A state trooper chases a speeder along a straight road; both vehicles move at 160 km/h. The siren on the trooper's vehicle produces sound at frequency of 500 Hz. What is the Doppler shift in the frequency heard by the speeder?
http://en.wikipedia.org/wiki/Doppler_effect
doppler shift depends on the relative difference between the source and the receiver, in this case, no relative motion, so no doppler shift.
To calculate the Doppler shift in frequency, we need to use the formula:
Δf/f = (v/v ± vs)
Where:
Δf is the change in frequency,
f is the original frequency,
v is the speed of sound,
vs is the speed of the source of the sound.
In this case, the state trooper's vehicle is the source of the sound, so we'll use the plus sign in the formula.
Let's break down the calculation step by step:
Step 1: Convert the given speeds to m/s
Since the speed of sound is typically given in meters per second, let's convert the given speeds to m/s. We'll convert the speed of both vehicles to meters per second.
Speed of sound (v) = 343 m/s (approximately)
Speed of the vehicles = 160 km/h = 44.44 m/s (approximately)
Step 2: Calculate the Doppler shift in frequency
Let's plug the values into the formula:
Δf/f = (v/v + vs)
Δf/f = (343)/(343 + 44.44)
Now, perform the calculation:
Δf/f = 0.888
Step 3: Calculate the actual shift in frequency
To calculate the actual shift in frequency, multiply the resulting value by the original frequency. In this case, the original frequency is given as 500 Hz.
Shift in frequency = Δf * f
Shift in frequency = 0.888 * 500
Now, perform the calculation:
Shift in frequency ≈ 444 Hz
So, the Doppler shift in the frequency heard by the speeder is approximately 444 Hz.