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Learning Objects 7 Beats
- 1. Physics Learning Object L07: Beats! ! Q1. Explain what a beat is.! ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________! ! Q2. As Rachel was walking through a garden, she hears the sounds of a duck and goose at frequencies fduck = 400Hz and fgoose = 420Hz respectively. ! ! (a) At what frequency does she hear them both? ! ! (b) What is the beat frequency?! ! (c) Explain what happens when Rachel hears the sounds of a duck at 400Hz and! ! the bird chirping at 200Hz respectively.! ! ! ! ! ! ______________________________________________________________________! ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________! ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________! ______________________________________________________________________ ______________________________________________________________________ _____________________________________________________________________! ! ! Page of1 2
- 2. SOLUTIONS: Physics Learning Object L07: Beats! ! Q1. Explain what a beat is.! ! A beat is the variance in amplitude where with the sounds of two waves that have slightly different frequencies, we hear the amplitude increasing and decreasing as a function of time. ! ! Q2. As Rachel was walking through a garden, she hears the sounds of a duck and goose at frequencies fduck = 400Hz and fgoose = 420Hz respectively. ! ! (a) At what frequency does she hear them both? ! ! (b) What is the beat frequency?! ! (c) Explain what happens when Rachel hears the sounds of a duck at 400Hz and! ! the bird chirping at 200Hz respectively.! ! (a) Frequency she hears them both: mean angular frequency = (w1+w2)/2! ! = (420Hz + 400Hz)/2 = (820Hz)/2 = 410Hz. ! She hears both of them at the frequency of 410Hz.! ! (b) Beat frequency: angular frequency difference = (w1-w2)/2 = (420Hz-400Hz)/2 ! ! = (20Hz)/2 = 10Hz! The beat frequency is 10Hz. ! ! (c) As there is a large frequency difference, the sounds will be heard as two distinct tones rather than one tone that varies in intensity. Therefore, Rachel will hear the sounds of the duck and the bird as two different tones. ! ! ! ! Page of2 2