Waves - 6.1.2 Properties of Waves (GCSE Physics AQA)

Properties of Waves

Describing Wave Motion

For AQA exams, you must be able to use various terms to describe the motion of waves. These include the following:

Amplitude

The amplitude of a wave is the distance from the midpoint of the wave all the way to the crest of the wave, as shown on the diagram below. Alternatively, the amplitude of a wave can be measured as the distance from the midpoint of the wave all the way to the trough of the wave.

Therefore, the amplitude of a wave is the maximum displacement (crest or trough) of a point on a wave away from its undisturbed position (the midpoint).

Wavelength

The wavelength of the wave is the distance between two crests or two troughs of a wave. It can also be measure as the distance between a point on one wave to the same point on the next wave.

Frequency

The frequency can be measured by looking at how many complete waves go past a certain point in one second. It is measured in Hertz, Hz.

Later in this section, we will link the concept of frequency to another concept known as time period, using an equation.

Period

The ‘period’ of a wave is more commonly known as the ‘time period’. This is the amount of time it takes for a complete wave to occur.

We know that frequency is the number of waves passing a point in one second. We can use this information to find the time period of a wave in the next section.

Calculating Frequency

Formula for Frequency

We can calculate frequency of waves using the following formula.

Where:

• period, T, in seconds, s
• frequency, f, in hertz, Hz

Since the frequency is the number of waves passing a point in one second, we can work out the time period of one wave by dividing the length of time (in this case, 1 second) by the number of waves (the frequency). This will give us the time period of one single wave.

Question: A sound wave has a time period of 0.0001 seconds. What is its frequency?

1. Write out the formula.
We need to use the formula T = 1/f.

T = 1/ f

2. Substitute in the numbers.

f = 1 ÷ T
f = 1 ÷ 0.0001 s
f = 10,000 Hz

Wave Speed

Wave speed tells us how fast the wave is moving. Therefore, it also tells us how fast energy is being transferred through a substance. We can calculate the speed of different waves using the equation in the following section.

Calculating Wave Speed

Formula for Wave Speed

We can calculate speed of waves using the following formula.

Where:

• wave speed, v, in metres per second, m/s
• frequency, f, in hertz, Hz
• wavelength, λ, in metres, m

Question: What is the speed of a wave with a frequency of 100 Hz and a wavelength of 2m?

1. Write out the equation.
For this question, we need to use the equation for wave speed.

v = fλ

2. Substitute in the numbers.

v = 100 x 2
v = 200 m/s

Linking the Variables

We have just seen the equation linking wave speed (velocity), frequency and wavelength. When one of these variables changes, the other variables must also change.

For example, if the frequency increases but the wavelength stays the same, then the velocity of the wave will increase. If the frequency increases but the velocity of the wave stays the same, then the wavelength will decrease.

Measuring Speed of Sound Waves

Now that we know the formula to find wave speed, we can apply this to real life situations. For AQA exams, you need to know how to measure sound waves in air.

Method

1. Gather all the equipment. For this experiment, you’ll need two microphones, an oscilloscope, a loudspeaker and a signal generator.
2. Set up the equipment. Attach the loudspeaker to the signal generator. Note down the frequency of the signal generator. Attach each microphone to the oscilloscope in order to see the trace of the wave on the screen.
3. Separate the microphones. Move the microphones so that they appear as two separate waves on the oscilloscope.
4. Align the wavelengths. Now, move one microphone away from the other very slowly. Whilst doing this, you should look at the oscilloscope screen. As you move the microphone, the wavelengths on the screen will align with each other. You should move the microphone until the wavelengths have moved exactly one wavelength apart.
5. Measure the distance. Now that you can see that the waves have moved exactly one wavelength apart, you should measure the distance in between the microphones. This is the length of one wavelength.
6. Use the formula. Now we have measurements of wavelength and frequency, we can use the formula for wave speed.

v = fλ

The speed of sound is around 330 m/s in air.

Measuring the Speed of Water Waves

For AQA exams, you need to know how to measure the speed of ripples on the surface of water.

Method

1. Gather all the equipment. For this experiment, you’ll need a tank, some water, a stopwatch and a ruler.
2. Set up the equipment. Fill the tank with water. Measure the length of the tank and note it down.
3. Create waves on the surface. By gently using the ruler, create some ripples on the surface of the water. The direction of the ripples should be from one end of the tank to the other, covering the distance that you measured.
4. Time the waves. Once you have created the wave, start the stopwatch. Stop the stopwatch when the wave reaches the other end of the container. This is the time taken for the wave to cover the distance from one end of the container to the other.
5. Calculate the speed. Using the formula speed = distance / time, we can calculate the speed of water waves on the surface. You should repeat the experiment at least 3 times and take an average of your readings (in order to rule out anomalies).

Investigating Waves

Method

1. We can investigate waves in solids through the use of strings in the following experiment.
2. Gather all the equipment. For this experiment, you will need a frequency generator, a transducer, some string, a pulley and some masses.
3. Set up the equipment. Attach the pulley onto the edge of a desk. Place the masses onto one end of the string. This end should also rest on the pulley. Attach the other end of the string to a transducer, which in turn will be attached to the frequency generator.
4. Switch on the generator. Write down the frequency of the generator. Along with the transducer, this will make the string start to vibrate. This is also the frequency of the wave.
5. Increase the frequency. Slowly, start to increase the frequency of the generator. This will make the string start to vibrate faster, creating ‘loops’ on the string. These loops will make the shapes of the waves.
6. Measure several wavelengths. As the frequency increases, more loops will start to form. Each loop is equivalent to half a wavelength. Once there are about 5 or 6 loops (half wavelengths), measure the length of string from the start to the end.
7. Calculate one wavelength. Now we have a measurement for 5 or 6 half wavelengths, we can calculate the length of one half wavelength. To find one wavelength, we simply multiply this value by 2.
8. Use the equation. Now that we have values for both the frequency (from the generator) and the wavelength, we can use our equation v = fλ to calculate wave speed.

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