The Doppler Effect

Classroom example!

What is The Doppler Effect?

• A phenomenon explaining that if there is relative motion between a sound source and a receiver, the received frequency will differ from that of the source.

• Example: As an ambulance (with siren) approaches a stationary observer, this observer will hear higher frequencies of sound than if the ambulance were moving away from the observer

How does this work?

The figure above demonstrates that when a car approaches a receiver, the wavelength of sound waves decreases.

How does the work (part 2)

• At constant temperatures, the speed of sound in air (air is the medium in our environment) is constant as well.

• Recall that wavespeed= frequency*wavelength

• For wavespeed to remain constant, a decrease in wavelength (as shown in figure on slide 3) is accompanied by an increase in frequency

• This explains why we receive higher sound frequencies when an ambulance approaches us, compared to when the ambulance is stationary!

Important Formula/Variables

freceived = n±vreceivern±vsource

fsourceRemember: The speed of sound in air (denoted by v in the formula) is approximately 343 m/s

Also, something that is stationary has no speed. For instance, if the receiver is not moving, vreceiver=0

Instead of memorizing when to add or subtract speed, let’s think about it conceptually. When the distance between the source and the receiver is increasing, freceived should decrease. On the other hand, if the distance between them is decreasing, freceived should increase.

Applied Problem

In Dr. Ives’ lecture, you raise your hand to ask a question (while sitting still). Dr. Ives walks towards you at a speed of 1.4 m/s to hand you the microphone. However, as he walks towards you, you realize that you don’t want to ask a question anymore. You want to speak up to tell him that you don’t need the microphone. However, Dr. Ives can only perceive frequencies greater than 20 Hz. At what wavelength do you need your soundwaves to be for him to hear you?

Assume a constant temperature environment

Hints

• Hint 1: Are both the receiver and the source moving? If not, who is stationary?

• Hint 2: Try to find frequency first

• Hint 3: At constant temperature, is there a way to relate sound wave speed to frequency and wavelength?

Solutions (Part 1)

Solutions (Part 2)

Adding Vs Subtracting

• You might notice that I added the Dr. Ives’ walking speed as opposed to subtracting it from 343 m/s. I did so because he is walking TOWARDS the source.

• When the distance between the source and receiver is shortening, more waves can reach the receiver each second.

• If you refer back to slide 5, when adding the receiver’s speed, received frequency increases. This is precisely what happens when a receiver walks towards a sound source.

Ask yourself: Does the answer make sense?

• The first part of the answer says that fs must be greater than 19.919 Hz. This makes sense, because since Dr. Ives is walking towards the source, the source doesn’t need as much frequency to have a receiver frequency greater than 20Hz.

• The second part of the answer states that wavelength must be less than 17.2197 m. This makes sense because wavelength and frequency have an inverse relationship. If frequency must be greater than a value, wavelength must be less than another value.

Word Cited

• Physics textbook (for equations and concepts)

Physics for Scientists and Engineers: An Interactive Approach

- ”Doppler Shift Formula.” Doppler shift formula. Web. 01 Mar. 2015.