A stationary observer hears a sound with a frequency of 450 Hz from an approaching car. If the car emits the sound at a frequency of 360 Hz, what would be the speed of the car? (Speed of sound 340 m/s)
using doppler equation:f2=f1[Vw/(Vw-Vs)] where f2=450hz f1=360hz Vw=340m/s Vs=? 450=360(340/340-vs) 1.25(340-vs)=340 340-vs=272 vs=68m/s
To calculate the speed of the car, we can use the concept of the Doppler effect. The Doppler effect describes the change in frequency of a wave (in this case, sound) as perceived by an observer when there is relative motion between the source of the sound and the observer.
In this scenario, the observer hears a sound with a frequency of 450 Hz coming from an approaching car. We also know that the car emits the sound at a frequency of 360 Hz. Based on this information, we can use the Doppler effect equation for sound:
f observed = f source * (v + v observer) / (v + v source)
Where:
f observed is the observed frequency
f source is the original frequency emitted by the source
v is the speed of sound
v observer is the velocity of the observer relative to the medium (in this case, stationary)
v source is the velocity of the source relative to the medium
By substituting the given values, we get:
450 Hz = 360 Hz * (340 m/s + 0) / (340 m/s + v source)
Now, we can rearrange the equation to solve for v source, the velocity of the car:
v source = (450 Hz / 360 Hz - 1) * 340 m/s
v source ≈ 77.22 m/s
Therefore, the approximate speed of the car is 77.22 m/s.