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A Jet Engine Emits a Whine of Frequency 3000 Hz. When the Engine Is Moving Directly Away from the Observer at Half the Speed of Sound

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A jet engine emits a whine of frequency 3000 Hz. When the engine is moving directly away from the observer at half the speed of sound The value of abcd is __ __ __ __ observer can be expressed as a.bctimes 10^dHz (v_(sound)=340m/s) engine directly away 1. An ocean wave has a wavelength of 10.0 m. Two wave crests passes by a point near a dock every 9.005. Determine the/speed of the wave The tip of a helicopter blade was measured to be traveling at 130m/s. Each blade is measured to be 6.5m long from the center. What would the frequency of the blades be?

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Answer

Here's the solution:**1. Doppler Effect for the Jet Engine:*** **Given:** * Source frequency (fs) = 3000 Hz * Source velocity (vs) = 0.5 * speed of sound (v) = 0.5 * 340 m/s = 170 m/s (moving away) * Speed of sound (v) = 340 m/s* **Formula:** When the source is moving away from the observer, the observed frequency (fo) is given by: fo = fs * (v / (v + vs))* **Calculation:** fo = 3000 Hz * (340 m/s / (340 m/s + 170 m/s)) fo = 3000 Hz * (340 / 510) fo = 3000 Hz * (2/3) fo = 2000 Hz* **Expressing in the required format:** fo = 2.00 x 10³ Hz* **Therefore:** a=2, b=0, c=0, d=3. The value of abcd is 2003.**2. Speed of the Ocean Wave:*** **Given:** * Wavelength (λ) = 10.0 m * Period (T) = 9.00 s (time for one full wavelength to pass)* **Formula:** Wave speed (v) = Wavelength (λ) / Period (T)* **Calculation:** v = 10.0 m / 9.00 s v ≈ 1.11 m/s* **Answer:** The speed of the wave is approximately 1.11 m/s.**3. Frequency of the Helicopter Blades:*** **Given:** * Tangential speed of the blade tip (v) = 130 m/s * Length of the blade (radius, r) = 6.5 m* **Concept:** The tip of the helicopter blade travels in a circular path. The tangential speed is related to the rotational speed (angular frequency, ω) by: v = ωr* **Calculation:** * First, find the angular frequency (ω): ω = v / r = 130 m/s / 6.5 m ≈ 20 rad/s * Then, convert angular frequency (ω) to frequency (f): f = ω / 2π ≈ 20 rad/s / (2 * 3.14) ≈ 3.18 Hz* **Answer:** The frequency of the helicopter blades is approximately 3.18 Hz.