Doppler Effect Analysis: A Car Approaching a Cyclist
In this article, we will explore the Doppler Effect, which describes how the frequency of a wave changes for an observer moving relative to the wave source. Specifically, we will analyze a scenario where a car traveling at 90 km/hr sounds its 512 Hz horn as it approaches a stationary cyclist. We'll calculate the frequency of the sound waves reaching the cyclist using the Doppler Effect formula and consider the effect of temperature on the speed of sound.
The Doppler Effect: A Fundamental Physics Phenomenon
The Doppler Effect is a well-known phenomenon in physics that describes the change in frequency or wavelength of a wave in relation to an observer moving relative to the wave source. This effect is not only applicable to sound but also to light and other waves. The Doppler Effect can be observed in many everyday situations, such as the changing pitch of a siren as an ambulance passes by.
Solving the Problem: Calculating the Frequency of the Sound Waves
Let's examine the given scenario—a car traveling at 90 km/hr sounding its horn as it approaches a stationary cyclist. The car horn is emitting sound at a frequency of 512 Hz, and the temperature of the air is 10 degrees Celsius.
Step 1: Convert the Speed of the Car to Meters per Second (m/s)
The speed of the car is 90 km/hr. To convert this to meters per second, we use the conversion factor 1 km/hr (frac{1000}{3600}) m/s.
Speed of the car: (90 times frac{1000}{3600} 25 , text{m/s})
Step 2: Determine the Speed of Sound in Air at 10 Degrees Celsius
The speed of sound in air depends on the temperature. At 10 degrees Celsius, the speed of sound is approximately 344 m/s.
Step 3: Apply the Doppler Effect Formula
The formula for the Doppler Effect when the source is moving toward the observer is:
(f' f times left(frac{v v_o}{v - v_s}right))
where:
(f') is the frequency observed by the cyclist (f) is the original frequency of the source (512 Hz) (v) is the speed of sound in air (344 m/s) (v_o) is the velocity of the observer (0 m/s, as the cyclist is stationary) (v_s) is the velocity of the source (25 m/s, the speed of the car)Substituting these values into the formula:
(f' 512 times left(frac{344 0}{344 - 25}right))
(f' 512 times left(frac{344}{319}right))
(f' approx 512 times 1.08)
(f' approx 551.84 , text{Hz})
Therefore, the frequency of the sound waves reaching the cyclist as the car approaches is approximately 551.84 Hz.
Understanding the Temperature Effect
The speed of sound in air also depends on the temperature. As the temperature increases, the speed of sound increases. Conversely, a decrease in temperature would slow down the speed of sound. This effect must be considered when performing accurate calculations involving the Doppler Effect in varying temperature conditions.
Conclusion
The Doppler Effect is a fascinating phenomenon that has numerous practical applications. By understanding and applying this effect, we can accurately determine how the frequency of sound waves changes as a result of the relative motion of the source and the observer. In the case of our car and cyclist scenario, the frequency of the car's horn as it approaches the cyclist is approximately 551.84 Hz, taking into account the speed of the car, the speed of sound in air, and the temperature of the environment.
Remember, mastering the Doppler Effect is not only educational but also practical, helping us to better understand various real-world phenomena and situations. Whether you're marveling at an ambulance's siren or analyzing the behavior of sound waves in different environments, the Doppler Effect is a fundamental concept worth exploring further.
References
For a more in-depth understanding of the Doppler Effect and related phenomena, you may want to refer to the following sources:
Young, H. D., Freedman, R. A. (2011). University Physics with Modern Physics. Pearson. Wikipedia contributors. (2023). Doppler Effect. Wikipedia, The Free Encyclopedia. Retrieved from _effectoldid1128335703