Quiz , Waves

QUIZ TEST – I

Question:1. The amplitude of resulting wave dues to superposition of y1 = A sin (ωt − kx) &  y2 = A sin (ωt − kx + δ) is

(A) 2A cos δ

(B) 2A tan (δ/2)

(C) A cos δ sin δ

(D) none

Click to See Answer :
Ans: (D)

 

Question: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.

Click to See Answer :
Ans: (A)

 

Question: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 + x2) . 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}))} $

Click to See Answer :
Ans: (B)

 

Question: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

Click to See Answer :
Ans: (D)

 

Question: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

Click to See Answer :
Ans: (B)

 

Question: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.

Click to See Answer :
Ans: (B)

 

Question: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

Click to See Answer :
Ans: (d)

 

Question:8. Under the same conditions of pressure and temperature, the velocity of sound in oxygen and hydrogen gases are vo and vH , then

(A) vH = vo

(B) vH = 4vo

(C) vo = 4 VH

(D) vH = 16 vo

Click to See Answer :
Ans: (B)

 

Question: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

Click to See Answer :
Ans: (A)

 

Question: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.

Click to See Answer :
Ans: (B)

 

Question: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.

Click to See Answer :
Ans: (A)

 

Question: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

Click to See Answer :
Ans: (A)

 

Question: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

Click to See Answer :
Ans: (A)

 

Question:14. Standing waves can be produced in

(A) solid only

(B) liquid only

(C) gases only

(D) all of the above

Click to See Answer :
Ans: (D)

 

Question: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 %

Click to See Answer :
Ans: (C)

 

Question: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)

Click to See Answer :
Ans: (C)

 

Question: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

Click to See Answer :
Ans: (B)

 

Question: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.

Click to See Answer :
Ans: (B)

 

Question: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.

Click to See Answer :
Ans: (B)

 

Question: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} $

Click to See Answer :
Ans: (A)

 

Click to See All Answers :
1.(D)   2. (A)  3. (B)  4. (D)  5. (B)  6. (B)  7. (D)  8. (B)  9. (A)  10.(B) 

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

 

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