Two cars are A and B moving in same direction at a speed of 25m/s and 20m/s respectively if a both car is blowing there horn at frequency 1000hz , what frequency is heard by the driver of the cars A and car B
To determine the frequency heard by the drivers of cars A and B, we need to consider the phenomenon of Doppler effect.
The Doppler effect describes how the frequency of a sound wave changes when the source of the sound and the observer are in relative motion. The frequency heard by the observer will differ depending on whether the source is moving toward or away from the observer.
Let's break down the problem step by step:
1. Determine the relative velocity between cars A and B.
The relative velocity can be found by subtracting the velocity of car B from that of car A:
Relative velocity = Velocity of car A - Velocity of car B
= 25 m/s - 20 m/s
= 5 m/s (assuming both cars are moving in the same direction)
2. Calculate the apparent frequency heard by the driver of car A.
The observed frequency, often denoted as f' (prime), can be calculated using the following formula:
f' = (vs ± vr / vs) * f
where vs is the velocity of the source, vr is the velocity of the receiver (observer), and f is the actual frequency of the source.
In this case, the source is the horn of the car (1000 Hz), and the observer is the driver of car A. Since both cars are moving in the same direction with car A in the front, the relative velocity (vr) would be positive (+5 m/s). Thus, the formula becomes:
f' = (25 m/s + 5 m/s / 25 m/s) * 1000 Hz
= (30 / 25) * 1000 Hz
= 1.2 * 1000 Hz
= 1200 Hz
Therefore, the driver of car A will hear the frequency as 1200 Hz.
3. Calculate the apparent frequency heard by the driver of car B.
Similarly, using the same formula, we can calculate the observed frequency for the driver of car B. However, since car B is behind car A, the relative velocity (vr) would be negative (-5 m/s). Thus, the formula becomes:
f' = (20 m/s - 5 m/s / 20 m/s) * 1000 Hz
= (15 / 20) * 1000 Hz
= 0.75 * 1000 Hz
= 750 Hz
Therefore, the driver of car B will hear the frequency as 750 Hz.
In conclusion, the driver of car A will hear a frequency of 1200 Hz, while the driver of car B will hear a frequency of 750 Hz.