Chapter 16: Problem 48
(a) A sound source producing 1.00-kHz waves moves toward a stationary listener at one-half the speed of sound. What frequency will the listener hear? (b) Suppose instead that the source is stationary and the listener moves toward the source at one-half the speed of sound. What frequency does the listener hear? How does your answer compare to that in part (a)? Explain on physical grounds why the two answers differ.
Short Answer
Step by step solution
Identify the Parameters and Formula for Part (a)
Plug Values into the Formula for Part (a)
Identify the Parameters and Formula for Part (b)
Plug Values into the Formula for Part (b)
Compare and Explain the Differences
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Wave Frequency
Similar to how the beat of music changes, frequency determines the pitch of the sound you hear. A higher frequency means a higher pitch. In problems involving the Doppler Effect, like our exercise, the wave frequency is affected by the relative motion between the sound source and the listener. The source frequency in the example is 1000 Hz, where the motion will adjust the wave frequency that the listener perceives. Different scenarios, such as sources or listeners moving, change this frequency, which is key to understanding how the Doppler Effect operates.
Sound Waves
These waves are longitudinal, meaning the vibration of the particles in the medium (like air) happens in the same direction as the wave travels. As such, when the source of the sound or the listener is moving, the nature of these waves can change – this is vital when examining the Doppler Effect. By measuring these changes, we can understand shifts in perceived frequency due to movement, illustrating the dynamics between the source and listener.
Stationary Source
This means when a listener approaches the stationary source, the waves will still compress because the listener is moving toward them, increasing the frequency perceived by the listener, even though the source itself doesn't change position. This highlights the principle that relative motion affects how sound is heard. The frequency perceived by the listener in this scenario was 1500 Hz, due to their movement toward the source.
Moving Source
This compression increases the wave frequency, making the sound pitch higher. The listener perceives the frequency as 2000 Hz, which is a doubling of the original frequency due to the continued motion of the source toward the observer. This effect is more noticeable than when the listener moves, showing how the source's speed and direction directly impact the perceived sound frequency.
Moving Listener
This action increases the frequency of waves received by the listener's ears, and therefore raises the pitch of the sound. However, the increase is not as significant as when the source is the one moving. The perceived frequency in this context was 1500 Hz, which is smaller than the frequency perceived when the source was moving. This demonstrates how the Doppler Effect operates differently depending on whether the source or the listener is the one in motion.