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Two point sound source A and B each of power 25πW and frequency 850 Hz are1m apart .the source are in phase a) Determine the phase difference between the waves emitting from A and B received by detector D such that BAD are in triangle angle A 90degree AD=2.4m and BA =1m?
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Two point sound source A and B each of power 25πW and frequency 850 Hz...
Identifying the Geometry of the Problem
To analyze the phase difference between the waves from sources A and B at detector D, we first determine the geometry involved. The triangle BAD is formed with:
- BAD = 90 degrees
- Lengths: AD = 2.4 m, BA = 1 m
This implies we can find the length of BD using the Pythagorean theorem, which states that in a right triangle:
- c^2 = a^2 + b^2
Where:
- c is the hypotenuse (BD)
- a is one leg (BA = 1 m)
- b is the other leg (AD = 2.4 m)
Calculating:
- BD = √(AD² + BA²) = √(2.4² + 1²) = √(5.76 + 1) = √6.76 ≈ 2.6 m
Calculating the Path Difference
The path difference (Δ) between the waves arriving at point D from sources A and B is given by the difference in distances:
- Path difference Δ = BD - AD = 2.6 m - 2.4 m = 0.2 m
Determining the Wavelength
The wavelength (λ) can be calculated using the formula:
- λ = v / f
Assuming the speed of sound in air (v) is approximately 343 m/s at room temperature:
- λ = 343 m/s / 850 Hz ≈ 0.404 m
Calculating the Phase Difference
The phase difference (Δϕ) can be calculated using the formula:
- Δϕ = (2π / λ) * Δ
Substituting the values:
- Δϕ = (2π / 0.404 m) * 0.2 m = (6.22) * 0.2 ≈ 1.244 radians
Conclusion
The phase difference between the waves emitted from sources A and B at detector D is approximately 1.244 radians. This indicates constructive or destructive interference, depending on the precise value in relation to multiples of π.
To analyze the phase difference between the waves from sources A and B at detector D, we first determine the geometry involved. The triangle BAD is formed with:
- BAD = 90 degrees
- Lengths: AD = 2.4 m, BA = 1 m
This implies we can find the length of BD using the Pythagorean theorem, which states that in a right triangle:
- c^2 = a^2 + b^2
Where:
- c is the hypotenuse (BD)
- a is one leg (BA = 1 m)
- b is the other leg (AD = 2.4 m)
Calculating:
- BD = √(AD² + BA²) = √(2.4² + 1²) = √(5.76 + 1) = √6.76 ≈ 2.6 m
Calculating the Path Difference
The path difference (Δ) between the waves arriving at point D from sources A and B is given by the difference in distances:
- Path difference Δ = BD - AD = 2.6 m - 2.4 m = 0.2 m
Determining the Wavelength
The wavelength (λ) can be calculated using the formula:
- λ = v / f
Assuming the speed of sound in air (v) is approximately 343 m/s at room temperature:
- λ = 343 m/s / 850 Hz ≈ 0.404 m
Calculating the Phase Difference
The phase difference (Δϕ) can be calculated using the formula:
- Δϕ = (2π / λ) * Δ
Substituting the values:
- Δϕ = (2π / 0.404 m) * 0.2 m = (6.22) * 0.2 ≈ 1.244 radians
Conclusion
The phase difference between the waves emitted from sources A and B at detector D is approximately 1.244 radians. This indicates constructive or destructive interference, depending on the precise value in relation to multiples of π.
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Two point sound source A and B each of power 25πW and frequency 850 Hz are1m apart .the source are in phase a) Determine the phase difference between the waves emitting from A and B received by detector D such that BAD are in triangle angle A 90degree AD=2.4m and BA =1m?
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Two point sound source A and B each of power 25πW and frequency 850 Hz are1m apart .the source are in phase a) Determine the phase difference between the waves emitting from A and B received by detector D such that BAD are in triangle angle A 90degree AD=2.4m and BA =1m? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two point sound source A and B each of power 25πW and frequency 850 Hz are1m apart .the source are in phase a) Determine the phase difference between the waves emitting from A and B received by detector D such that BAD are in triangle angle A 90degree AD=2.4m and BA =1m? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two point sound source A and B each of power 25πW and frequency 850 Hz are1m apart .the source are in phase a) Determine the phase difference between the waves emitting from A and B received by detector D such that BAD are in triangle angle A 90degree AD=2.4m and BA =1m?.
Two point sound source A and B each of power 25πW and frequency 850 Hz are1m apart .the source are in phase a) Determine the phase difference between the waves emitting from A and B received by detector D such that BAD are in triangle angle A 90degree AD=2.4m and BA =1m? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two point sound source A and B each of power 25πW and frequency 850 Hz are1m apart .the source are in phase a) Determine the phase difference between the waves emitting from A and B received by detector D such that BAD are in triangle angle A 90degree AD=2.4m and BA =1m? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two point sound source A and B each of power 25πW and frequency 850 Hz are1m apart .the source are in phase a) Determine the phase difference between the waves emitting from A and B received by detector D such that BAD are in triangle angle A 90degree AD=2.4m and BA =1m?.
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Two point sound source A and B each of power 25πW and frequency 850 Hz are1m apart .the source are in phase a) Determine the phase difference between the waves emitting from A and B received by detector D such that BAD are in triangle angle A 90degree AD=2.4m and BA =1m?, a detailed solution for Two point sound source A and B each of power 25πW and frequency 850 Hz are1m apart .the source are in phase a) Determine the phase difference between the waves emitting from A and B received by detector D such that BAD are in triangle angle A 90degree AD=2.4m and BA =1m? has been provided alongside types of Two point sound source A and B each of power 25πW and frequency 850 Hz are1m apart .the source are in phase a) Determine the phase difference between the waves emitting from A and B received by detector D such that BAD are in triangle angle A 90degree AD=2.4m and BA =1m? theory, EduRev gives you an
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