A car horn emits \(380-\mathrm{Hz}\) sound. If the car moves at \(17 \mathrm{m} / \mathrm{s}\) with its horn blasting, what frequency will a person standing in front of the car hear?

The Doppler effect is a fascinating phenomenon that occurs when there is a relative movement between a wave source and an observer. To calculate the observed frequency, which is the frequency detected by the observer, we use a specific formula that takes into account this relative movement.

When the source is moving towards the observer, the waves seem to 'compress,' and the frequency appears higher. Conversely, when the source is moving away, the waves 'stretch,' making the frequency seem lower. This change in perceived frequency is quantifiable and key to calculating the observed frequency. For a sound source moving towards a stationary observer, the formula is:
\[\begin{equation}f_o = f_s \frac{v + v_o}{v - v_s}\end{equation}\]
where,

• \(f_o\) is the observed frequency,
• \(f_s\) is the source frequency,
• \(v\) is the speed of sound in air,
• \(v_o\) is the observer's velocity, and
• \(v_s\) is the source's velocity.

In our example, by substituting the given values into our equation, we were able to calculate the frequency that a person standing in front of a moving car would hear. The calculated observed frequency is higher than the emitted frequency due to the movement of the car towards the observer.

Sound waves, like any other waves, have a frequency, which is the number of waves that pass a point in a certain period of time. The frequency of a sound wave determines its pitch; the higher the frequency, the higher the pitch. The unit of frequency is hertz (Hz), which equates to one wave per second.

The source frequency in our exercise is the frequency at which the car horn emits sound (380 Hz). This frequency is a characteristic of the sound source itself and remains constant regardless of the motion of the source, but the frequency observed by an individual can vary due to the relative motion between them and the source. It's this interplay of source frequency and relative motion that's at the heart of the Doppler effect and why the observed frequency can differ from the source frequency.

Relative motion is a core concept when discussing wave propagation, especially in the context of the Doppler effect. It refers to the movement of the wave source in relation to the observer.

When considering sound waves, if the source of the sound is moving towards you, the waves are reaching you more frequently than if the source were stationary, leading to a higher frequency or pitch. If the source moves away, it's the opposite—the waves are spread out, and the observed frequency or pitch is lower. This effect is not only observed with sound but with all types of waves, including light waves, which is why it's such a fundamental concept in wave physics.

Application in Everyday Life

Understanding the principles of relative motion in wave propagation isn't just academically interesting; it has practical implications. For example, it's applied in radar technology used by police to determine the speed of cars. It's also important in astrophysics, such as measuring the redshift of galaxies to determine their speed and distance from us. In essence, grasping this concept enriches our comprehension of not just theoretical physics but also its numerous applications in our daily lives.