When two sources located at different positions produce the same pure tone, the human ear will often hear one sound that is equal to the sum of the individual tones. Since the sources are at different locations, they will have different phase angles p. If two speakers located at different positions produce pure tones P, = A, sin (2xft + b1 ) and P, = A2 sin (2xft + 2), where -s.2 s, then the resulting tone heard by a listener can be written as P = A sin (2xft + 4»), where A, sin p, + Az sin z = arctan A, cos 4, + Az cos Þ2 and A = (A, cos 41 + Az cos 2) ² + (A, sin 4, + A2 sin 2) ² . Complete parts a and b. a) Calculate A and if A, = 0.0009, Þ1 = 0.057, A2=0.004, and Þ2 = 0.68. Also find an expression for P = A sin (2xft + 4) if f = 220. Do not round until the final answer. Then round to five decimal places as needed.) (Do not round until the final answer. Then round to five decimal places as needed.) Find an expression for P = A sin (2xft + 4p) if f= 220. (Use integers or decimals for any numbers in the expression. Round to five decimal places as needed.) (b) Graph Y, = P and Y2 = P, +P2 on the same coordinate axes over the interval [0,.01]. Are the two graphs the same?
When two sources located at different positions produce the same pure tone, the human ear will often hear one sound that is equal to the sum of the individual tones. Since the sources are at different locations, they will have different phase angles p. If two speakers located at different positions produce pure tones P, = A, sin (2xft + b1 ) and P, = A2 sin (2xft + 2), where -s.2 s, then the resulting tone heard by a listener can be written as P = A sin (2xft + 4»), where A, sin p, + Az sin z = arctan A, cos 4, + Az cos Þ2 and A = (A, cos 41 + Az cos 2) ² + (A, sin 4, + A2 sin 2) ² . Complete parts a and b. a) Calculate A and if A, = 0.0009, Þ1 = 0.057, A2=0.004, and Þ2 = 0.68. Also find an expression for P = A sin (2xft + 4) if f = 220. Do not round until the final answer. Then round to five decimal places as needed.) (Do not round until the final answer. Then round to five decimal places as needed.) Find an expression for P = A sin (2xft + 4p) if f= 220. (Use integers or decimals for any numbers in the expression. Round to five decimal places as needed.) (b) Graph Y, = P and Y2 = P, +P2 on the same coordinate axes over the interval [0,.01]. Are the two graphs the same?
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Categories of Sound Wave
People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.
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![When two sources located at different positions produce the same pure tone, the human ear will often hear one sound that is equal to the sum of the individual tones.
Since the sources are at different locations, they will have different phase angles p. If two speakers located at different positions produce pure tones
元
P, =A, sin (2uft + 1) and P, = A2 sin (2nft + dp2) , where - s41,.427, then the resulting tone heard by a listener can be written as P = A sin (2nft + 4), where
A, sin 4, + A, sin p2
4 = arctan
(A, cos 4, + A, cos
42)² + (A, sin d, + A2 sin 2) 2 . Complete parts a and b.
and A =
1
A, cos , + A2 cos 42
(a) Calculate A and p if A, = 0.0009, , =0.057, A2=0.004, and p2 = 0.68. Also find an expression for P = A sin (2xft + 4p) if f= 220.
A =
(Do not round until the final answer. Then round to five decimal places as needed.)
(Do not round until the final answer. Then round to five decimal places as needed.)
Find an expression for P = A sin (2xft + 4) if f= 220.
P=
(Use integers or decimals for any numbers in the expression. Round to five decimal places as needed.)
(b) Graph Y, = P and Y2 = P, +P2 on the same coordinate axes over the interval [0,.01]. Are the two graphs the same?
Choose the correct graph below. All graphs are [0,.01] by [-.01,.01].
O A.
OB.
OC.
OD.
Q
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Transcribed Image Text:When two sources located at different positions produce the same pure tone, the human ear will often hear one sound that is equal to the sum of the individual tones.
Since the sources are at different locations, they will have different phase angles p. If two speakers located at different positions produce pure tones
元
P, =A, sin (2uft + 1) and P, = A2 sin (2nft + dp2) , where - s41,.427, then the resulting tone heard by a listener can be written as P = A sin (2nft + 4), where
A, sin 4, + A, sin p2
4 = arctan
(A, cos 4, + A, cos
42)² + (A, sin d, + A2 sin 2) 2 . Complete parts a and b.
and A =
1
A, cos , + A2 cos 42
(a) Calculate A and p if A, = 0.0009, , =0.057, A2=0.004, and p2 = 0.68. Also find an expression for P = A sin (2xft + 4p) if f= 220.
A =
(Do not round until the final answer. Then round to five decimal places as needed.)
(Do not round until the final answer. Then round to five decimal places as needed.)
Find an expression for P = A sin (2xft + 4) if f= 220.
P=
(Use integers or decimals for any numbers in the expression. Round to five decimal places as needed.)
(b) Graph Y, = P and Y2 = P, +P2 on the same coordinate axes over the interval [0,.01]. Are the two graphs the same?
Choose the correct graph below. All graphs are [0,.01] by [-.01,.01].
O A.
OB.
OC.
OD.
Q
Q
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