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A source of frequency 50Hz is moving towards an observer with a deceleration of 2m/s2. If its initial speed is 20m/s, what will be the maximum frequency heard by the observer? Initial distance between source and observer is 100m. Speed of sound = 330m/s.
- a)47.14Hz
- b)0
- c)53.22Hz
- d)53.03Hz
Correct answer is option 'C'. Can you explain this answer?
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A source of frequency 50Hz is moving towards an observer with a decele...
Max Frequency Heard by the Observer
To determine the maximum frequency heard by the observer, we need to consider the Doppler effect. The Doppler effect is the change in frequency of a wave for an observer moving relative to the source of the wave. In this case, the source is a moving object emitting sound waves, and the observer is stationary.
Doppler Effect Formula
The formula for the Doppler effect is given by:
f' = f(v + vo) / (v - vs)
where:
- f' is the observed frequency
- f is the source frequency
- v is the speed of sound
- vo is the speed of the observer
- vs is the speed of the source
In this case, the speed of sound (v) is given as 330 m/s, and the speed of the observer (vo) is 0 m/s since the observer is stationary. We need to determine the speed of the source (vs) at any given time.
Calculating the Speed of the Source
The acceleration of the source is given as -2 m/s^2 (deceleration). We can use the following kinematic equation to determine the speed of the source at any given time:
v = u + at
where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is the time
Initially, the speed of the source (u) is 20 m/s, and the time (t) is the time taken for the source to reach the observer. We can determine the time using the following kinematic equation:
s = ut + (1/2)at^2
where:
- s is the initial distance between the source and the observer
Rearranging the equation, we get:
t^2 - (2u/a)t - (2s/a) = 0
Solving this quadratic equation, we can find the time it takes for the source to reach the observer. Once we have the time, we can substitute it into the equation for the speed of the source to find its value.
Substituting Values and Calculating the Frequency
Once we have the speed of the source, we can substitute all the values into the Doppler effect formula to calculate the observed frequency (f').
f' = f(v + vo) / (v - vs)
Substituting the given values, we get:
f' = f(330 + 0) / (330 - vs)
The maximum frequency heard by the observer will occur when the source is closest to the observer. At this point, the speed of the source will be at its minimum. Substituting this minimum speed into the formula will give us the maximum frequency.
Final Answer
By calculating the time it takes for the source to reach the observer, determining the speed of the source at that time, and substituting the values into the Doppler effect formula, we can find the maximum frequency heard by the observer. The correct answer is option C, 53.22 Hz.
To determine the maximum frequency heard by the observer, we need to consider the Doppler effect. The Doppler effect is the change in frequency of a wave for an observer moving relative to the source of the wave. In this case, the source is a moving object emitting sound waves, and the observer is stationary.
Doppler Effect Formula
The formula for the Doppler effect is given by:
f' = f(v + vo) / (v - vs)
where:
- f' is the observed frequency
- f is the source frequency
- v is the speed of sound
- vo is the speed of the observer
- vs is the speed of the source
In this case, the speed of sound (v) is given as 330 m/s, and the speed of the observer (vo) is 0 m/s since the observer is stationary. We need to determine the speed of the source (vs) at any given time.
Calculating the Speed of the Source
The acceleration of the source is given as -2 m/s^2 (deceleration). We can use the following kinematic equation to determine the speed of the source at any given time:
v = u + at
where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is the time
Initially, the speed of the source (u) is 20 m/s, and the time (t) is the time taken for the source to reach the observer. We can determine the time using the following kinematic equation:
s = ut + (1/2)at^2
where:
- s is the initial distance between the source and the observer
Rearranging the equation, we get:
t^2 - (2u/a)t - (2s/a) = 0
Solving this quadratic equation, we can find the time it takes for the source to reach the observer. Once we have the time, we can substitute it into the equation for the speed of the source to find its value.
Substituting Values and Calculating the Frequency
Once we have the speed of the source, we can substitute all the values into the Doppler effect formula to calculate the observed frequency (f').
f' = f(v + vo) / (v - vs)
Substituting the given values, we get:
f' = f(330 + 0) / (330 - vs)
The maximum frequency heard by the observer will occur when the source is closest to the observer. At this point, the speed of the source will be at its minimum. Substituting this minimum speed into the formula will give us the maximum frequency.
Final Answer
By calculating the time it takes for the source to reach the observer, determining the speed of the source at that time, and substituting the values into the Doppler effect formula, we can find the maximum frequency heard by the observer. The correct answer is option C, 53.22 Hz.
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Community Answer
A source of frequency 50Hz is moving towards an observer with a decele...
Apparent frequency only depends on velocity and not the distance between source and observer. So, maximum frequency will be heard when speed is maximum, which is at the start. F = 50(330)/(330-20)
= 53.22Hz.
= 53.22Hz.
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A source of frequency 50Hz is moving towards an observer with a deceleration of 2m/s2. If its initial speed is 20m/s, what will be the maximum frequency heard by the observer? Initial distance between source and observer is 100m. Speed of sound = 330m/s.a)47.14Hzb)0c)53.22Hzd)53.03HzCorrect answer is option 'C'. Can you explain this answer?
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