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Exercise:
Two loudspeakers are placed at a mutual distance of dO. They are connected to a signal generator providing a sinusoidal fO signal. abcliste abc Where are the erference maxima and minima on the line between the loudspeakers? abc What is the condition for the erference maxima on the line perpicular to the line connecting the loudspeakers and going through a po at a distance x_ from the first loudspeaker? abcliste

Solution:
abcliste abc At a distance x from the centre along the line connecting the loudspeakers the distances to the two loudspeakers are r_d/-x and r_d/+x. The path difference is therefore Delta r r_-r_ x The maxima are given by Delta r x m lambdaquadtextrmwith m in Z The positions relative to the centre of the maxima are therefore x fracmlambdaxF mtimesfracvstimesf mtimesx mtimesxP- Between the loudspeakers there are maxima for m-dots+ so a total of maxima. The erference minima are exactly between two maxima so there is a total of minima. abc The distances to a po at a distance y from the line connecting the two loudspeakers are r_ sqrtx_^+y^ r_ sqrtd-x_^+y^ Where d is the distance between the loudspeakers. The maxima are defined by Delta r r_-r_ sqrtd-x_^+y^-sqrtx_^+y^ m lambda quad textrmwith lambdainZ abcliste
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Exercise:
Two loudspeakers are placed at a mutual distance of dO. They are connected to a signal generator providing a sinusoidal fO signal. abcliste abc Where are the erference maxima and minima on the line between the loudspeakers? abc What is the condition for the erference maxima on the line perpicular to the line connecting the loudspeakers and going through a po at a distance x_ from the first loudspeaker? abcliste

Solution:
abcliste abc At a distance x from the centre along the line connecting the loudspeakers the distances to the two loudspeakers are r_d/-x and r_d/+x. The path difference is therefore Delta r r_-r_ x The maxima are given by Delta r x m lambdaquadtextrmwith m in Z The positions relative to the centre of the maxima are therefore x fracmlambdaxF mtimesfracvstimesf mtimesx mtimesxP- Between the loudspeakers there are maxima for m-dots+ so a total of maxima. The erference minima are exactly between two maxima so there is a total of minima. abc The distances to a po at a distance y from the line connecting the two loudspeakers are r_ sqrtx_^+y^ r_ sqrtd-x_^+y^ Where d is the distance between the loudspeakers. The maxima are defined by Delta r r_-r_ sqrtd-x_^+y^-sqrtx_^+y^ m lambda quad textrmwith lambdainZ abcliste
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Attributes & Decorations
Branches
Interference
Tags
acoustic, soundwave, superposition
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Decoration
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