DHS 13 Wave Motion (Tutorial Solutions)

Topic 11 : Wave Motion Tutorial Solutions (2025) 1. (i) Displacement: The distance in a specific direction from the equilibrium position of the simple harmonic motion. (ii) Amplitude: Maximum displacement from the equilibrium point in either direction. (iii) Wavelength: The shortest distance between two points on a progressive w a v e which are vibrating in phase. (iv) Frequency: Number of oscillations per unit time of a particle in a wave. (v) Period: Time taken for a particle in the wave to undergo one complete oscillation. (vi) Phase difference: A measure of how much one wave is out of step with another. It is measured in either degrees or radians. (b) One wavelength  is equal to the distance travelled by the wave energy during one complete oscillation of the source. The distance travelled by the wave energy during n complete oscillation of the source = n Speed is the distance travelled pe r unit time by the wave energy i . e . v = t n Frequency is numbe r of oscillations per unit time i.e. f = t n Therefore speed v = f (c) Progressive wave: A progressive wave transfers energy from one point to another by means of oscillations. Intensity of a wave: Wave energy incident per unit time per unit area normal to the direction of energy transfer.

(d) Transverse wave: Waves in which the oscillation of the particles in the wave is perpendicular to the direction of transfer of energy of the wave. Longitudinal wave: Oscillations of the particles in the wave are along the direction of transfer of energy of the wave. 2. (a)  = T 1 = 100 Hz, T = 0.01 s (b)  = T 1 = 200 Hz, T = 0.005 s 0.005 0.0075 0.01 0.01 y/m Time / s 0 0.0025 - 0.01 0.005 (a) (b) - 0.005

(c) For wave 1, v = f λ λ = 330/100 = 3.3 m For wave 2, v = f λ λ = 330/200 = 1.65 m (d) Sound wave. Horizontal displacement-distance graph. 3. v = f λ  vf  Minimum f = Hz14 9 8 103.410700 100.3    (red) Maximum f = Hz14 9 8 105.710400 100.3    (violet) 4. Answer: 50 mm outwards Diameter of bowl = 400 mm Radius of bowl = 200 mm Since the wave travel 250 mm in 1 second, it will travel 200 mm inward, then the remaining 50 mm outwards. 5. P gives the period T of the motion and Q the wavelength λ. v = f λ => P Q Tv   1.65 2.475 3.30 0.01 y/m Distance/ m 0 0.825 - 0.01 0.005 (a) (b) -0.005

6. Draw a graph moments after. 7. (a) False. Speed at P is a minimum (zero) (b) False. This graph is not that of a stationary wave. It will follow an oscillatory motion. (c) False. Energy of R is entirely potential energy. (d) False. Energy of S is entirely kinetic energy. 8. (a) Ans: C I 2 1 r By similar triangle, r is 8 times, I will be 64 1 I 2A Since I is 64 1 , then A is 8 1 (b) Ans: D I rh P A P