Two eagles fly directly toward one another, the first at 13 m/s and the second at 21 m/s. Both screech, the first emitting a frequency of 3200 Hz and the second, a frequency of 3800 Hz. What frequencies do they hear if the speed of sound is 345 m/s? (Tip: keep 4 significant figures on this one.)
a) Frequency heard by the first eagle = Hz
HELP: This is a Doppler effect problem.
HELP: Each eagle is the source of the sound heard by the other eagle. Each eagle is also the observer of the sound made by other eagle.
HELP: What is the source velocity in this case? What is the observer velocity in this case?
b) Frequency heard by the second eagle = Hz
HELP: What is the source velocity in this case? What is the observer velocity in this case?
To solve this problem, we can use the Doppler effect formula for frequency:
f' = ((v + vo) / (v + vs)) * f
Where:
f' is the observed frequency
f is the actual frequency
v is the speed of sound
vo is the observer velocity
vs is the source velocity
Let's start by calculating the frequency heard by the first eagle:
a) Frequency heard by the first eagle:
Given data:
Speed of sound (v) = 345 m/s
Source velocity (vs) = 21 m/s
Observer velocity (vo) = -13 m/s (negative sign because the first eagle is moving towards the second eagle)
Actual frequency (f) = 3200 Hz
Using the Doppler effect formula:
f' = ((v + vo) / (v + vs)) * f
Substituting the values:
f' = ((345 + (-13)) / (345 + 21)) * 3200
Calculating the numerator:
345 + (-13) = 332
Calculating the denominator:
345 + 21 = 366
Calculating the fraction:
332 / 366 = 0.9071
Calculating the observed frequency:
f' = 0.9071 * 3200 Hz = 2903.12 Hz
Therefore, the frequency heard by the first eagle is approximately 2903.12 Hz (rounded to 4 significant figures).
b) Frequency heard by the second eagle:
Now let's calculate the frequency heard by the second eagle:
Given data:
Speed of sound (v) = 345 m/s
Source velocity (vs) = -13 m/s (negative sign because the second eagle is moving towards the first eagle)
Observer velocity (vo) = 21 m/s
Actual frequency (f) = 3800 Hz
Using the Doppler effect formula:
f' = ((v + vo) / (v + vs)) * f
Substituting the values:
f' = ((345 + 21) / (345 + (-13))) * 3800
Calculating the numerator:
345 + 21 = 366
Calculating the denominator:
345 + (-13) = 332
Calculating the fraction:
366 / 332 = 1.1024
Calculating the observed frequency:
f' = 1.1024 * 3800 Hz = 4188.72 Hz
Therefore, the frequency heard by the second eagle is approximately 4188.72 Hz (rounded to 4 significant figures).
To summarize:
a) Frequency heard by the first eagle = 2903.12 Hz
b) Frequency heard by the second eagle = 4188.72 Hz
To solve this Doppler effect problem, we need to use the formulas for the apparent frequency heard by an observer when the source and observer are in relative motion.
a) Frequency heard by the first eagle:
The source velocity is the velocity at which the second eagle is moving towards the first eagle, which is 21 m/s.
The observer velocity is the velocity at which the first eagle is moving towards the second eagle, which is -13 m/s (negative because it is moving in the opposite direction).
Using the formula for the apparent frequency heard by an observer moving towards a source:
f' = f * (v + vo) / (v + vs)
where f is the source frequency, v is the speed of sound, vo is the observer velocity, and vs is the source velocity.
Plugging in the values:
f' = 3200 Hz * (345 m/s - 13 m/s) / (345 m/s - 21 m/s)
= 3200 Hz * 332 m/s / 324 m/s
= 3289 Hz (rounded to four significant figures)
Therefore, the frequency heard by the first eagle is 3289 Hz.
b) Frequency heard by the second eagle:
The source velocity is the velocity at which the first eagle is moving towards the second eagle, which is 13 m/s.
The observer velocity is the velocity at which the second eagle is moving towards the first eagle, which is -21 m/s (negative because it is moving in the opposite direction).
Using the same formula as above:
f' = 3800 Hz * (345 m/s - 21 m/s) / (345 m/s - 13 m/s)
= 3800 Hz * 324 m/s / 332 m/s
= 3693 Hz (rounded to four significant figures)
Therefore, the frequency heard by the second eagle is 3693 Hz.