Title WAVES.pdf ✅

CHAPTER WAVES 14 Exercise 1: NCERT Based Topic-wise MCQs 14.1 INTRODUCTION 1. When a sound wave goes from one medium to another, the quantity that remains unchanged is (a) frequency NCERT Page-368 / N-279 (c) wavelength (b) amplitude (d) speed 14.2 TRANSVERSE AND LONGITUDINAL WAVES 2. Sound waves transfer NCERT Page-368 / N-280 (a) energy (b) momentum (c) both energy and momentum (d) only energy not momentum 3. For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5m, while the distance between one crest and one trough is 1.5m. The possible wavelengths (in m ) of the waves are : (a) 1,3,5, ... ... NCERT Page-369 / N-280 (b) 1 1 , 1 3 , 1 5 , ... ... (c) 1,2,3, .... (d) 1 2 , 1 4 , 1 6 , ... ... 4. For which of the following do the longitudinal waves exist? NCERT Page-369 / N-280 (a) Vacuum (b) Air (c) Water (d) Both (b) and (c) 5. Sound travels in rocks in the form of NCERT Page-369 / N-280 (a) longitudinal elastic waves only (b) transverse elastic waves only (c) both longitudinal and transverse elastic waves (d) non-elastic waves
14.3 DISPLACEMENT RELATION IN A PROGRESSIVE WAVE 6. A progressive wave travelling along the positive x-direction is represented by y(x,t) = Asin (kx − ωt + φ). Its snapshot at t = 0 is given in the figure. NCERT Page-370 / N-282 For this wave, the phase φ is : (a) − π 2 (b) π (c) 0 (d) π 2 7. The equation y = Asin2 (kx − ωt) represents a wave with (a) amplitude A, frequency ω/2π NCERT Page-371 / N-283 (b) amplitude A/2, frequency ω/π (c) amplitude 2A, frequency ω/4π (d) it does not represent a wave motion 8. The equation of wave is given by Y = 10−2 sin 2π (160t − 0.5x + π 4 ) Where x and Y are in m and t in s. The speed of the wave is NCERT & Page-371 / N-283 (a) 1052kmh −1 (c) 1264kmh −1 (b) 1152kmh −1 (d) 1348kmh −1 9. The equation of plane progressive wave motion is y = asin 2π λ (vt − x). Velocity of the particle is (a) y dv dx NCERT Page-371 / N-283 (b) v dy dx (c) −y dv dx (d) −v dy dx 10. The equation y = asin 2π λ (vt − x) is expression for NCERT Page-371 / N-283 (a) stationary wave of single frequency along x-axis (b) a simple harmonic motion (c) a progressive wave of single frequency along x-axis (d) the resultant of two SHMs of slightly different frequencies 11. A transverse wave is represented by y = Asin (ωt − kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity?
(a) πA 2 (b) πA (c) 2πA (d) A 12. The rate of transfer of energy in a wave depends NCERT Page-370/N-282 (a) directly on the square of the wave amplitude and square of the wave frequency (b) directly on the square of the wave amplitude and root of the wave frequency (c) directly on the wave amplitude and square of the wave frequency (d) None of these 13. For a sinusoidal wave represented by y(x,t) = a sin (kx − ωt + φ), for a given a, the factor determines the displacement of the wave of any position and at any instant is NCERT Page-371 / N-283 (a) constant k (b) angular velocity ω (c) time interval t (d) phase (kx − ωt + φ) 14. When a sound wave of frequency 300Hz passes through a medium, the maximum displacement of a particle of the medium is 0.1cm. The maximum velocity of the particle is equal to NCERT & Page-373 / N-283 (a) 60πcms−1 (b) 30πcms−1 (c) 30cms−1 (d) 60cms−1 15. The displacement y of a particle in a medium can be expressed as, y = 10−6 sin (100t + 20x + π 4 ) m. where t is in second and x in meter. The speed of the wave is NCERT Page-373 / N-283 (a) 20m s (b) 5m s (c) 2000m s (d) 5πm/s 16. Two waves are represented by the equations y1 = asin(ωt + kx + 0.57)m and y2 = acos (ωt + kx)m, where x is in meter and t in sec. The phase difference between them is NCERT Page-371 / N-283 (a) 1.0 radian (b) 1.25 radian (c) 1.57 radian (d) 0.57 radian 17. In the wave equation y = 0.5sin 2π λ (400t − x)m the velocity of the wave will be : (a) 200m/s (b) 200√2m/s (c) 400m/s (d) 400√2m/s 18. The diagram below shows the propagation of a wave. Which points are in same phase? NCERT Page-371 / N-283
(a) F and G (b) C and E (c) B and G (d) B and F 19. A wave travelling in the + ve x-direction having displacement along y-direction as 1m, wavelength 2πm and frequency 1 π Hz is represented by NCERT Page-372 / N-283 (a) y = sin (2πx − 2πt) (c) y = sin (2πx + 2πt) (b) y = sin (10πx − 20πt) (d) y = sin (x − 2t) 20. A progressive sound wave of frequency 500Hz is travelling through air with a speed of 350ms−1 . A compression maximum appears at a place at a given instant. The minimum time interval after which the rarefraction maximum occurs at the same point, is NCERT Page-372 / N-283 (a) 200s (b) 1 250 s (c) 1 500 s (d) 1 1000 s 21. A wave travelling on a string is described by y(x,t) = 0.005sin (80.0x − 3.0t) NCERT Page-372 / N-283 The period of the wave is (a) 3.00s (b) 2.09s (c) 0.48s (d) 0.05s 22. A transverse wave is represented by y = 2sin (ωt − kx)cm. The value of wavelength (in cm ) for which the wave velocity becomes equal to the maximum particle velocity, will be : (a) 4π (b) 2π (c) π (d) 2 23. A sound wave of frequency 245Hz travels with the speed of 300ms−1 along the positive x-axis. Each point of the wave moves to and fro through a total distance of 6cm. What will be the mathematical expression of this travelling wave? NCERT Page-373 / N-284 (a) Y(x,t) = 0.06[sin 0.8x − (0.5 × 103 )t] (b) Y(x,t) = 0.03[sin 5.1x − (1.5 × 103 )t]