Doppler Effect - UNSOLVED PRACTICE SET

Q7. State the Doppler effect. Write the general formula for apparent frequency when both source and observer are moving.

Q8. A police siren emits sound at 500 Hz. A person standing on the road hears 550 Hz as the police car approaches. Is the car moving towards or away from the person? Explain.

Q9. Why is there no Doppler effect when the source and observer move at right angles to each other?

Q10. A source moves towards a stationary observer at speed v_s. Show that the apparent wavelength changes to λ' = λ(v – v_s)/v, where v is the speed of sound.

Q11. Explain why the Doppler effect is said to be asymmetric for sound waves (i.e., it matters whether the source moves or the observer moves).

Q12. A star emits light of a certain wavelength. Astronomers observe that the wavelength is shifted towards the red end of the spectrum. What does this tell us about the motion of the star? Name this phenomenon.

Q13. Derive the expression for apparent frequency in the Doppler effect for sound when:

(i) The source moves towards a stationary observer

(ii) The source moves away from a stationary observer

(iii) The observer moves towards a stationary source

(iv) The observer moves away from a stationary source

For each case, clearly state the assumptions and draw a diagram showing the wavefronts.

Q14. Discuss the Doppler effect in light and compare it with the Doppler effect in sound. Explain:

(i) Why the Doppler effect in light is symmetric (unlike sound)

(ii) Red shift and blue shift in astronomical observations

(iii) How the Doppler effect is used to measure the speed of distant galaxies

(iv) The relativistic Doppler effect and why it differs from the classical case

Q15. A student stands at a railway crossing as a train approaches, passes, and moves away.

(i) Describe how the frequency of the train whistle changes as heard by the student.

(ii) At what instant is the frequency exactly equal to the actual frequency?

(iii) If the student were on the train, would she hear the Doppler effect? Explain.

(iv) How would the observations change if there were a strong wind blowing from the train towards the student?

Q16. A train approaches a stationary observer at 30 m/s while blowing a whistle of frequency 500 Hz. The speed of sound in air is 340 m/s.

(i) Calculate the apparent frequency heard by the observer as the train approaches.

(ii) Calculate the apparent frequency heard after the train passes the observer.

(iii) Calculate the wavelength of sound in front of the train.

(iv) Calculate the wavelength of sound behind the train.

(v) A second observer is in a car moving towards the train at 20 m/s. Calculate the frequency heard by this observer.

Q17. A bat emits ultrasonic waves of frequency 80 kHz while flying towards a wall at 10 m/s. The speed of sound is 340 m/s.

(i) Calculate the frequency of the waves hitting the wall.

(ii) Calculate the frequency of the reflected waves as received by the bat.

(iii) What is the beat frequency between the emitted and received waves?

(iv) Explain how the bat uses this information to judge the distance to the wall.

(v) If the bat were flying away from the wall at the same speed, how would the beat frequency change?

Q18. In a school science exhibition, a student builds a Doppler effect demonstration using a buzzer attached to a rotating arm of length 0.5 m. The buzzer emits sound at 1000 Hz and the arm rotates at 2 revolutions per second. An observer stands far away from the setup.

(i) Calculate the speed of the buzzer.

(ii) Calculate the maximum apparent frequency heard by the observer.

(iii) Calculate the minimum apparent frequency heard by the observer.

(iv) Calculate the difference between maximum and minimum frequencies.

(v) The student replaces the buzzer with a light source. Explain whether the same frequency variation would be observed for light, and discuss any differences from the sound case.