1. A train whistle has a frequency of 1000 Hz. If the train is speeding
at a velocity of 60 km/h past a stationary railroad crossing
attendant, what is the apparent frequency a) as the train approaches him, b) as it moves away from him?
Assume speed of sound to be 350 m/s.
2. A second train is approaching the first train (above) with a speed of
60 km/h. Obtain the frequency of the whistle of the first as heard by
the engineer of the second train.
3. Sound is reflected by a screen moving with a speed 20 km/h toward
the source and observer. If the frequency of the source is 450 khz,
what is the apparent frequency of the reflected sound?
Help me solve these questions
Sure! I can help you solve these questions. Let's start with the first one:
1. Apparent frequency as the train approaches the railroad crossing attendant:
To calculate the apparent frequency, we need to take into account the Doppler effect. The formula for Doppler effect when the source is in motion and the observer is stationary is:
f' = f * (v+u)/(v),
where f' is the apparent frequency, f is the actual frequency, v is the speed of sound, and u is the speed of the source. In this case, the speed of sound is given as 350 m/s and the speed of the train is 60 km/h.
First, we need to convert the speed of the train from km/h to m/s:
60 km/h = (60 * 1000 m) / (3600 s) = 16.67 m/s.
Now we can substitute the values into the formula:
f' = 1000 Hz * (350 m/s + 16.67 m/s) / 350 m/s.
Calculating this, the apparent frequency as the train approaches the attendant is f' ≈ 1048.34 Hz.
2. Apparent frequency as the train moves away from the railroad crossing attendant:
Using the same formula as before, but this time the observer (railroad crossing attendant) is moving instead of the source. The formula becomes:
f' = f * (v)/(v-u),
where u is now the speed of the observer.
Using the given values, the speed of sound is still 350 m/s, and the speed of the train is -16.67 m/s (negative because it is moving away).
Now we can substitute the values into the formula:
f' = 1000 Hz * (350 m/s) / (350 m/s - (-16.67 m/s)).
Calculating this, the apparent frequency as the train moves away from the attendant is f' ≈ 951.52 Hz.
Now let's move on to the second question:
2. Frequency of the whistle of the first train as heard by the engineer of the second train:
Here, both the source and the observer are in motion, so we'll use the formula:
f' = f * (v + u)/(v - v2),
where u is the speed of the first train and v2 is the speed of the second train.
The speed of sound is still 350 m/s, and the speed of the first train is 60 km/h (converted to m/s as 16.67 m/s). The speed of the second train is also given as 60 km/h, so it's also 16.67 m/s.
Now we can substitute the values into the formula:
f' = 1000 Hz * (350 m/s + 16.67 m/s)/(350 m/s - 16.67 m/s).
Calculating this, the frequency of the whistle of the first train as heard by the engineer of the second train is f' ≈ 1111.11 Hz.
Finally, let's solve the third question:
3. Apparent frequency of the reflected sound:
In this case, the source and observer are stationary, but the screen is moving with a speed of 20 km/h towards both the source and the observer.
Using the formula for Doppler effect when the observer is stationary and the source is approaching, we get:
f' = f * (v + u)/(v),
where u is the speed of the screen.
The frequency of the source is given as 450 kHz (converted to 450,000 Hz), and the speed of sound is still 350 m/s. The speed of the screen is 20 km/h, which we convert to 5.56 m/s.
Now we can substitute the values into the formula:
f' = 450,000 Hz * (350 m/s + 5.56 m/s)/(350 m/s).
Calculating this, the apparent frequency of the reflected sound is f' ≈ 455,161.29 Hz.
I hope this explanation helps you understand how to solve these types of questions! Let me know if you have any more questions.