CBSE Class 11 Physics Wave Motion Assignment

Comprehension-1

Doppler’s effect is of great importance in determining the velocity of approach or recession of heavenly bodies towards or away from the earth. When the light coming from a distant star is examined by a spectroscope, the spectrum consists of well defined lines. By Doppler’s effect we know that when a source of light moves towards the observer, the frequency of light increases (i.e., the wavelength decreases) and vice versa. When the star approaches the earth, the lines are shifted towards the shorter wavelength i.e., towards the blue end of the spectrum. On the other hand, when the star moves away from the earth, the lines are shifted towards the red end. By measuring the shift, the velocity of the star can be calculated. Let a star be moving with a velocity v with respect to the earth. Now by Doppler’s principle, the altered frequency n′ is given by n′ = cn/ c + v where c is the velocity of light and n is the true frequency of the light waves. If λ′ and λ are the altered and true wavelengths respectively, then the change in wavelength dλ = λ v/ c.

Thus knowing the change in wavelength, v can be calculated.

1. A radar operates at wavelength 50 cm. If the beat frequency between transmitted signal and signal reflected from an aircraft is equal to 1 kHz at the radar location, the velocity of approaching aircraft will be
(a) 900 m/sec (b) 450 m/sec (c) 1000 m/sec (d) 500 m/sec

2. A radio wave of frequency 840 MHz is sent towards an aeroplane. The frequency of the radio echo has a frequency 2.8 kHz more than the original frequency. The velocity of the aeroplane is
(a) 3 km s^–1 (b) 2 km s^–1 (c) 4 km s^–1 (d) 0.1 km s^–1

3. A star is moving away from the Earth with a velocity of 105 ms^–1. The shift in the spectral line of wavelength 5700 Å as observed on Earth is
(a) 0.53 Å (b) 1.06 Å (c) 1.90 Å (d) 3.08 Å

4. Radio waves are sent towards aeroplane flying high. Change in frequency will be
(a) higher when plane is moving away with speed v compare to change in frequency when plane is moving towards earth with same speed
(b) higher when plane is moving towards earth with speed v compare to change in frequency when plane is moving away with same speed.
(c) change in frequency is independent of whether plane moving towards or away.
(d) none of these

Comprehension-2
Any function y = f (ax ± bt) defines wave provided function is bounded. wave velocity = b/a frequency is b/2π Amplitude is defined as maximum displacement of particle

5. The equation of transverse wave in a string is y = 8 sin [1.256 x – 25.12 t] cm, x is in cm. What is the amplitude of the wave?
(a) 8 cm (b) 1.256 cm (c) 25.12 cm (d) 0.0208 m

6. The frequency of the wave is
(a) 1 Hz (b) 2 Hz (c) 3 Hz (d) 4 Hz

7. λ is
(a) 2 cm (b) 3 cm (c) 4 cm (d) 5 cm

8. The speed of the wave is
(a) 5 cm s^–1 (b) 4 cm s^–1 (c) 20 cm s^–1 (d) 332 m s^–1

Each of the questions given below consists of two statements, an assertion (A) and reason (R).
Select the number corresponding to the appropriate alternative as follows
(a) If both A and R are true and R is the correct explanation of A
(b) If both A and R are true but R is not the correct explanation of A
(c) If A is true but R is false
(d) If A is false but R is true

9. A: There is no effect of change in pressure on velocity of sound in air, provided temperature remains
constant.
R: Because of change in pressure, density of air also changes. Therefore p/ρ becomes constant.
10. A: Sound passes through air in the form of longitudinal waves.
R: Air possesses volume elasticity, which is the requirement for the propagation of longitudinal wave.