1.
a. To find the period T, we divide the total time by the number of cycles.
T = 210 minutes / 3 classes = 70 minutes/class = 70 * 60 seconds/class = 4200 seconds/class
b. To find the period T, we divide the total time by the number of cycles.
T = 6 seconds / 5 swings = 1.2 seconds/swing
2.
a. To find the frequency f, we divide the number of cycles by the total time.
f = 210 oscillations / 5.0 seconds = 42 Hz
b. To find the frequency f, we divide the number of cycles by the total time.
f = 25 revolutions / 0.5 minutes = 50 Hz
3. The frequency heard by the train is affected by the train's velocity. We can use the formula for Doppler effect to find the new frequency:
f1 = frequency heard by the passengers still at the station = 373 Hz
v = velocity of the train = 45 m/s
v_sound = speed of sound = 343 m/s (assumed)
The formula for the Doppler effect is given by:
f2 = f1 * (v_sound / (v_sound ± v))
If the train and the sound source are moving towards each other, we use the plus sign. If they are moving away from each other, we use the minus sign. In this case, since the train is moving away from the source, we use the minus sign.
f2 = 373 Hz * (343 m/s / (343 m/s - 45 m/s))
f2 = 373 Hz * (343 m/s / 298 m/s)
f2 ≈ 429 Hz
So, the frequency heard by the train is approximately 429 Hz.
Solve each question using GRASS method.
1. Calculate the period T, in seconds (s), for the following cyclical events:
a. 3 classes every 210 minutes
b. 5 swings of a pendulum in 6 s
2. Calculate the frequency f, in hertz (Hz), for the following cyclical events:
a. 210 oscillations in 5.0 s
b. 25 revolutions of a turntable in 0.5 minute
3. As a train pulls out of the station going 45 m/s it blasts its horn, what is the frequency heard by the train if the passengers still at the station are hearing 373 Hz?
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Yes, these answers are correct.
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Apologies for the confusion in my previous response. Let's double-check the answers.
1.
a. To find the period T, we divide the total time by the number of cycles.
T = 210 minutes / 3 classes = 70 minutes/class = 70 * 60 seconds/class = 4200 seconds/class
b. To find the period T, we divide the total time by the number of cycles.
T = 6 seconds / 5 swings = 1.2 seconds/swing
2.
a. To find the frequency f, we divide the number of cycles by the total time.
f = 210 oscillations / 5.0 seconds = 42 Hz
b. To find the frequency f, we divide the number of cycles by the total time.
f = 25 revolutions / (0.5 minutes * 60 seconds/minute) = 0.83 Hz
3. To calculate the frequency heard by the train, we can use the formula for Doppler effect:
f' = f * (v_sound / (v_sound ± v))
Given:
f = 373 Hz
v = 45 m/s
v_sound = 343 m/s (assumed)
Using the minus sign since the train is moving away from the sound source:
f' = 373 Hz * (343 m/s / (343 m/s - 45 m/s))
f' ≈ 404 Hz
So, the corrected frequency heard by the train is approximately 404 Hz.
Thank you for catching the mistake, and I apologize for any confusion caused.
1.
a. To find the period T, we divide the total time by the number of cycles.
T = 210 minutes / 3 classes = 70 minutes/class = 70 * 60 seconds/class = 4200 seconds/class
b. To find the period T, we divide the total time by the number of cycles.
T = 6 seconds / 5 swings = 1.2 seconds/swing
2.
a. To find the frequency f, we divide the number of cycles by the total time.
f = 210 oscillations / 5.0 seconds = 42 Hz
b. To find the frequency f, we divide the number of cycles by the total time.
f = 25 revolutions / (0.5 minutes * 60 seconds/minute) = 0.83 Hz
3. To calculate the frequency heard by the train, we can use the formula for Doppler effect:
f' = f * (v_sound / (v_sound ± v))
Given:
f = 373 Hz
v = 45 m/s
v_sound = 343 m/s (assumed)
Using the minus sign since the train is moving away from the sound source:
f' = 373 Hz * (343 m/s / (343 m/s - 45 m/s))
f' ≈ 404 Hz
So, the corrected frequency heard by the train is approximately 404 Hz.
Thank you for catching the mistake, and I apologize for any confusion caused.
1 answer