Loudspeaker Interference
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
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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
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
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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