As you stand near a railroad track, a train passes by at a speed of 33.5 m/s while sounding its horn at a frequency of 219 Hz. What frequency do you hear as the train approaches you? What frequency do you hear while it recedes? Use 344 m/s for the speed of sound in air.
Properties of sound
A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).
Quality Of Sound
A sound or a sound wave is defined as the energy produced due to the vibrations of particles in a medium. When any medium produces a disturbance or vibrations, it causes a movement in the air particles which produces sound waves. Molecules in the air vibrate about a certain average position and create compressions and rarefactions. This is called pitch which is defined as the frequency of sound. The frequency is defined as the number of oscillations in pressure per second.
Categories of Sound Wave
People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.
![**Title: Understanding the Doppler Effect in Sound Waves**
**Introduction**
As you stand near a railroad track, a train passes by at a speed of 33.5 m/s while sounding its horn at a frequency of 219 Hz. To understand how the perceived frequency of sound changes with motion, we can analyze the situation using the Doppler Effect. This effect describes the change in frequency or wavelength of a wave in relation to an observer moving relative to the source of the wave.
**Problem Statement**
- **Given:**
- Speed of the train: 33.5 m/s
- Frequency of the train horn: 219 Hz
- Speed of sound in air: 344 m/s
**Questions:**
1. What frequency do you hear as the train approaches you?
2. What frequency do you hear while it recedes?
**Solution:**
**Approaching Frequency:**
Using the Doppler Effect formula for a source approaching a stationary observer:
\[ f' = f \left(\frac{v + v_0}{v - v_s}\right) \]
Where:
- \( f' \) = observed frequency
- \( f \) = source frequency (219 Hz)
- \( v \) = speed of sound in air (344 m/s)
- \( v_0 \) = speed of observer (0 m/s, since the observer is stationary)
- \( v_s \) = speed of the source (33.5 m/s)
**Receding Frequency:**
Using the Doppler Effect formula for a source moving away from a stationary observer:
\[ f' = f \left(\frac{v - v_0}{v + v_s}\right) \]
**Interactive Examples and Calculation Tool:**
Provide a tool to allow students to input different speeds and frequencies to observe changes in perceived sound frequency.
**Conclusion:**
By applying the Doppler Effect equations, students can calculate the changes in frequency perceived as the train approaches and recedes. This example illustrates the practical application of sound wave physics in a real-world scenario.
**Exercises:**
1. Calculate the frequency heard when the train is at different speeds.
2. Discuss how this principle applies to other everyday situations, such as ambulance sirens or passing cars.
**Additional Resources:**
Links to simulations or videos on the Doppler Effect for further study.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6dbc0877-d53f-4c9c-9eec-5fc7749c806c%2F096c2dc2-689d-41ce-9d82-93d666845c2b%2Fds6fx4p_processed.jpeg&w=3840&q=75)
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