Question

you are traveling due east at speed of 20.0m/s. a train is travelling directly toward you with a speed of 40.0m/s. the train whistle is emitting sound waves that have a frequency of 500 hz. what frequency will you hear? take the speed of sound in air to be 340m/s.

Answer 1

The frequency heard by the observer due to the Doppler Effect, with the observer moving at 20.0 m/s east and the train at 40.0 m/s towards the observer, is 600 Hz.

Step-by-step explanation:

The question involves calculating the frequency of a sound as heard by an observer when both the observer and the source of the sound are in motion relative to each other. This is a classic example of the Doppler Effect in physics.

To find the frequency that you will hear (the observer's frequency), we use the Doppler Effect formula for sound:

f' = f (v + vo) / (v - vs)

• f' is the observed frequency by you.
• f is the source frequency, which is the train whistle frequency of 500 Hz.
• v is the speed of sound in air, which is 340 m/s.
• vo is the velocity of the observer relative to the medium (air), moving toward the source at 20.0 m/s.
• vs is the velocity of the source relative to the medium (air), moving toward the observer at 40.0 m/s.

Using the formula, the observed frequency can be calculated as:

f' = 500 Hz (340 m/s + 20.0 m/s) / (340 m/s - 40.0 m/s) = 500 Hz (360 m/s / 300 m/s) = 500 Hz × 1.2 = 600 Hz

Therefore, the frequency that you will hear is 600 Hz.