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If a source of sound was moving toward a receiver at 1/3 the speed of sound, what would the resulting wavelength be?
- a)6 times the emitted wavelength
- b)2/3 of the emitted wavelength
- c)1/3 of the emitted wavelength
- d)Can not be found
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If a source of sound was moving toward a receiver at 1/3 the speed of ...
We need to find the resulting wavelength of the sound wave, which can be calculated using the formula: λ' = λ(v +/- vs) / (v + u) Since the source is moving towards the observer, we can use the negative sign for vs: λ' = λ(v - vs) / (v + u) λ' = λ(v - (-1/3)v) / (v + u) λ' = λ(4/3v) / (v + u) We can also use the formula for the speed of the sound wave: v = fλ which gives us: λ = v/f Substituting this value in the above equation, we get: λ' = (4/3)(v/f) / (v + u) λ' = (4/3)f / (3v + u) We know that the velocity of the observer (u) is zero since it is stationary. Thus, the equation simplifies to: λ' = (4/9)f/v This means that the resulting wavelength is 2/3 of the emitted wavelength since: λ' / λ = (4/9f/v) / (f/v) = 4/9 = 0.44 Therefore, the correct answer is option B, 2/3 of the emitted wavelength.
Most Upvoted Answer
If a source of sound was moving toward a receiver at 1/3 the speed of ...
Concept:
The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. When the source moves toward the observer, the frequency and wavelength are increased, while moving away from the observer decreases the frequency and wavelength.
Formula:
The formula for the Doppler Effect for sound waves is given by:
f' = f(v + u) / (v +/- vs)
where,
f' = frequency of the observed wave
f = frequency of the emitted wave
v = velocity of sound
u = velocity of the observer
vs = velocity of the source
Calculation:
Given, the source of sound is moving towards the receiver at 1/3 the speed of sound. This means that the velocity of the source (vs) is (-1/3)v since it is moving towards the observer.
We need to find the resulting wavelength of the sound wave, which can be calculated using the formula:
λ' = λ(v +/- vs) / (v + u)
Since the source is moving towards the observer, we can use the negative sign for vs:
λ' = λ(v - vs) / (v + u)
λ' = λ(v - (-1/3)v) / (v + u)
λ' = λ(4/3v) / (v + u)
We can also use the formula for the speed of the sound wave:
v = fλ
which gives us:
λ = v/f
Substituting this value in the above equation, we get:
λ' = (4/3)(v/f) / (v + u)
λ' = (4/3)f / (3v + u)
We know that the velocity of the observer (u) is zero since it is stationary. Thus, the equation simplifies to:
λ' = (4/9)f/v
This means that the resulting wavelength is 2/3 of the emitted wavelength since:
λ' / λ = (4/9f/v) / (f/v) = 4/9 = 0.44
Therefore, the correct answer is option B, 2/3 of the emitted wavelength.
The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. When the source moves toward the observer, the frequency and wavelength are increased, while moving away from the observer decreases the frequency and wavelength.
Formula:
The formula for the Doppler Effect for sound waves is given by:
f' = f(v + u) / (v +/- vs)
where,
f' = frequency of the observed wave
f = frequency of the emitted wave
v = velocity of sound
u = velocity of the observer
vs = velocity of the source
Calculation:
Given, the source of sound is moving towards the receiver at 1/3 the speed of sound. This means that the velocity of the source (vs) is (-1/3)v since it is moving towards the observer.
We need to find the resulting wavelength of the sound wave, which can be calculated using the formula:
λ' = λ(v +/- vs) / (v + u)
Since the source is moving towards the observer, we can use the negative sign for vs:
λ' = λ(v - vs) / (v + u)
λ' = λ(v - (-1/3)v) / (v + u)
λ' = λ(4/3v) / (v + u)
We can also use the formula for the speed of the sound wave:
v = fλ
which gives us:
λ = v/f
Substituting this value in the above equation, we get:
λ' = (4/3)(v/f) / (v + u)
λ' = (4/3)f / (3v + u)
We know that the velocity of the observer (u) is zero since it is stationary. Thus, the equation simplifies to:
λ' = (4/9)f/v
This means that the resulting wavelength is 2/3 of the emitted wavelength since:
λ' / λ = (4/9f/v) / (f/v) = 4/9 = 0.44
Therefore, the correct answer is option B, 2/3 of the emitted wavelength.
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If a source of sound was moving toward a receiver at 1/3 the speed of sound, what would the resulting wavelength be?a)6 times the emitted wavelengthb)2/3 of the emitted wavelengthc)1/3 of the emitted wavelengthd)Can not be foundCorrect answer is option 'B'. Can you explain this answer?
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