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 (a) approaching the first

Verified step by step guidance

1. Identify the given values: speed of the first train (v_s1) = 30.0 m/s, speed of the second train (v_s2) = 18.0 m/s, frequency of the whistle (f_s) = 352 Hz, and the speed of sound in air (v) is approximately 343 m/s.
2. Understand that since the trains are moving towards each other, the relative speed of the source (first train) towards the observer (second train) is the sum of their speeds. Calculate the relative speed: v_s = v_s1 + v_s2.
3. Use the Doppler Effect formula for the frequency heard by an observer moving towards a source: f_o = f_s * (v + v_o) / (v - v_s). Here, v_o is the speed of the observer (second train) and v_s is the speed of the source (first train).
4. Substitute the values into the Doppler Effect formula: f_o = 352 Hz * (343 m/s + 18.0 m/s) / (343 m/s - (30.0 m/s + 18.0 m/s)).
5. Calculate the expression to find the frequency heard by the passenger on the second train.

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 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 phenomenon is crucial for understanding how the frequency of sound changes based on the relative motion of the source and the observer.

Relative Velocity

Relative velocity is the velocity of one object as observed from another object. In this scenario, the relative velocity between the train emitting the whistle and the passenger's train is essential for calculating the perceived frequency. The effective speed of sound waves changes based on the direction and speed of both the source and the observer, which directly influences the frequency heard by 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 focus on the relative motion of the trains. Understanding how sound waves travel and how their speed interacts with moving sources and observers is vital for accurately determining the frequency perceived by the passenger.