A stationary motion detector sends sound waves of frequency 0.0953 MHz toward a truck approaching at a speed of 42.6 m/s. What is the frequency of the waves reflected back to the detector? (Take the speed of sound to be 343 m/s.)
Fr = ((Vs+Vt)/(Vs-Vd))*Fd
Fr = ((343+42.6)/(343-0))*95300Hz =
107,136 Hz = Freq. reflected.
To solve this problem, we can use the concept of the Doppler effect. The Doppler effect describes the change in frequency of a wave due to the relative motion between the source of the wave and the observer.
The frequency observed by the stationary motion detector can be calculated using the equation:
f' = f * (v + vd) / (v + vs)
Where:
f' is the observed frequency
f is the frequency of the waves emitted (0.0953 MHz)
v is the speed of sound (343 m/s)
vd is the velocity of the detector (0 m/s because it is stationary)
vs is the velocity of the source (42.6 m/s away)
Plugging in the values:
f' = 0.0953 MHz * (343 m/s + 0 m/s) / (343 m/s + 42.6 m/s)
Simplifying:
f' = 0.0953 MHz * 343 m/s / 385.6 m/s
f' = 0.0863 MHz
Therefore, the frequency of the waves reflected back to the detector is 0.0863 MHz.
To find the frequency of the waves reflected back to the detector, we need to consider the Doppler effect.
The Doppler effect is the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave. In this case, the observer is the stationary motion detector and the source is the truck.
The formula to calculate the observed frequency due to the Doppler effect is:
f' = (v + vr) / (v + vs) * f
Where:
f' is the observed frequency
f is the frequency of the source
v is the speed of sound
vr is the velocity of the receiver (motion detector)
vs is the velocity of the source (truck)
Given:
Frequency of the source, f = 0.0953 MHz (0.0953 x 10^6 Hz)
Speed of sound, v = 343 m/s
Velocity of the receiver (motion detector), vr = 0 m/s (stationary)
Velocity of the source (truck), vs = 42.6 m/s (approaching)
Plugging these values into the formula, we can calculate the observed frequency:
f' = (v + vr) / (v + vs) * f
f' = (343 m/s + 0 m/s) / (343 m/s + 42.6 m/s) * (0.0953 x 10^6 Hz)
f' = 343 m/s / 385.6 m/s * (0.0953 x 10^6 Hz)
f' = 0.8888 * (0.0953 x 10^6 Hz)
f' = 0.0847 x 10^6 Hz
Therefore, the frequency of the sound waves reflected back to the detector is approximately 0.0847 MHz.