You are moving at 120 km/h toward a stationary train. The train blows its 400-Hz whistle. Take the speed of sound to be 340 m/s. What frequency do you hear?
F = ((V+Vr) / (V+Vs)) * Fo.
V = 120000m/h * (1/3600)h/s = 33.33m/s.
F=((340+33.33) / (340+0))*400=439.2Hz.
To determine the frequency you hear from the stationary train's whistle, we need to consider the Doppler effect. The Doppler effect is the change in frequency or wavelength of a sound wave caused by the relative motion between the source of the wave and the observer.
In this scenario, you are the observer moving towards the stationary train. The formula to calculate the observed frequency is given by:
f' = (v + vo) / (v + vs) * f
Where:
f' is the observed frequency (the frequency you hear)
f is the source frequency (the whistle's frequency)
v is the speed of sound (given as 340 m/s)
vo is the velocity of the observer (your velocity)
vs is the velocity of the source (the train's velocity)
Given that your velocity (vo) is 120 km/h and the speed of sound (v) is 340 m/s, we need to convert your velocity to m/s.
1 km/h = 1000 m/3600 s ≈ 0.2778 m/s
So, your velocity (vo) is:
vo = 120 km/h * 0.2778 m/s = 33.333 m/s
Since the train is stationary, its velocity (vs) is 0 m/s.
Now, we can substitute the values into the formula to find the observed frequency (f'):
f' = (v + vo) / (v + vs) * f
f' = (340 m/s + 33.333 m/s) / (340 m/s + 0 m/s) * 400 Hz
Calculating this expression will give us the observed frequency.
To find the frequency that you hear, we need to consider the Doppler effect. The Doppler effect describes the change in frequency of a wave, such as sound, as the source and/or observer moves relative to each other.
In this scenario, you are moving towards the stationary train. As you move towards the train, the sound waves emitted by the train are compressed, leading to a higher frequency being heard.
The formula for the observed frequency in the case of the Doppler effect when the source of the sound is moving towards the observer is:
f' = (v + vr) / (v + vs) * f
Where:
- f' is the observed frequency
- v is the speed of sound
- vr is the velocity of the moving observer (you)
- vs is the velocity of the source (train)
- f is the frequency of the source (train whistle)
Given:
- Speed of sound (v) = 340 m/s
- Your velocity (vr) = 120 km/h towards the train = 120,000 m/3,600 s = 33.3 m/s (convert km/h to m/s)
- Train's velocity (vs) = 0 m/s (stationary train)
- Train's frequency (f) = 400 Hz
Now we can substitute these values into the formula to find the observed frequency (f'):
f' = (v + vr) / (v + vs) * f
f' = (340 + 33.3) / (340 + 0) * 400
f' = 373.3 / 340 * 400
f' = 437.35 Hz
So, the frequency that you hear from the train's whistle is approximately 437.35 Hz.