Calculating Fractional Change in Frequency of Whistling Sound
How can we calculate the fractional change in the frequency of the whistling sound heard by a person as a bullet passes by?
The fractional change in the frequency of the whistling sound heard by the person as the bullet crosses is a decrease from the actual frequency to approximately 391.13 Hz.The fractional change in the frequency of the whistling sound heard by the person as the bullet passes by can be determined using the Doppler effect formula. The formula for the apparent frequency, or the frequency heard by the person, is: f' = f x (v + v_observer) / (v + v_source) Where: - f\' is the apparent frequency - f is the actual frequency of the whistling sound - v_observer is the velocity of the observer (person) - v_source is the velocity of the source (bullet) - v is the speed of sound in air In this case, the bullet is passing by the person, so the observer's velocity (v_observer) is zero. The speed of sound in air (v) is typically around 343 m/s. Using the given information: - The bullet's speed (v_source) is 220 m/s - The speed of sound in air (v) is 343 m/s We can substitute these values into the formula: f' = f x (0 + 220) / (220 + 343) Simplifying further: f' = f x 220 / 563 Now, let's assume the actual frequency of the whistling sound is f = 1000 Hz. Substituting this value: f' = 1000 x 220 / 563 Simplifying further: f' ≈ 391.13 Hz So, the apparent frequency of the whistling sound heard by the person as the bullet crosses is approximately 391.13 Hz. In conclusion, the fractional change in the frequency of the whistling sound heard by the person as the bullet crosses is a decrease from the actual frequency to approximately 391.13 Hz.