A train whistle emits a sound with a frequency of 1000 Hz when standing in the station. If the same whistle is blown when it is moving away from the station at 40 mph what will be the approximate frequency someone standing at the station will hear?

You need to review the Doppler shift equations. They should be in your textbook or class notes, and are easily found onlkne.

You will also need to know the velocity of sound. Assume it is 340 m/s, which is 760 mph.

The frequency heard at the station will be less than 1000 Hz.

The answer will be about 950 Hz, but you should do the exact calculation yourself.

To determine the approximate frequency someone standing at the station will hear when the train whistle is moving away, we can use the Doppler effect equation:

\(f' = f \left( \frac{v + v_o}{v + v_s} \right)\)

Where:
- \(f\) is the original frequency of the sound emitted by the whistle (1000 Hz)
- \(f'\) is the frequency observed by the person standing at the station
- \(v\) is the speed of sound (approximately 343 m/s)
- \(v_o\) is the velocity of the observer (0 m/s, as the person standing is stationary)
- \(v_s\) is the velocity of the source (40 mph, which we will convert to m/s)

To convert 40 mph to m/s, we know that 1 mph is approximately 0.447 m/s. So, 40 mph is approximately 40 * 0.447 = 17.88 m/s.

Now we can plug in the values into the equation to find the approximate frequency observed by the person at the station:

\(f' = 1000 \left( \frac{343 + 0}{343 + 17.88} \right)\)

Calculating this expression:

\(f' = 1000 \left( \frac{343}{360.88} \right)\)

\(f' \approx 947.79 \, \text{Hz}\)

Therefore, the person standing at the station will hear an approximate frequency of 947.79 Hz when the train whistle is moving away at 40 mph.

To determine the approximate frequency someone standing at the station will hear, we can use the concept of the Doppler effect.

The Doppler effect is the change in frequency or wavelength of sound (or any wave) due to the relative motion between the source of the sound and the observer. For an observer moving towards a source of sound, the frequency appears higher, while for an observer moving away from the source, the frequency appears lower.

In this case, the train whistle emits a sound with a frequency of 1000 Hz when standing in the station. When the train is moving away from the station at 40 mph, the frequency heard by someone standing at the station will be lower than the emitted frequency.

To calculate the approximate frequency, we can use the formula:

f' = f * (v + v_o) / (v - v_s)

Where:
f' = Frequency observed by the observer (in this case, the person standing at the station)
f = Frequency emitted by the source (1000 Hz)
v = Speed of sound in air (approximately 343 meters/second)
v_o = Speed of the observer (0, as the person is standing still)
v_s = Speed of the source (40 mph = 17.88 meters/second)

Now, let's plug in the values into the formula:

f' = 1000 Hz * (343 + 0) / (343 - 17.88)

Calculating the expression:

f' ≈ 961 Hz

Therefore, someone standing at the station will hear an approximate frequency of 961 Hz.