Ch 16: Sound & Hearing

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 16: Sound & Hearing

Problem 46b

Chapter 16, Problem 46b

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 receding from the first?

Verified step by step guidance

Identify the problem as a Doppler effect scenario, where the frequency of a sound changes due to the relative motion between the source and the observer.

Use the Doppler effect formula for sound: \( f' = f \frac{v + v_o}{v + v_s} \), where \( f' \) is the observed frequency, \( f \) is the source frequency, \( v \) is the speed of sound in air (approximately 343 m/s at room temperature), \( v_o \) is the speed of the observer, and \( v_s \) is the speed of the source.

For part (a), where the observer is moving towards the source, set \( v_o = 18.0 \text{ m/s} \) and \( v_s = 30.0 \text{ m/s} \). Substitute these values into the formula: \( f' = 352 \text{ Hz} \times \frac{343 + 18}{343 - 30} \).

For part (b), where the observer is receding from the source, set \( v_o = -18.0 \text{ m/s} \) (since the observer is moving away) and \( v_s = 30.0 \text{ m/s} \). Substitute these values into the formula: \( f' = 352 \text{ Hz} \times \frac{343 - 18}{343 - 30} \).

Calculate the observed frequencies for both scenarios using the substituted values in the Doppler effect formula to find the frequencies heard by the passenger in each case.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Doppler Effect

The Doppler Effect describes the change in frequency or wavelength of a wave in relation to an observer moving relative to the wave source. In this scenario, the frequency of the train whistle changes as perceived by a passenger on another train moving in the opposite direction, due to their relative motion.

Relative Velocity

Relative velocity is the velocity of an object as observed from a particular reference frame, and it is crucial for calculating the perceived frequency in the Doppler Effect. Here, the relative velocity between the two trains affects the frequency heard by the passenger, as it determines the rate at which the distance between the source and observer changes.

Wave Frequency

Wave frequency refers to the number of oscillations or cycles per unit time, measured in Hertz (Hz). The original frequency of the train whistle is 352 Hz, and understanding how this frequency is altered by the Doppler Effect due to the relative motion of the trains is essential for solving the problem.

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Textbook Question

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 approaching the first?

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The siren of a fire engine that is driving northward at 30.0 m/s emits a sound of frequency 2000 Hz. A truck in front of this fire engine is moving northward at 20.0 m/s. (a) What is the frequency of the siren's sound that the fire engine's driver hears reflected from the back of the truck?

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