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Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneouly. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1, T2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension,
- a)T2 was decreased
- b)T2 was increased
- c)T1 was decreased
- d)T1 was increased
Correct answer is option 'B,C'. Can you explain this answer?
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Two identical straight wires are stretched so as to produce 6 beats pe...
Solution:
Given that two identical straight wires produced 6 beats per second when vibrating simultaneously. Let the initial tensions in the strings be T1 and T2 (T1 > T2).
After changing the tension slightly in one of them, the beat frequency remains unchanged. This means that the new tension in one of the wires is equal to the average of the initial tensions.
Let the new tension in the wire with the lower tension be T2' and the new tension in the wire with the higher tension be T1'. Then we have:
(T1 + T2')/2 = (T1' + T2)/2
T1 + T2' = T1' + T2
T1 - T1' = T2 - T2'
Now, the beat frequency is given by:
fbeat = |f1 - f2|
where f1 and f2 are the frequencies of the two wires.
Initially, the two wires produced 6 beats per second. This means that their frequencies differ by 3 Hz. That is,
|f1 - f2| = 3
Now, after changing the tension slightly in one of the wires, the beat frequency remains unchanged. This means that the frequencies of the two wires are still different by 3 Hz. That is,
|f1' - f2'| = 3
Now, we know that the frequency of a wire is proportional to the square root of its tension. That is,
f ∝ √T
So, we can write:
f1/f2 = √(T1/T2)
f1'/f2' = √(T1'/T2')
Multiplying these two equations, we get:
(f1/f2) x (f1'/f2') = √(T1/T2) x √(T1'/T2')
fbeat x fbeat = √(T1/T2) x √(T1'/T2')
Squaring both sides, we get:
fbeat^2 = T1T1'/(T2T2')
Now, we know that T1 > T2. So, if T2' < t2,="" then="" t1'="" /> T1. This would mean that the beat frequency would increase. But we know that the beat frequency remains unchanged. Therefore, T2' cannot be less than T2.
Similarly, we can show that T1' cannot be greater than T1. Therefore, the only possible options are that either T2' > T2 or T1' < />
Hence, the correct options are B and C:
B. T2 was increased
C. T1 was decreased.
Given that two identical straight wires produced 6 beats per second when vibrating simultaneously. Let the initial tensions in the strings be T1 and T2 (T1 > T2).
After changing the tension slightly in one of them, the beat frequency remains unchanged. This means that the new tension in one of the wires is equal to the average of the initial tensions.
Let the new tension in the wire with the lower tension be T2' and the new tension in the wire with the higher tension be T1'. Then we have:
(T1 + T2')/2 = (T1' + T2)/2
T1 + T2' = T1' + T2
T1 - T1' = T2 - T2'
Now, the beat frequency is given by:
fbeat = |f1 - f2|
where f1 and f2 are the frequencies of the two wires.
Initially, the two wires produced 6 beats per second. This means that their frequencies differ by 3 Hz. That is,
|f1 - f2| = 3
Now, after changing the tension slightly in one of the wires, the beat frequency remains unchanged. This means that the frequencies of the two wires are still different by 3 Hz. That is,
|f1' - f2'| = 3
Now, we know that the frequency of a wire is proportional to the square root of its tension. That is,
f ∝ √T
So, we can write:
f1/f2 = √(T1/T2)
f1'/f2' = √(T1'/T2')
Multiplying these two equations, we get:
(f1/f2) x (f1'/f2') = √(T1/T2) x √(T1'/T2')
fbeat x fbeat = √(T1/T2) x √(T1'/T2')
Squaring both sides, we get:
fbeat^2 = T1T1'/(T2T2')
Now, we know that T1 > T2. So, if T2' < t2,="" then="" t1'="" /> T1. This would mean that the beat frequency would increase. But we know that the beat frequency remains unchanged. Therefore, T2' cannot be less than T2.
Similarly, we can show that T1' cannot be greater than T1. Therefore, the only possible options are that either T2' > T2 or T1' < />
Hence, the correct options are B and C:
B. T2 was increased
C. T1 was decreased.
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Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneouly. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1, T2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension,a)T2 was decreasedb)T2 was increasedc)T1 was decreasedd)T1 was increasedCorrect answer is option 'B,C'. Can you explain this answer?
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Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneouly. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1, T2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension,a)T2 was decreasedb)T2 was increasedc)T1 was decreasedd)T1 was increasedCorrect answer is option 'B,C'. 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 Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneouly. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1, T2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension,a)T2 was decreasedb)T2 was increasedc)T1 was decreasedd)T1 was increasedCorrect answer is option 'B,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneouly. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1, T2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension,a)T2 was decreasedb)T2 was increasedc)T1 was decreasedd)T1 was increasedCorrect answer is option 'B,C'. Can you explain this answer?.
Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneouly. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1, T2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension,a)T2 was decreasedb)T2 was increasedc)T1 was decreasedd)T1 was increasedCorrect answer is option 'B,C'. 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 Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneouly. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1, T2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension,a)T2 was decreasedb)T2 was increasedc)T1 was decreasedd)T1 was increasedCorrect answer is option 'B,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneouly. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1, T2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension,a)T2 was decreasedb)T2 was increasedc)T1 was decreasedd)T1 was increasedCorrect answer is option 'B,C'. Can you explain this answer?.
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Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneouly. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1, T2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension,a)T2 was decreasedb)T2 was increasedc)T1 was decreasedd)T1 was increasedCorrect answer is option 'B,C'. Can you explain this answer?, a detailed solution for Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneouly. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1, T2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension,a)T2 was decreasedb)T2 was increasedc)T1 was decreasedd)T1 was increasedCorrect answer is option 'B,C'. Can you explain this answer? has been provided alongside types of Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneouly. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1, T2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension,a)T2 was decreasedb)T2 was increasedc)T1 was decreasedd)T1 was increasedCorrect answer is option 'B,C'. Can you explain this answer? theory, EduRev gives you an
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