Optics Answers

Use examples to explain why and how waves are classified.

(a.) A motorcyclist travels at a constant speed of 72 km/h along a straight level road towards an

observer standing at the center of the bridge over the road. When the motor-cyclist is distant, the

observer hears a sound of frequency 65,0 //z from the engine of the motorcycle. 

(b.) A second motor-cyclist now rides along-side the one mentioned in (b), at the same constant

speed of 72 km/h. The frequency of the sound of the second motorcycle is lower than that of the

first motorcycle. When the two machines are traveling towards the observer, from the same

direction, the intensity of the sound received varies with a frequency of 3.0 Hz.

Name the effect causing the variation of sound intensity and explain how it arises in this case. What

would be the frequency of the variation of sound intensity after the motor-cycles have passed under

the bridge and are moving away from the observer?

A motor-cyclist travels at a constant speed of 72 kmh^-1 along a straight tevel road towards an

observer standing at the center of the bridge over the road. When the motor- cyclist is distant, the

observer hears a sound of frequency 65,0 Hz from the engine of the motor-cycle. What would be

the frequency of the sound heard by the observer after the motor cycle has passed under the bridge

and is along way from the observer?

Describe a simple laboratory demonstration of the Doppler Effect for sound waves.

 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.