How fast is a car moving and in what direction if the frequency of the horn drops from 900 Hz to 875 Hz, as heard by a stationary listener? The air temperature is 0oC.

How to solve? I have no idea...

the frequency is lower, so the car is moving away from the listener

875/900 = (speed of sound) /
... (speed of sound + speed of car)

they give you the temperature so that you can find the speed of sound (in air)

To solve this question, we can use the Doppler effect formula for sound:

Δf/f = (v/(v±vs)),

where:
Δf is the change in frequency (875 Hz - 900 Hz = -25 Hz),
f is the original frequency (900 Hz),
v is the speed of sound in air,
vs is the speed of the source relative to the medium (in this case, the car).

First, we need the speed of sound in air at 0°C. The formula to calculate this is:

v = 331.4 + (0.6 × T),

where T is the temperature in degrees Celsius.

Substituting T = 0°C into the formula, we get:

v = 331.4 + (0.6 × 0),
v = 331.4 m/s.

Now we can rearrange the Doppler equation to solve for vs:

-Δf/f = (v/(v±vs)).

Substituting the given values, we get:

-25/900 = (331.4/(331.4±vs)).

We can solve for both possibilities:

1. 331.4 + vs:

-25/900 = (331.4/(331.4 + vs)).

Cross-multiplying, we get:

-25 × (331.4 + vs) = 900 × 331.4.

Simplifying the equation, we get:

vs = - 20.13 m/s.

2. 331.4 - vs:

-25/900 = (331.4/(331.4 - vs)).

Cross-multiplying, we get:

-25 × (331.4 - vs) = 900 × 331.4.

Simplifying the equation, we get:

vs = 19.67 m/s.

Therefore, the car is either moving at -20.13 m/s (towards the stationary listener) or +19.67 m/s (away from the stationary listener). The negative sign indicates that the car is moving towards the stationary listener

To solve this problem, we can use the Doppler effect equation, which relates the observed frequency of a sound to the relative velocity between the source of the sound and the observer.

The equation for the Doppler effect is given by:

f' = (v + vo) / (v + vs) * f,

where:
- f' is the observed frequency (in Hz),
- v is the speed of sound in air at the given temperature (which can be found using a reference table or formula),
- vo is the velocity of the observer (in this case, zero since the listener is stationary),
- vs is the velocity of the source (which is the unknown we want to find),
- f is the original frequency of the source (in Hz).

In this scenario, we know the observed frequency f' (875 Hz), the original frequency f (900 Hz), and the air temperature (0°C), which can be used to find the speed of sound in air.

To find the speed of sound in air:
- Look up a reference table that provides the speed of sound in air at different temperatures, or
- Use the formula: v = 331.45 + 0.6T, where T is the temperature in Celsius. For 0°C, the speed of sound would be v = 331.45 + 0.6 * 0 = 331.45 m/s.

Now, substitute the known values into the Doppler effect equation:

875 Hz = (331.45 m/s) / (331.45 m/s + vs) * 900 Hz.

Simplifying this equation will allow us to solve for vs, the velocity of the source.

To solve for vs:
1. Multiply both sides of the equation by (331.45 m/s + vs) and then divide both sides by 900 Hz.
2. Rearrange the equation to isolate vs.

Once you solve for vs, you will have the velocity of the car (source) relative to the stationary listener. The direction of the car's movement can be determined by comparing the frequency change to the original frequency. In this case, since the frequency drops, the car is moving away from the listener.

would the answer be approx. 9.4557m/s?

cz on the document it says the answer should be 4.68m/s