A railroad train is traveling at 30.0 m>s in still air. The frequency of the note emitted by the train whistle is 352 Hz. What frequency is heard by a passenger on a train moving in the opposite direction to the first at 18.0 m>s and(b) receding from the first?

Verified step by step guidance

1. Step 1: Identify the given values. The speed of the source train (v_s) is 30.0 m/s, the speed of the observer train (v_o) is 18.0 m/s, and the frequency of the whistle (f_s) is 352 Hz.
2. Step 2: Use the Doppler Effect formula for sound when both the source and the observer are moving. The formula is f_o = f_s * (v + v_o) / (v - v_s), where v is the speed of sound in air (approximately 343 m/s at 20°C).
3. Step 3: Calculate the frequency heard by the passenger when the observer train is moving towards the source train. Substitute v_o with -18.0 m/s (since it's moving towards the source) into the Doppler Effect formula.
4. Step 4: Calculate the frequency heard by the passenger when the observer train is moving away from the source train. Substitute v_o with +18.0 m/s (since it's moving away from the source) into the Doppler Effect formula.
5. Step 5: Evaluate the results from steps 3 and 4 to understand how the relative motion of the source and the observer affects the perceived frequency of the sound.

Key Concepts

Doppler Effect

The Doppler Effect is 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 towards an observer, the frequency increases, resulting in a higher pitch. Conversely, if the source moves away, the frequency decreases, leading to a lower pitch. This effect is crucial for understanding how the frequency of the train whistle changes for the passenger.

Relative Velocity

Relative velocity refers to the velocity of one object as observed from another object. In this scenario, the velocities of the train and the passenger must be considered in relation to each other to determine the effective speed at which sound waves travel between them. This concept is essential for calculating the observed frequency of the whistle as it accounts for the motion of both the source and the observer.

Sound Wave Propagation

Sound waves propagate through a medium, such as air, at a speed that is influenced by factors like temperature and pressure. In this problem, the speed of sound in still air is assumed to be constant, allowing us to apply the Doppler Effect equations. Understanding how sound waves travel and how their speed is affected by the motion of the source and observer is vital for accurately determining the frequency heard by the passenger.