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Two sources of sound moving with same speed v and emitting frequency of 1400 Hz are moving such that one source s1 is moving towards the observer and s2 is moving away from observer. If observer hears beat frequency of 2 Hz. Then find the speed of source. Given
Vsound >> VSource
Vsound = 350 m/s
Vsound >> VSource
Vsound = 350 m/s
- a)1/4
- b)4
- c)2
- d)1/2
Correct answer is option 'A'. Can you explain this answer?
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Two sources of sound moving with same speed v and emitting frequency o...
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Two sources of sound moving with same speed v and emitting frequency o...
Given:
Frequency emitted by each source, f = 1400 Hz
Beat frequency, fb = 2 Hz
Speed of sound, Vsound = ?
Let's assume the speed of source 1 (s1) as Vs1 and the speed of source 2 (s2) as Vs2.
Since source 1 is moving towards the observer, the frequency heard by the observer from source 1 (f1) will be higher than the emitted frequency (f) due to the Doppler effect. The formula for the observed frequency is given by:
f1 = f * (Vsound + Vs1) / (Vsound)
Similarly, since source 2 is moving away from the observer, the frequency heard by the observer from source 2 (f2) will be lower than the emitted frequency (f). The formula for the observed frequency is given by:
f2 = f * (Vsound - Vs2) / (Vsound)
The beat frequency (fb) is the difference between the observed frequencies:
fb = f1 - f2
Substituting the values of f1 and f2:
fb = f * (Vsound + Vs1) / (Vsound) - f * (Vsound - Vs2) / (Vsound)
Simplifying the equation:
fb = f * (Vs1 + Vs2) / (Vsound)
Now, we can solve the equation for the speed of sound (Vsound):
fb * Vsound = f * (Vs1 + Vs2)
Vsound = f * (Vs1 + Vs2) / fb
Vsound = 1400 Hz * (Vs1 + Vs2) / 2 Hz
Vsound = 700 * (Vs1 + Vs2)
Therefore, the speed of sound (Vsound) is 700 times the sum of the speeds of the sources (Vs1 + Vs2).
Frequency emitted by each source, f = 1400 Hz
Beat frequency, fb = 2 Hz
Speed of sound, Vsound = ?
Let's assume the speed of source 1 (s1) as Vs1 and the speed of source 2 (s2) as Vs2.
Since source 1 is moving towards the observer, the frequency heard by the observer from source 1 (f1) will be higher than the emitted frequency (f) due to the Doppler effect. The formula for the observed frequency is given by:
f1 = f * (Vsound + Vs1) / (Vsound)
Similarly, since source 2 is moving away from the observer, the frequency heard by the observer from source 2 (f2) will be lower than the emitted frequency (f). The formula for the observed frequency is given by:
f2 = f * (Vsound - Vs2) / (Vsound)
The beat frequency (fb) is the difference between the observed frequencies:
fb = f1 - f2
Substituting the values of f1 and f2:
fb = f * (Vsound + Vs1) / (Vsound) - f * (Vsound - Vs2) / (Vsound)
Simplifying the equation:
fb = f * (Vs1 + Vs2) / (Vsound)
Now, we can solve the equation for the speed of sound (Vsound):
fb * Vsound = f * (Vs1 + Vs2)
Vsound = f * (Vs1 + Vs2) / fb
Vsound = 1400 Hz * (Vs1 + Vs2) / 2 Hz
Vsound = 700 * (Vs1 + Vs2)
Therefore, the speed of sound (Vsound) is 700 times the sum of the speeds of the sources (Vs1 + Vs2).
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Two sources of sound moving with same speed v and emitting frequency of 1400 Hz are moving such that one source s1 is moving towards the observer and s2 is moving away from observer. If observer hears beat frequency of 2 Hz. Then find the speed of source. GivenVsound >> VSourceVsound = 350 m/sa)1/4b)4c)2d)1/2Correct answer is option 'A'. Can you explain this answer?
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