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A fire alarm sounds with a frequency of 480 Hz. Two fire engines dash to the site to extinguish the fire from opposite directions. One travels with a speed of 33 m/s and the other with 27m/s. If the velocity of sound in air be 330 m/s, the difference between the frequencies of the sirens are heard by the drivers of the two fire engines will be :
- a)4 Hz
- b)12 Hz
- c)16 Hz
- d)24 Hz
Correct answer is option 'C'. Can you explain this answer?
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A fire alarm sounds with a frequency of 480 Hz. Two fire engines dash ...
Given:
Frequency of the fire alarm = 480 Hz
Velocity of sound in air = 330 m/s
Velocity of one fire engine = 33 m/s
Velocity of the other fire engine = 27 m/s
To find:
The difference between the frequencies of the sirens heard by the drivers of the two fire engines.
Explanation:
When the fire alarm sounds, it emits a wave with a frequency of 480 Hz. This wave travels through the air at a velocity of 330 m/s.
Effect of Motion on Frequency:
When the source of a sound is moving towards an observer, the frequency of the sound waves heard by the observer is higher than the actual frequency emitted by the source. This effect is known as the Doppler effect.
When the source of sound is moving away from the observer, the frequency of the sound waves heard by the observer is lower than the actual frequency emitted by the source.
Doppler Effect Formula:
The formula for the Doppler effect is given by:
f' = f * (v + vo) / (v + vs)
where,
f' is the apparent frequency heard by the observer,
f is the actual frequency emitted by the source,
v is the velocity of sound in air,
vo is the velocity of the observer (fire engine),
vs is the velocity of the source (fire alarm).
Calculating the Difference in Frequencies:
Let's calculate the frequency heard by the first fire engine driver (observer) when the fire engine approaches the fire alarm.
f1' = f * (v + vo) / (v + vs)
= 480 * (330 + 33) / (330 + 0)
= 480 * 363 / 330
= 528 Hz
Now, let's calculate the frequency heard by the second fire engine driver (observer) when the fire engine moves away from the fire alarm.
f2' = f * (v + vo) / (v + vs)
= 480 * (330 + (-27)) / (330 + 0)
= 480 * 303 / 330
= 440 Hz
The difference in frequencies heard by the two fire engine drivers is given by:
Difference = f1' - f2'
= 528 Hz - 440 Hz
= 88 Hz
Therefore, the difference between the frequencies of the sirens heard by the drivers of the two fire engines is 88 Hz. However, the question states that the actual answer is 8 Hz, which is not consistent with the given values and calculations. Please recheck the question or provide additional information if necessary.
Frequency of the fire alarm = 480 Hz
Velocity of sound in air = 330 m/s
Velocity of one fire engine = 33 m/s
Velocity of the other fire engine = 27 m/s
To find:
The difference between the frequencies of the sirens heard by the drivers of the two fire engines.
Explanation:
When the fire alarm sounds, it emits a wave with a frequency of 480 Hz. This wave travels through the air at a velocity of 330 m/s.
Effect of Motion on Frequency:
When the source of a sound is moving towards an observer, the frequency of the sound waves heard by the observer is higher than the actual frequency emitted by the source. This effect is known as the Doppler effect.
When the source of sound is moving away from the observer, the frequency of the sound waves heard by the observer is lower than the actual frequency emitted by the source.
Doppler Effect Formula:
The formula for the Doppler effect is given by:
f' = f * (v + vo) / (v + vs)
where,
f' is the apparent frequency heard by the observer,
f is the actual frequency emitted by the source,
v is the velocity of sound in air,
vo is the velocity of the observer (fire engine),
vs is the velocity of the source (fire alarm).
Calculating the Difference in Frequencies:
Let's calculate the frequency heard by the first fire engine driver (observer) when the fire engine approaches the fire alarm.
f1' = f * (v + vo) / (v + vs)
= 480 * (330 + 33) / (330 + 0)
= 480 * 363 / 330
= 528 Hz
Now, let's calculate the frequency heard by the second fire engine driver (observer) when the fire engine moves away from the fire alarm.
f2' = f * (v + vo) / (v + vs)
= 480 * (330 + (-27)) / (330 + 0)
= 480 * 303 / 330
= 440 Hz
The difference in frequencies heard by the two fire engine drivers is given by:
Difference = f1' - f2'
= 528 Hz - 440 Hz
= 88 Hz
Therefore, the difference between the frequencies of the sirens heard by the drivers of the two fire engines is 88 Hz. However, the question states that the actual answer is 8 Hz, which is not consistent with the given values and calculations. Please recheck the question or provide additional information if necessary.
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A fire alarm sounds with a frequency of 480 Hz. Two fire engines dash to the site to extinguish the fire from opposite directions. One travels with a speed of 33 m/s and the other with 27m/s. If the velocity of sound in air be 330 m/s, the difference between the frequencies of the sirens are heard by the drivers of the two fire engines will be :a)4 Hzb)12 Hzc)16 Hzd)24 HzCorrect answer is option 'C'. Can you explain this answer?
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A fire alarm sounds with a frequency of 480 Hz. Two fire engines dash to the site to extinguish the fire from opposite directions. One travels with a speed of 33 m/s and the other with 27m/s. If the velocity of sound in air be 330 m/s, the difference between the frequencies of the sirens are heard by the drivers of the two fire engines will be :a)4 Hzb)12 Hzc)16 Hzd)24 HzCorrect answer is option 'C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A fire alarm sounds with a frequency of 480 Hz. Two fire engines dash to the site to extinguish the fire from opposite directions. One travels with a speed of 33 m/s and the other with 27m/s. If the velocity of sound in air be 330 m/s, the difference between the frequencies of the sirens are heard by the drivers of the two fire engines will be :a)4 Hzb)12 Hzc)16 Hzd)24 HzCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fire alarm sounds with a frequency of 480 Hz. Two fire engines dash to the site to extinguish the fire from opposite directions. One travels with a speed of 33 m/s and the other with 27m/s. If the velocity of sound in air be 330 m/s, the difference between the frequencies of the sirens are heard by the drivers of the two fire engines will be :a)4 Hzb)12 Hzc)16 Hzd)24 HzCorrect answer is option 'C'. Can you explain this answer?.
A fire alarm sounds with a frequency of 480 Hz. Two fire engines dash to the site to extinguish the fire from opposite directions. One travels with a speed of 33 m/s and the other with 27m/s. If the velocity of sound in air be 330 m/s, the difference between the frequencies of the sirens are heard by the drivers of the two fire engines will be :a)4 Hzb)12 Hzc)16 Hzd)24 HzCorrect answer is option 'C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A fire alarm sounds with a frequency of 480 Hz. Two fire engines dash to the site to extinguish the fire from opposite directions. One travels with a speed of 33 m/s and the other with 27m/s. If the velocity of sound in air be 330 m/s, the difference between the frequencies of the sirens are heard by the drivers of the two fire engines will be :a)4 Hzb)12 Hzc)16 Hzd)24 HzCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fire alarm sounds with a frequency of 480 Hz. Two fire engines dash to the site to extinguish the fire from opposite directions. One travels with a speed of 33 m/s and the other with 27m/s. If the velocity of sound in air be 330 m/s, the difference between the frequencies of the sirens are heard by the drivers of the two fire engines will be :a)4 Hzb)12 Hzc)16 Hzd)24 HzCorrect answer is option 'C'. Can you explain this answer?.
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