A whistle giving out 450hz approaches stationary observe at a speed of 33m/s. What is the frequency heard by the observer ? ( velocity of sound in air=330m/s)
The observed frequency can be calculated using the Doppler effect formula:
f' = f * (v_sound +/- v_observer) / (v_sound +/- v_source)
where:
f = original frequency of the whistle (given as 450 Hz)
v_sound = velocity of sound in air (given as 330 m/s)
v_observer = velocity of the observer (given as 33 m/s in the opposite direction)
v_source = velocity of the source (assumed to be stationary)
Plugging in the values:
f' = 450 * (330 - 33) / (330 + 0)
f' = 450 * 297 / 330
f' = 405 Hz (rounded to the nearest Hz)
Therefore, the frequency heard by the observer is 405 Hz.
To determine the frequency heard by the stationary observer, we can use the formula for the Doppler effect:
f' = (v + v₀) / (v + vs) * f₀
Where:
f' = frequency heard by the observer
f₀ = frequency of the sound source (whistle)
v₀ = velocity of the observer (in this case, 0 m/s as the observer is stationary)
v = velocity of sound in air (330 m/s)
vs = velocity of the source (whistle) relative to the medium (air)
Given:
f₀ = 450 Hz
v₀ = 0 m/s
v = 330 m/s
vs = -33 m/s (negative because the source is approaching)
Substituting the values into the formula:
f' = (330 + 0) / (330 + (-33)) * 450
Simplifying:
f' = 330 / 297 * 450
f' = 1.1111 * 450
f' = 500 Hz
Therefore, the frequency heard by the observer is 500 Hz.