A person standing close to a railroad crossing hears the whistle of an approaching train. He notes that the pitch of the whistle drops as the train passes by and moves away from the crossing. The frequency of the approaching whistle is 523 Hz, and drops to 491 Hz after the train is well past the crossing. What is the speed of the train? Use 340 m/s for the speed of sound in air. show work.
A player passes a 0.600- basketball downcourt for a fast break. The ball leaves the player's hands with a speed of 8.10 and slows down to 7.20 at its highest point.How would doubling the ball's mass affect Explain.
To determine the speed of the train, we can use the Doppler effect equation for sound:
Δf/f₀ = v/(v + vo)
Where:
Δf = change in frequency (Hz)
f₀ = original frequency (Hz)
v = velocity of sound (m/s)
vo = velocity of observer (m/s)
Given:
f₀ = 523 Hz (original frequency)
Δf = f₀ - f = 523 Hz - 491 Hz = 32 Hz (change in frequency)
v = 340 m/s (speed of sound in air)
We need to find the velocity of the observer (vo), which is the speed of the train.
Rearranging the equation:
v/(v + vo) = Δf/f₀
Substituting the given values:
vo/(340 m/s + vo) = 32 Hz / 523 Hz
Cross multiplying:
523 vo = 32 (340 + vo)
523 vo = 10880 + 32 vo
523 vo - 32 vo = 10880
491 vo = 10880
vo = 10880 / 491
vo ≈ 22.15 m/s
Therefore, the speed of the train is approximately 22.15 m/s.
To find the speed of the train, we can use the Doppler effect formula:
Δf/f = v/(v ± vs)
where Δf is the change in frequency, f is the initial frequency, v is the speed of sound, and vs is the speed of the source of the sound relative to the observer.
In this case, the initial frequency is 523 Hz, and after the train passes by, the frequency drops to 491 Hz. The speed of sound in air, v, is given as 340 m/s. We need to find the speed of the train, vs.
First, let's calculate the change in frequency:
Δf = f - f' = 523 Hz - 491 Hz = 32 Hz
The plus or minus sign in the formula depends on whether the source is moving towards or away from the observer. In this case, since the pitch (frequency) drops, the source is moving away from the observer, so we use the minus sign in the formula.
Now we can rearrange the formula to solve for the speed of the train:
vs = v * Δf / f
vs = 340 m/s * 32 Hz / 523 Hz
vs = 20.68 m/s
Therefore, the speed of the train is approximately 20.68 m/s.
F = ((V+Vr) / (V+Vs))*Fo = 491.
((340+0) / (340+Vs)))*523 = 491,
177820 / (340+Vs) = 491,
166,940 + 491Vs = 177,820,
Vs = 22.2m/s = Speed of train.