A friend of yours is loudly singing a single note at 400 Hz while racing toward you at 25.0 m/s on a day when the speed of sound is 340 m/s. a. What frequency do you hear?

Key Concepts

Doppler Effect

The Doppler Effect describes the change in frequency or wavelength of a wave in relation to an observer moving relative to the source of the wave. When the source of sound moves toward an observer, the frequency increases, leading to a higher pitch, while it decreases when moving away. This phenomenon is crucial for understanding how the frequency of sound changes based on the relative motion of the source and the observer.

Frequency and Wavelength

Frequency is the number of cycles of a wave that pass a point in one second, measured in Hertz (Hz). Wavelength is the distance between successive crests of a wave. The relationship between frequency and wavelength is inversely proportional; as frequency increases, wavelength decreases. This concept is essential for calculating the perceived frequency when the source is in motion.

Speed of Sound

The speed of sound is the rate at which sound waves propagate through a medium, typically air, water, or solids. At 340 m/s in air at room temperature, this speed can vary based on factors like temperature and humidity. Understanding the speed of sound is vital for applying the Doppler Effect, as it helps determine how the motion of the source and observer affects the frequency heard.