Question

t = 0 ms (a) (4 marks) A sinusoidal wave moving along a string is shown twice in the figure at time t = 0 (top) and time t = 4t (bottom). After At = 4.0 ms, the crest travels d=6.0 cm in the positive x direction. The equation for the wave is in the form 8 mm H HHHx y(x, t) =Ym sin(kx = wt). t = 4 ms What are (i) ym, (ii)k, (iii) w, and (iv) the correct choice of sign in front of w? HHHHX (b) (6 marks) Two equations describe transverse waves traveling along the same string: Wave 1: Wave 2: yi(x, t) = (4.60 mm) sin(k) x-wit), y2(x, t) = (5.60 mm) sin(k2 x - W2t +), Where k, = k2 = 21, w, = W2 = 4007 and 6 = 0.707 rad. Draw a phasor diagram to calculate (i) the amplitude and (ii) the phase angle of the resultant wave relative to Wave 1. (c) (4 marks) The sound level of an angry conversation is 70 dB. If the frequency of the sound is 500 Hz, determine: (i) sound intensity, (ii) wave amplitude. Assume the speed of sound in air is y = 343 m s' and the air density is p= 1.21 kg mº. (d) (6 marks) A cyclist is pedalling along a straight road at a steady speed of 9.0 ms'. (i) Behind the cyclist is a building with an alarm emitting sound waves at a frequency of 550 Hz. What frequency does the cyclist hear? (ii) Ahead of the cyclist, travelling in the same direction but at a steady speed of 33.0 m s', is a truck emitting sound at a frequency of 310 Hz. What frequency does the cyclist hear? Assume the speed of sound in air is v = 343 ms.

Answer 1

27 400) = 15.7 "ad 1) The amplitude is giving by the maximum distance form the equilibrium point, in this case: Ym = 8.0 mm From the first graph, the wavelength is: 1 = 40 cm = 0.400 m The wave number is: k = ER (0.400) 13. m The sped of the wave is: w d 0.06 m VEK At4.0 10-35 Then: rad w = 235.5 Since, the wave is moving to the positive x direction, the sign must be negative: The equation is: y(x,t) = (8.0 mm) sin(15.7x – 235.5t)