Vidaara.orgClass 11 · Physics
CodeVID-P11-14-BDE-01
Beats & the Doppler Effect — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
Beats are produced by the superposition of two waves of:
- A.the same frequency
- B.slightly different frequencies
- C.very different frequencies
- D.opposite amplitudes
2.
If two forks of 300 Hz and 305 Hz sound together, the beat frequency is:
- A.5 Hz
- B.305 Hz
- C.300 Hz
- D.2.5 Hz
3.
The apparent change in pitch due to relative motion is called the:
- A.interference effect
- B.Doppler effect
- C.beat effect
- D.resonance effect
4.
When the source and observer move apart, the observed frequency:
- A.increases
- B.decreases
- C.is unchanged
- D.becomes infinite
5.
The Doppler effect for sound is:
- A.symmetric in source and observer speeds
- B.not symmetric in source and observer speeds
- C.independent of the medium
- D.only seen for light
Section B — Short Answer (2 marks)
3 × 2 = 6 marks
6.
Define beats and write the formula for beat frequency.
7.
A 512 Hz fork gives 6 beats per second with another fork. What are the possible frequencies of the second fork?
8.
State two practical applications of the Doppler effect.
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
9.
A train horn of 400 Hz approaches a station at 34 m/s. Find the frequency heard by a stationary observer. ($v=340$ m/s.)
10.
Explain why a musician uses beats to tune an instrument.
Section D — Long Answer (5 marks)
1 × 5 = 5 marks
11.
State the Doppler effect for sound and write the general formula. Discuss the cases of (i) source approaching observer at rest and (ii) observer approaching source at rest, and explain why the effect is not symmetric.
Answer Key
Section A — Multiple Choice Questions
- (B) slightly different frequencies
- (A) 5 Hz
- (B) Doppler effect
- (B) decreases
- (B) not symmetric in source and observer speeds
Section B — Short Answer (2 marks)
- The periodic variation in loudness when two slightly different frequencies are sounded together; beat frequency $=|f_1-f_2|$.
- $512+6=518\ \text{Hz}$ or $512-6=506\ \text{Hz}$.
- Speed-detecting traffic radar guns and medical ultrasound to measure blood flow (also weather radar, sonar).
Section C — Short Answer (3 marks)
- $f'=400\left(\frac{340}{340-34}\right)=400\times\frac{340}{306}\approx444\ \text{Hz}$.
- Beats slow down as the instrument's frequency approaches the reference frequency, and vanish when the two match exactly, giving a precise tuning indicator.
Section D — Long Answer (5 marks)
- Relative motion between source and observer changes the observed frequency: $f'=f\left(\frac{v\pm v_o}{v\mp v_s}\right)$. (i) Source approaching: $f'=f\frac{v}{v-v_s}$ (pitch rises). (ii) Observer approaching: $f'=f\frac{v+v_o}{v}$ (pitch rises). The two give different shifts because sound travels through a medium (air) that provides a preferred reference frame, so source motion (which changes wavelength) is not equivalent to observer motion (which changes the rate of meeting wavefronts).
Generated by Vidaara.org · Assignment VID-P11-14-BDE-01 · vidaara.org