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Sound Waves and Doppler Shift



Unlike light waves, sound waves are disturbances that propagate through a medium, which could be solid, gas, or liquid.

Light waves are transverse waves that have oscillations perpendicular to the direction of propagation. Whereas sound waves are longitudinal pressure waves whose oscillations are parallel to the direction of propagation.

In this video, we will explore various properties of sound waves, and learn about the Doppler Effect -- a phenomenon discovered by Austrian physicist Christian Doppler. Next, we will learn how to measure the speed of sound coming out of speakers, and how to visualize Doppler effect in the lab. Finally, we will see some examples where these concepts are applicable.

Let's begin by discussing the properties of the sound waves and the Doppler Shift phenomenon. When sound is introduced through the vibration of an object, such as a guitar string, the particles in the air experience forward and backward motion.

This creates regions in the air where particles are compressed, called compressions, or spread apart, called rarefactions. These features can be used to define the relationship between the sound waves speed and frequency.

The distance between the compressions is the wavelength, or lambda, which has the unit of meters. Frequency is the number of wavelength cycles per second and it is expressed in Hertz. The speed of sound is the product of these two qualities.

Since the sound waves travel due to compression of the particles in the medium, the density of the air molecules have an effect on the speed of the sound. The density of air depends on the surrounding's temperature, so the speed of the sound wave also depends on temperature.

Assuming the air is at a standstill, the speed of the sound wave through air can be calculated using the following equation, where Tc is the air temperature in Celsius.

If the air is moving, the speed of sound will change depending on the direction of air movement. For example, if the sound wave is moving in the opposite direction of a strong wind, the waves speed is decreased by the speed of the wind.

Now, let's look at what happens when the source of the sound is moving. Take for example, an ambulance emitting a siren at a fixed frequency, ft. As the ambulance is approaching, the perceived pitch of the siren, fr, increases until it reaches you. This is because as the siren moves towards you, the relative positions of the sound waves bunch together, and the sound appears to have a higher frequency than the transmitted frequency.

By the same logic, as the ambulance drives away, you hear the siren at a lower and lower pitch, as the sound waves spread apart and the sound appears to have a lower frequency than the transmitted frequency. The difference between the emitted and perceived frequencies at any given time is called the Doppler effect, or the Doppler shift.

Now that we've discussed the basics of sound waves and the Doppler shift, let's first take a look at how to measure the speed of sound at different frequencies. Then, we'll demonstrate how to visualize the Doppler effect using a moving apparatus.

First, set up two speakers facing one another on an optical bench. Connect one speaker to a function generator using a BNC tee, with the other side of the BNC tee connected to channel 1 or A on an oscilloscope

Then, connect the second speaker to channel 2 or B on the oscilloscope.

Turn on the function generator and oscilloscope, and adjust the dial on the function generator to produce a wave with 5 kHz frequency. The speaker connected to the function generator should produce a steady pitch that sounds like an alarm. Two 5kHz waves that are out of phase with one another, one for the emitting speaker and one for the receiving speaker should appear in different colors on the oscilloscope.

Slowly slide the speaker connected to channel B along the bench until the two waves are in phase. Then, record the distance between the two speakers.

Next, slowly slide the channel B speaker away from the emitting speaker so the waves are out of phase. Continue sliding the speaker backwards until the waves are in phase again. Record the new distance between the speakers. Repeat the experiment for 8 kHz and 3 kHz frequencies

To calculate the speed of the soundwave, first subtract the final distance from the initial to give the wavelength of the sound wave. Then, use this value and the frequency to obtain the speed. Note the inversely proportional relationship between wavelength and frequency.

Compare the experimental speeds with the expected speed using the temperature of the room. The experimental values for different frequencies appear to be approximately the same, and the difference between them and the expected value is equal to or less than one percent.

First, tie a one-meter-long piece of string to the end of a Doppler apparatus. When held at waist height, the apparatus should get close to, but not touch the floor.

Next, connect a microphone to an oscilloscope channel and place the microphone at a fixed distance --1.5 m -- from where you are standing.

Turn on the Doppler apparatus, and hold it in place 1.5 m away from the microphone. Observe the wave on the oscilloscope.

Begin swinging the apparatus around in circles at a steady speed. Those observing the swinging apparatus will notice that the pitch, or frequency, gets higher as it swings closer to them, and lower as it swings away.

Simultaneously, the oscilloscope will show more waves, or a higher frequency, when the apparatus is close to the microphone. When the apparatus is far from the microphone the frequency decreases.

Sound and sound waves are found in everyday life and are used in many areas of arts, science, and medicine.

When someone uses an open-end air column instrument, like the trumpet, the sound waves produced inside the tube create music. As air is pushed into the instrument, a vibration occurs inside that causes the pressure waves to reflect off the insides of the tube.

Only pressure waves of certain wavelengths and frequencies fit inside of the tube and resonate, creating sound. All other wavelengths and frequencies are lost.

The Doppler effect is the basis of the Doppler ultrasound instrument, which is used for vascular assessment. The handheld Doppler device consists of a probe which is placed on the patient's skin. The probe emits ultrasound waves at a specific frequency, which reflect off of the blood cells and are detected by the receiving element in the probe. The velocity of the blood flow is evident by the change in frequency of the reflected wave.

You've just watched JoVE's introduction the Doppler effect. You should now understand the basic principles of the Doppler effect, how to measure the speed of sound waves in the laboratory, and some applications of the technique in the real world. Thanks for watching!

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