Question
3. A source emitting a sound at 300.0 Hz is moving toward an observer at 25m/s The air temperature is 15^circ C What is the frequency detected by the observer? K/U
Solution
3.9
(127 Votes)
Lyle
Master · Tutor for 5 years
Answer
Here's how to calculate the frequency detected by the observer:**1. Determine the speed of sound in air:**The speed of sound in air is temperature-dependent and can be calculated using the formula:v = 331 m/s + (0.6 m/s/°C) * TWhere:* v is the speed of sound* T is the air temperature in CelsiusIn this case, T = 15°C, so:v = 331 m/s + (0.6 m/s/°C) * 15°C = 340 m/s**2. Apply the Doppler effect formula:**The Doppler effect formula for a moving source and a stationary observer is:f' = f * (v / (v - vs))Where:* f' is the observed frequency* f is the source frequency* v is the speed of sound* vs is the speed of the source (positive if moving towards the observer)**3. Plug in the values and solve:**f' = 300.0 Hz * (340 m/s / (340 m/s - 25 m/s))f' = 300.0 Hz * (340 m/s / 315 m/s)f' ≈ 323.8 Hz**Answer:** The frequency detected by the observer is approximately 323.8 Hz.