a truck travelling along at straight road sounds its horn, which has a frequency of 500HZ. if an observer besides the road behind the truck measures the frequency to be 480Hz ,how fast is the truck moving?assume the speed of sound in air to be 337 m/s
the frequency heard is lower so the truck is moving away from your microphone.
c = 337 m/s
https://formulas.tutorvista.com/physics/doppler-shift-formula.html
480 = 337 (500) / [337 + v]
337 + v = 337 (500/480)
337 + v = 351.04
v = 14.04 m/s
Fo = (Vs - Vo)/(Vs + Vt) * Fh = 480.
(337-0)/(337 + Vt) * 500 = 480,
Vt = 14.0 m/s = Velocity of the truck.
Fo = Freq. heard by observer.
To determine the speed of the truck, we can use the Doppler effect formula:
frequency observed / frequency emitted = (speed of sound + speed of observer) / (speed of sound + speed of source)
Given:
- Frequency emitted (f) = 500 Hz
- Frequency observed (f') = 480 Hz
- Speed of sound (v) = 337 m/s
Let's plug the values into the formula:
480 Hz / 500 Hz = (337 m/s + speed of observer) / (337 m/s + speed of source)
To simplify the equation, let's assume the observer is stationary (speed of observer = 0). With this assumption, the equation becomes:
480 Hz / 500 Hz = 337 m/s / (337 m/s + speed of source)
Let's solve for the speed of the source:
480 Hz / 500 Hz = 337 m/s / (337 m/s + speed of source)
Cross multiplying gives:
480 Hz * (337 m/s + speed of source) = 500 Hz * 337 m/s
161,760 Hz * m/s + 480 Hz * speed of source = 168,500 Hz * m/s
480 Hz * speed of source = 6,740 Hz * m/s
Dividing both sides by 480 Hz:
speed of source = 6,740 Hz * m/s / 480 Hz
speed of source = 14.04 m/s
Therefore, the truck is moving at a speed of approximately 14.04 meters per second.
To determine the speed of the truck, we can use the Doppler effect formula:
f' = f * (v + V) / (v + Vs)
Where:
f' is the measured frequency (480 Hz),
f is the original frequency (500 Hz),
v is the speed of sound in air (337 m/s),
V is the velocity of the observer (0 m/s),
Vs is the velocity of the source (the truck).
Rearranging the formula to solve for Vs:
Vs = (f - f') * (v + V) / f'
Plugging in the given values:
Vs = (500 Hz - 480 Hz) * (337 m/s + 0 m/s) / 480 Hz
= 20 Hz * 337 m/s / 480 Hz
= 14.03 m/s
Therefore, the truck is moving at a speed of approximately 14.03 m/s.