Car A and Car B approach each other
on the same road. Car A is driving
35.0 m/s, while Car B is driving
15.0 m/s. When Car A honks its horn,
Car B hears a frequency of 1140 Hz.
What is the frequency of Car A's horn
when stationary?
(Hint: 1140 Hz is the Doppler-shifted frequency.).
(Speed of sound = 343 m/s)
(Unit = Hz)

The original frequency of horn of Car A is 1071 Hz.

Explanation:

Doppler effect describes the change in the frequency of sound waves with respect to the observer. As the sound waves emitted from a source need to travel the air medium to reach observer, it will undergo loss in energy. So there will be change in its frequency compared to original frequency. Depending upon the direction of travel of source and observer the shifting of frequency will vary.

Here vo is the observer velocity and vs is the velocity of the source. So Vo = 15 m/s as car B is the observer and Vs = 35 m/s as car A is the source. And f is the frequency of sound wave at source that is car A.

Similarly, the doppler shift in frequency is the frequency of sound heard by car B which is f' = 1140 Hz. And v is the speed of sound that is v = 343 m/s

1140 =

f = 1140/1.0649= 1071 Hz.

Thus, the original frequency of horn of Car A is 1071 Hz.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .