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A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that train A is
- a)242/252
- b)2
- c)5/6
- d)11/6
Correct answer is option 'B'. Can you explain this answer?
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A siren placed at a railway platform is emitting sound of frequency 5 ...
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A siren placed at a railway platform is emitting sound of frequency 5 ...
Given:
Frequency of siren at the railway platform, f = 5 kHz
Frequency heard by passenger in train A while approaching the siren, f₁ = 5.5 kHz
Frequency heard by passenger in train B while approaching the siren, f₂ = 6.0 kHz
We need to find the ratio of the velocity of train B to that of train A.
Let's assume:
v₁ = velocity of train A
v₂ = velocity of train B
v = velocity of sound in air
We know that the apparent frequency heard by an observer moving towards a source of sound is given by:
f₁ = (v + v₁) / (v - v)
Similarly, the apparent frequency heard by an observer moving towards a source of sound is given by:
f₂ = (v + v₂) / (v - v)
We can rearrange the above equations to solve for v₁ and v₂:
(v + v₁) = f₁(v - v)
(v + v₂) = f₂(v - v)
Dividing the above equations, we get:
(v + v₁) / (v + v₂) = f₁ / f₂
Substituting the given values, we have:
(5v + 5v₁) / (5v + 5v₂) = 5.5 / 6.0
Simplifying the equation, we get:
(1 + v₁/v) / (1 + v₂/v) = 11/12
Cross-multiplying, we have:
12 + 12(v₁/v) = 11 + 11(v₂/v)
Rearranging the equation, we get:
v₁/v - v₂/v = -1/12
Dividing throughout by v, we have:
v₁ - v₂ = -v/12
Dividing throughout by v₁, we get:
(v₁ - v₂)/v₁ = -v/12v₁
Simplifying the equation, we have:
1 - v₂/v₁ = -1/12
Rearranging the equation, we get:
v₂/v₁ = 1 - 1/12
Simplifying the equation, we have:
v₂/v₁ = 11/12
Therefore, the ratio of the velocity of train B to that of train A is 11/12, which is approximately 0.917.
Frequency of siren at the railway platform, f = 5 kHz
Frequency heard by passenger in train A while approaching the siren, f₁ = 5.5 kHz
Frequency heard by passenger in train B while approaching the siren, f₂ = 6.0 kHz
We need to find the ratio of the velocity of train B to that of train A.
Let's assume:
v₁ = velocity of train A
v₂ = velocity of train B
v = velocity of sound in air
We know that the apparent frequency heard by an observer moving towards a source of sound is given by:
f₁ = (v + v₁) / (v - v)
Similarly, the apparent frequency heard by an observer moving towards a source of sound is given by:
f₂ = (v + v₂) / (v - v)
We can rearrange the above equations to solve for v₁ and v₂:
(v + v₁) = f₁(v - v)
(v + v₂) = f₂(v - v)
Dividing the above equations, we get:
(v + v₁) / (v + v₂) = f₁ / f₂
Substituting the given values, we have:
(5v + 5v₁) / (5v + 5v₂) = 5.5 / 6.0
Simplifying the equation, we get:
(1 + v₁/v) / (1 + v₂/v) = 11/12
Cross-multiplying, we have:
12 + 12(v₁/v) = 11 + 11(v₂/v)
Rearranging the equation, we get:
v₁/v - v₂/v = -1/12
Dividing throughout by v, we have:
v₁ - v₂ = -v/12
Dividing throughout by v₁, we get:
(v₁ - v₂)/v₁ = -v/12v₁
Simplifying the equation, we have:
1 - v₂/v₁ = -1/12
Rearranging the equation, we get:
v₂/v₁ = 1 - 1/12
Simplifying the equation, we have:
v₂/v₁ = 11/12
Therefore, the ratio of the velocity of train B to that of train A is 11/12, which is approximately 0.917.
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A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train Arecords a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that train A isa)242/252b)2c)5/6d)11/6Correct answer is option 'B'. Can you explain this answer?
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A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train Arecords a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that train A isa)242/252b)2c)5/6d)11/6Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train Arecords a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that train A isa)242/252b)2c)5/6d)11/6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train Arecords a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that train A isa)242/252b)2c)5/6d)11/6Correct answer is option 'B'. Can you explain this answer?.
A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train Arecords a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that train A isa)242/252b)2c)5/6d)11/6Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train Arecords a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that train A isa)242/252b)2c)5/6d)11/6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train Arecords a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that train A isa)242/252b)2c)5/6d)11/6Correct answer is option 'B'. Can you explain this answer?.
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