How to Calculate Frequency Changes Due to Motion of a Bus?

When a bus is in motion and a student is standing near a bus stop, the frequency of a horn beep heard by the student can change depending on the bus's motion relative to the student's position. There are three cases to consider:

Case 1: When the bus is crossing the student, the student will hear the same frequency emitted by the horn.

Case 2: When the bus is approaching the student, the frequency heard by the student will be less than the original frequency of the horn.

Case 3: When the bus is moving away from the student, the frequency heard by the student will be more than the original frequency of the horn.

Understanding Frequency Changes Due to Motion:

When a bus is in motion, the frequency of a horn beep can change based on the speed of the bus, speed of sound, and the relative motion between the bus and the student.

In the scenario provided, where the frequency emitted by the horn is 440 Hz, the speed of sound is 330 m/s, and the speed of the bus is 20 m/s, we can calculate the frequency heard by the student in each case:

Case 1: When the bus is crossing the student:

In this case, the student will hear the same frequency emitted by the horn, which is 440 Hz.

Case 2: When the bus is approaching the student:

We can calculate the frequency using the formula:
f = f₀ ( v / v+v₀ )
f = 440 ( 330/ 330+20 )
f = 440 ( 330/ 350 )
f = 440 ( 0.943 )
f = 414.9 Hz

Case 3: When the bus is moving away from the student:

We can calculate the frequency using the formula:
f = f₀ ( v / v-v₀ )
f = 440 ( 330/ 330-20 )
f = 440 ( 330/ 310 )
f = 440 ( 1.0645 )
f = 468.4 Hz

Therefore, the frequency heard by the student varies in each case based on the motion of the bus relative to the student's position.