as observer travelling with a constant velocity of 20m/s passes close to a stationary source of sound and noticed that there is a change of frequency of 50Hz as he passes the source. What is the frequency of the source? (speed of sound in air=340m/s)
Fo = Freq. of observer.
Vs = Velocity of sound.
Vg = Velocity of generator or stationary source.
Vo = Velocity of observer.
To find the frequency of the source, we need to use the concept of the Doppler effect. The Doppler effect explains how the frequency of a wave changes when there is relative motion between the source of the wave and the observer.
The formula to calculate the observed frequency (f observer) when an observer is moving relative to the source is:
f observer = (v + v observer) / (v + v source) * f source
Where:
- v is the speed of sound in air (340 m/s)
- v observer is the velocity of the observer (20 m/s)
- v source is the velocity of the source (0 m/s since the source is stationary)
- f source is the frequency of the source (unknown)
Given:
- f observer - f source = change in frequency = 50 Hz
Substituting the given values into the formula, we get:
50 Hz = (340 + 20) / (340 + 0) * f source
Now, let's solve for f source:
50 Hz = 360 / 340 * f source
Divide both sides by 360/340:
50 Hz * (340/360) = f source
f source = 47.2 Hz
Therefore, the frequency of the source is approximately 47.2 Hz.
Fo = (Vs-Vo)/(Vs+Vg) * Fg = Fg-50.
(340-20)/(340+0) * Fg = Fg-50,
(320/340)* Fg = Fg - 50,
32Fg = 34Fg - 1700,
Fg = 850 Hz. = Frequency of generator or stationary source.