Question

Can anyone just check my answers and tell me if correct or not. If I’m incorrect, please tell me the correct answers...

On a windless day, train A is traveling down a grade at 50 m/s and passes train B, which is moving up the grade at half that speed. After the trains pass, train A blows it’s 300 Hz whistle. What frequency is heard by a passenger on train B.
312 Hz
435 Hz
243 Hz(my choice)
186 Hz
A police officer parked at the curb turns on his lights and siren, waits for traffic to clear, then pulls out and heads down the street. For an observer down the street, which is true?
The frequency of the siren is higher and the wavelength is shorter than it was at first.
The wavelength of the siren is shorter than it was at first, but the frequency is the same(my choice)
The wavelength of the siren is shorter and the frequency is lower than it was at first.
The frequency of the siren is higher than it was at first, but the wavelength is the same

Answer 1

Part 1

Your choice of 243Hz for the first part is correct. The frequency perceived by a passenger on train B is:

`f_B=((343-25)(m)/(s))/((343+50)(m)/(s))\cdot 300 Hz \approx 242.75Hz`

Part 2

Your choice in the second part is not correct - you are right to say the wavelength is shorter, but the frequency cannot be the same. In fact Frequency (f) and wavelength (lambda) are indirectly proportional (with v the speed of sound):

`f = (v)/(\lambda)`

So when the wavelength of the siren is shorter, the frequency must be higher. Therefore the answer "The frequency of the siren is higher and the wavelength is shorter than it was at first." is the correct choice

Answer 2

The frequency heard by a passenger on train B is 243 Hz. Your choice is correct.

"The frequency of the siren is higher and the wavelength is shorter than it was at first" is the correct choice

Step-by-step explanation:

The Doppler effect is defined as the change in apparent frequency of a wave produced by the relative movement of the source with respect to its observer. In other words, this effect is the change in the perceived frequency of any wave movement when the sender and the receiver, or observer, move relative to each other.

This is what happens in the first part of this problem, where the transmitter is train A and the receiver is train B. Both are moving in opposite directions. In this case, where both are in motion, the frequency perceived by the receiver will increase when the receiver and sender increase their separation distance and will decrease whenever the separation distance between them is reduced. The following expression is considered the general case of the Doppler effect:

`f'=f*(v+-vR)/(v-+vE)`

Where:

f ’, f: Frequency perceived by the receiver and frequency emitted by the transmitter respectively. Its unit of measurement in the International System (S.I.) is hertz (Hz), which is the inverse unit of the second (1 Hz = 1 s⁻¹)

v: Speed ​​of propagation of the wave in the middle. It is constant and depends on the characteristics of the medium. In this case it is considered that the speed of sound in the air is 343 m / s

vR, vE: Speed ​​of the receiver and the transmitter respectively. Your unit of measure in the S.I. is the m / s

±, ∓:

• The + sign is used if:

In the numerator if the receiver approaches the sender

In the denominator if the sender moves away from the receiver

• The sign is used - if:

In the numerator if the receiver moves away from the sender

In the denominator if the sender approaches the receiver

In that case the receiver moves away from the transmitter because train B climbs the grade while train A descends the grade.Then in the numerator the sign will be - and in the denominator it will be +.

And considering that:

• v=343 m/s
• vE= 50 m/s
• vR= 25 m/s because the train B is moving up the grade at half that speed of the train A (vE), which is 50 m/s
• f=300 Hz

`f'=300Hz*(343 (m)/(s) -25 (m)/(s) )/(343 (m)/(s) +50 (m)/(s) )`

f'=242.75 Hz≅243 Hz

Then the frequency heard by a passenger on train B is 243 Hz. Your choice is correct.

The doppler effect indicates that if a source of waves, in this case the police officer with the siren on, approaches an observer, in this case the observer down the street, the frequency of the waves that the effect measures is greater than the which the emitter measures. In short, the observer located down the street in front of the transmitter measures a frequency of reception greater than that of emission. So, the frequency of the siren is higher.

On the other hand, the propagation speed is the speed with which the wave propagates in the middle. Relate wavelength (λ) and frequency (f) inversely proportionally using the following equation:

v = f * λ.

Expressed in another way:

f = v / λ

This indicates that the frequency and wavelength are inversely proportional. Then, as in this case the frequency increases, the wavelength will decrease, v being constant whose value is the speed of sound (343 m / s)

Finally, "The frequency of the siren is higher and the wavelength is shorter than it was at first" is the correct choice