Consider two sound waves travelling with the same speed and amplitude but having similar but slightly...

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Consider two sound waves travelling with the same speed and amplitude but having similar but slightly different wavelengths, A₁ and 2, and angular frequencies, w₁ and ₂. The two waves are described with the functions = y₁ (x, t) Y2(x, t) What is the speed u in terms of the angular frequencies and wavelengths? Sketch y₁ + y₂ as a function of r, at some time t. If you stood in the path of these sound waves, what frequency would you hear (assuming you can hear it)? What is the distance between points where the sound disappears? [Hint: you can use the formula cos x + cos y = 2 cos + cos"] A cos A cos 2πx = = wit) - w₂t). A₁ 2πx 1₂ [8] Consider two sound waves travelling with the same speed and amplitude but having similar but slightly different wavelengths, A₁ and 2, and angular frequencies, w₁ and ₂. The two waves are described with the functions = y₁ (x, t) Y2(x, t) What is the speed u in terms of the angular frequencies and wavelengths? Sketch y₁ + y₂ as a function of r, at some time t. If you stood in the path of these sound waves, what frequency would you hear (assuming you can hear it)? What is the distance between points where the sound disappears? [Hint: you can use the formula cos x + cos y = 2 cos + cos"] A cos A cos 2πx = = wit) - w₂t). A₁ 2πx 1₂ [8]

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