LEVEL – I

1. The amplitude of resulting wave dues to superposition of y_{1} = A sin (ωt − kx) &

y_{2} = A sin (ωt − kx + δ) is

(A) 2A cos δ

(B) 2A tan (δ/2)

(C) A cos δ sin δ

(D) none

2. A sine wave has an amplitude A and wavelength λ . The ratio of particle velocity and the wave velocity is equal to ( 2πA = λ )

(A) ≤ 1

(B) = 1

(C) ≥ 1

(D) data insufficient.

3. The equation of a wave pulse moving with a speed 1 m/sec at time t = 0 is given as

y = f(x) = 1/(1 + x^{2}) . Its equation at time t = 1 second can be given as

(A) $ \displaystyle y = \frac{1}{1+(1+x)^2} $

(B) $ \displaystyle y = \frac{1}{1+(1-x)^2} $

(C) $ \displaystyle y = \frac{1}{1+(1+x^2)} $

(D) $ \displaystyle y = \frac{1}{1+ (\frac{1}{1+x^2}))} $

4. The velocity of a transverse wave in a string does not depend on

(A) tension

(B) density of material of string

(C) radius of string

(D) length of string

5. The frequency of a tuning fork with an amplitude A = 1 cm is 250 Hz. The maximum velocity of any particle in air is equal to

(A) 2.5 m/s

(B) 5 π m/s

(C) 3.30 /π m/sec

(D) none of these

6. In a resonance column experiment, the first resonance is obtained when the level of the water in tube is 20 cm from the open end. Resonance will also be obtained when the water level is at a distance of

(A) 40 cm from the open end.

(B) 60 cm from the open end.

(C) 80 cm from the open end.

(D) data insufficient.

7. A wire of length l having tension T and radius r vibrates with natural frequency f. Another wire of same metal with length 2l having tension 2T and radius 2r will vibrate with natural frequency

(A) f

(B) 2f

(C) 2√2 f

(D) f /2√2

8. Under the same conditions of pressure and temperature, the velocity of sound in oxygen and hydrogen gases are v_{o} and v_{H} , then

(A) v_{H} = v_{o}

(B) v_{H} = 4v_{o}

(C) v_{o} = 4 V_{H}

(D) v_{H} = 16 v_{o}

9. A tuning for of frequency 600 Hz produces a progressive travelling wave having wave velocity 300 m/s. Two particles of a medium, separated by 1.5 m, vibrate being affected by the wave (A) in phase

(B) in opposite phase.

(C) 45° out of phase.

(D) none of these

10. At t = 0 source starts falling under gravity and a detector is projected upwards with a velocity 10 m/s. For the vertical upward motion of detector

(A) apparent frequency received by detector = source frequency.

(B) initially apparent frequency > source frequency and finally less than source frequency.

(C) apparent frequency depends only on the detector velocity.

(D) date insufficient.

__Answers:__

1.(D) 2. (A) 3. (B) 4. (D) 5. (B) 6. (B) 7. (D) 8. (B) 9. (A) 10.(B)

LEVEL – I

11. A string is clamped on both ends. Which of the following wave equations is valid for a stationary wave set up on this string ? (Origin is at one end of string.)

(A) y = A sin kx. sin ωt

(B) y = A cos kx sin ωt

(C) y = A cos kx. cos ωt

(D) None of the above.

12. A string is hanging from a rigid support. A transverse wave pulse is set up at the bottom. The velocity v of the pulse related to the distance covered by it is given as

(A) v ∝ √x

(B) v ∝ x

(C) v ∝ 1/x

(D) none of these

13. The third overtone of a closed organ pipe is equal to the second harmonic of an open organ pipe. Then the ratio of their lengths is equal to

(A) 7/4

(B) 3/5

(C) 3/2

(D) none of these

14. Standing waves can be produced in

(A) solid only

(B) liquid only

(C) gases only

(D) all of the above

15. If the temperature of the medium drops by 1 %, the velocity of sound in that medium

(A) increases by 5 %

(B) remains unchanged

(C) decreases by 0.5 %

(D) decreases by 2 %

16. The velocity of sound through a diatomic gaseous medium of molecular weight M at 0°C is approximately.

(A) √(R / M)

(B) √(3R / M)

(C) √(382R / M)

(D) √(273R / M)

17. The amplitude of a wave disturbance propagating in the positive x direction is given by $ \displaystyle y = \frac{1}{(1+x^2)} $ at time t = 0 and by $ \displaystyle y = \frac{1}{(1+(x-2)^2)} $ at time t = 2 seconds where x and y are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is

(A) 0.5 m/s

(B) 1 m/sec

(C) 2 m/s

(D) 1.5 m/sec

18. A wave is represented by the equation y = [A sin {10πx + 15π t + (π/3)}] where x is in meters and t is in seconds. The expression represents

(A) A wave travelling in positive x-direction with a velocity 1.5 m/s.

(B) A wave travelling in negative x-direction with a velocity 1.5 m/s.

(C) A wave travelling in the negative x-direction having a wavelength 2 m.

(D) A wave travelling in positive x-direction having a wavelength 2 m.

19. A transverse wave is given by A sin(ωt − αx) where ω and α are constants. The ratio of wave velocity to maximum particle velocity is

(A) αA

(B) 1/αA

(C) 1

(D) none of the above.

20. Two blocks, each of mass m, are connected by a massless thread Y and A represent Young’s modulus and cross sectional area of wire respectively. The strain developed in the thread is

(A) $ \displaystyle y = \frac{mg(1 + sin\theta)}{2 Y A} $

(B) $ \displaystyle y = \frac{m g}{ Y A} $

(C) $ \displaystyle y = \frac{m g sin\theta}{ Y A} $

(D) $ \displaystyle y = \frac{2 m g}{ Y A} $

__Answers:__

11.(A) 12.(A) 13.(A) 14.(D) 15.(C) 16.(C) 17.(B) 18.(B) 19.(B) 20.(A)