

       (a.) Derive an expression for the time it takes for the wave front of the radiation initially a distance

       λo from the car, to reach the car.

 An observer travelling with a constant velocity of 20ms^-1, passes close to a stationary source of sound and notices that there is a change of frequency of 50 Hz as he passes the source. What is the frequency of the source? 

  (a.) Describe one method by which the speed of light can be measured, explaining how the result is calculated from the observations. Describe one practical situation in which a knowledge of the speed of light, or other electromagnetic radiation is needed.

A car travelling at 10ms^-1 sounds its horn, which has a frequency of 500 Hz, and this is heard in

      another car which is travelling behind the first car, in the opposite direction, with a velocity of

      20ms^-1. The sound can also be heard in the second car by reflection from a bridge ahead, in the

      direction of the first car. What frequencies will the driver in the second car hear?