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Question 3 (5 Marks) Noise cancelling headphones work by sampling the external noise outside the headphones and adding this to the noise entering a person's ear canal in an attempt to ‘cancel out the external noise. Consider the plot below showing two sound waves, Wave 1 and Wave 2, with different amplitudes meeting at the same point in space inside a person's ear canal. Wave 1 Yi -Y 0 Displacement, y Wave 2 Y2 Time, t a) Are the waves out of phase, or in phase? [1] b) Write equations for the displacement y of Wave 1 and Wave 2 in terms of time t. State the meaning of any other constants used in your equations. [1] c) If the waves are added together, describe in words what will happen. Write an equation for the resulting wave. [1] d) If we wanted the smallest possible amplitude for the resulting wave, describe in words what we would have to change about Wave 2. [1] e) Even if Wave 1 and Wave 2 are perfectly configured, complete cancellation is not possible to achieve in a human's ear canal. Suggest a physical or technical reason why might this be the case. [1]