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A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is [NEET 2013]
- a)246 Hz
- b)240 Hz
- c)260 Hz
- d)254 Hz
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A source of unknown frequency gives 4 beats/s, when sounded with a sou...
When sounded with a source of known frequency fundamental frequency = 250 ± 4 Hz = 254 Hz or 246 Hz
2nd harmonic if unknown frequency (suppose) 254 Hz = 2 × 254 = 508 Hz
As it gives 5 beats
∴ 508 + 5 = 513 Hz
Hence, unknown frequency is 254 Hz
2nd harmonic if unknown frequency (suppose) 254 Hz = 2 × 254 = 508 Hz
As it gives 5 beats
∴ 508 + 5 = 513 Hz
Hence, unknown frequency is 254 Hz
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A source of unknown frequency gives 4 beats/s, when sounded with a sou...
Given data:
- When the unknown frequency source is sounded with a known frequency source of 250 Hz, it produces 4 beats per second.
- When the second harmonic of the unknown frequency source is sounded with a known frequency source of 513 Hz, it produces 5 beats per second.
Let's analyze the given information and find the unknown frequency step by step.
Step 1: Finding the unknown frequency using the first harmonic
- When two sources with different frequencies produce beats, the frequency of the beats is equal to the difference in frequencies between the two sources.
- In this case, when the unknown frequency source is sounded with a known frequency source of 250 Hz, it produces 4 beats per second.
- Thus, the difference between the unknown frequency and 250 Hz is 4 Hz.
- Therefore, the unknown frequency can be written as f1 = 250 Hz ± 4 Hz.
Step 2: Finding the unknown frequency using the second harmonic
- The second harmonic of a frequency is twice the frequency itself.
- When the second harmonic of the unknown frequency source is sounded with a known frequency source of 513 Hz, it produces 5 beats per second.
- Thus, the difference between the second harmonic of the unknown frequency and 513 Hz is 5 Hz.
- Therefore, the second harmonic of the unknown frequency can be written as 2f1 = 513 Hz ± 5 Hz.
Step 3: Solving the equations to find the unknown frequency
- From step 1, we have f1 = 250 Hz ± 4 Hz.
- From step 2, we have 2f1 = 513 Hz ± 5 Hz.
- By comparing the two equations, we can see that the unknown frequency f1 is the same in both equations.
- Solving the equations simultaneously, we can eliminate the ± signs and solve for the unknown frequency f1.
- Subtracting the first equation from the second equation, we get: 2f1 - f1 = 513 Hz - 250 Hz ± (5 Hz - 4 Hz).
- Simplifying the equation, we get: f1 = 263 Hz ± 1 Hz.
Step 4: Final answer
- From step 3, we found that the unknown frequency f1 is 263 Hz ± 1 Hz.
- Among the given options, the only option that falls within this range is 254 Hz (263 Hz - 1 Hz = 262 Hz, 263 Hz + 1 Hz = 264 Hz).
- Therefore, the correct answer is option 'D' - 254 Hz.
- When the unknown frequency source is sounded with a known frequency source of 250 Hz, it produces 4 beats per second.
- When the second harmonic of the unknown frequency source is sounded with a known frequency source of 513 Hz, it produces 5 beats per second.
Let's analyze the given information and find the unknown frequency step by step.
Step 1: Finding the unknown frequency using the first harmonic
- When two sources with different frequencies produce beats, the frequency of the beats is equal to the difference in frequencies between the two sources.
- In this case, when the unknown frequency source is sounded with a known frequency source of 250 Hz, it produces 4 beats per second.
- Thus, the difference between the unknown frequency and 250 Hz is 4 Hz.
- Therefore, the unknown frequency can be written as f1 = 250 Hz ± 4 Hz.
Step 2: Finding the unknown frequency using the second harmonic
- The second harmonic of a frequency is twice the frequency itself.
- When the second harmonic of the unknown frequency source is sounded with a known frequency source of 513 Hz, it produces 5 beats per second.
- Thus, the difference between the second harmonic of the unknown frequency and 513 Hz is 5 Hz.
- Therefore, the second harmonic of the unknown frequency can be written as 2f1 = 513 Hz ± 5 Hz.
Step 3: Solving the equations to find the unknown frequency
- From step 1, we have f1 = 250 Hz ± 4 Hz.
- From step 2, we have 2f1 = 513 Hz ± 5 Hz.
- By comparing the two equations, we can see that the unknown frequency f1 is the same in both equations.
- Solving the equations simultaneously, we can eliminate the ± signs and solve for the unknown frequency f1.
- Subtracting the first equation from the second equation, we get: 2f1 - f1 = 513 Hz - 250 Hz ± (5 Hz - 4 Hz).
- Simplifying the equation, we get: f1 = 263 Hz ± 1 Hz.
Step 4: Final answer
- From step 3, we found that the unknown frequency f1 is 263 Hz ± 1 Hz.
- Among the given options, the only option that falls within this range is 254 Hz (263 Hz - 1 Hz = 262 Hz, 263 Hz + 1 Hz = 264 Hz).
- Therefore, the correct answer is option 'D' - 254 Hz.
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A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is [NEET 2013]a)246 Hzb)240 Hzc)260 Hzd)254 HzCorrect answer is option 'D'. Can you explain this answer?
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A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is [NEET 2013]a)246 Hzb)240 Hzc)260 Hzd)254 HzCorrect answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is [NEET 2013]a)246 Hzb)240 Hzc)260 Hzd)254 HzCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is [NEET 2013]a)246 Hzb)240 Hzc)260 Hzd)254 HzCorrect answer is option 'D'. Can you explain this answer?.
A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is [NEET 2013]a)246 Hzb)240 Hzc)260 Hzd)254 HzCorrect answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is [NEET 2013]a)246 Hzb)240 Hzc)260 Hzd)254 HzCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is [NEET 2013]a)246 Hzb)240 Hzc)260 Hzd)254 HzCorrect answer is option 'D'. Can you explain this answer?.
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