Solve each question using grass method.

Question

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?

Answer 1

1.
a. To find the period T, we need to divide the total time by the number of events. In this case, we have 3 classes every 210 minutes.
T = 210 minutes / 3 = 70 minutes.

Since we want the period in seconds, we convert 70 minutes to seconds by multiplying by 60:
T = 70 minutes * 60 seconds/minute = 4200 seconds.

b. To find the period T, we need to divide the total time by the number of events. In this case, we have 5 swings of a pendulum in 6 seconds.
T = 6 seconds / 5 = 1.2 seconds.

2.
a. To find the frequency f, we need to divide the number of events by the total time. In this case, we have 210 oscillations in 5.0 seconds.
f = 210 oscillations / 5.0 seconds = 42 Hz.

b. To find the frequency f, we need to divide the number of events by the total time. In this case, we have 25 revolutions of a turntable in 0.5 minutes.
f = 25 revolutions / 0.5 minutes = 50 Hz.

3. The frequency heard by the train is affected by the Doppler effect. The formula for calculating the frequency heard by the train is:
f' = f * (v + v0) / (v + vs)

where f' is the frequency heard by the train, f is the frequency heard by the passengers at the station, v is the speed of sound, v0 is the speed of the train, and vs is the speed of the source (in this case, the speed of sound is not given, but it is approximately 343 m/s).

Plugging in the given values:
f' = 373 Hz * (343 m/s + 45 m/s) / (343 m/s + 0 m/s)
f' = 373 Hz * (388 m/s) / (343 m/s)
f' ≈ 420.96 Hz

So, the frequency heard by the train is approximately 420.96 Hz.

Answer 2

What is the formula used for all three questions?

Answer 3

The formula used to solve the questions in all three cases is:

Frequency (f) = 1 / Period (T)

This formula relates the frequency of a cyclical event to its period. The reciprocal of the period gives the frequency, and vice versa.

Answer 4

What formula was used for question 1?

Answer 5

For question 1, the formula used was:

T = Total time / Number of events

This formula calculates the period T (in seconds) by dividing the total time by the number of events.