Wave Speed, Frequency, and Wavelength
Introduction


When the apparatus below is set up and the air is removed from the jar, it might seem quite strange to be able to see the hammer hitting the bell and not hear any sound. However, from this observation we can conclude that the longitudinal sound waves need a medium to travel through, whereas the transverse light waves do not. Earlier you will also have met the terms wavelength, frequency, amplitude, and phase, which are used to describe wave motion.



Thunder and lightning are produced simultaneously, but we always see the lightning shortly before hearing the thunder. Similarly when a sonic boom is created by an aeroplane, it appears to come from a position behind the aircraft even though it is created at the front. These observations show us that light waves travel faster than sound waves.

Speed, frequency, and wavelength
If a source is producing waves at a
frequency
The wave frequency f is the number of complete waves passing any point each second. Frequency is measured in hertz, Hz.
frequency
of 100 Hz, it is creating 100 waves per second. The time interval between peaks is therefore one hundredth of a second. In mathematical notation, if a signal source is producing continuous waves of frequency f, the time between the peak of one wave and the following peak on the following wave is given by 1/f . This time is called the
periodic time
The periodic time is the time for one repetition of an oscillation
periodic time
or period and is given the symbol T.



When waves leave a source, one complete wave will pass a point in one periodic time.

Figure 1.   Click to advance the wave.
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In one periodic time T, we can say that each wave travels a distance of 1 wavelength . This enables us to determine the average speed v at which the wave is travelling through a medium.
    



This equation applies to both longitudinal and transverse waves. Sound waves travel at different speeds in different materials.


Wave Description Speed / ms−1
Sound waves in air 340
Sound waves in water 1500
Light in a vacuum 300,000,000
Light in glass 200,000,000



The speed at which sound travels through a particular material depends on the temperature of the material. Generally sound travels through room temperature air at approximately 330 ms−1. Its speed through helium gas at the same temperature is about five times faster.

Measuring the speed of sound in air
Sound waves in air are longitudinal. In the set-up shown in Fig.2, sound waves are produced by banging a hammer against a metal block.

Figure 2.   Bang the block and measure the time.
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Complete the following statements to summarize this method for measuring the speed of sound in air.

  • Banging the block with the hammer produces a longitudinal wave. When this is detected by the first microphone the timer . The timer stops when the sound pulse is detected by the microphone. The timer displays the time taken for the sound to travel between the microphones. To calculate the speed of sound through air we would need to measure the between the microphones as well as the travel time.
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Summary


Longitudinal sound waves need a medium to travel through, whereas transverse light waves do not.

Observations in nature, such as the time lag between thunder and lightning, show us that light waves travel faster than sound waves.

The time between the peak of one wave and the peak of the following wave is called the periodic time or period of the wave and is given the symbol T.



The speed v, frequency f, and wavelength of a wave are connected by the equation



The speed at which sound travels through a particular material depends on the type of material as well as other physical parameters such as its temperature.

Exercises
1. The clock at a town hall chimes exactly at 12:00. A student in her classroom hears the sound from the chime 1.50 s later. The speed of the sound in the air is 330 ms−1.

  • Calculate the distance between the classroom and the town hall.
     m   (to the nearest whole number)

    The student determines that the sound waves from the bell have a frequency of 290 Hz. Calculate the periodic time of these waves.
     × 10−3 s   (to 1 d.p.)

    Calculate the wavelength of the sound waves from the bell.
     m   (to 2 d.p.)
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2. A student making notes on waves writes down the following statements. Which of these statements are correct?
  • Sound waves are longitudinal, but light waves are transverse.
    Light waves can travel through a vacuum, but sound waves require a medium.
    Transverse waves travel faster than longitudinal waves.
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3. A student making notes on the properties of waves writes down the following definitions. Which of these statements are correct?
  • The frequency of waves is the number of waves that pass a given point each second.
    The wavelength is the distance between two identical points on a wave.
    The wave amplitude is the distance from the top of a crest to the bottom of a trough.
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4. The following passages, describing transverse and longitudinal waves, are taken from a physics textbook. Fill in the blanks.

  • In a transverse wave, each part of the medium through which the wave travels moves at to the direction in which the wave is travelling.

    As a wave moves through a medium the particles of the medium move to and fro along the direction in which the energy of the wave travels.

    is a longitudinal wave while light and waves are transverse waves.
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5. An
electromagnetic
Electromagnetic waves, such as light, are made up from oscillating electric and magnetic fields. Because of this, they are self-propagating and can travel through a vacuum. All types of electromagnetic wave travel at the same speed in a vacuum, 3 × 108 ms−1.
electromagnetic
wave has a frequency of 330 kHz. In which part of the electromagnetic spectrum does this wave occur?
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6. A sound source produces waves of
wavelength
The wavelength is the distance from one point on a wave to the identical point on the next wave. This can be stated as the distance from a crest on a wave to the next crest on the wave.
wavelength
0.7 m. The sound lasts for 0.5 s and the speed of sound through the air is 330 ms−1.

  • Calculate the frequency of the sound waves.
    Hz   (to the nearest whole number)

    How many complete waves does the sound source emit in the 0.5 s?
       (to the nearest whole number)

    How far has the front of the first wave travelled from the source in 0.5 s?
    m   (to the nearest whole number)
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7. An electromagnetic wave has a frequency of 3 terahertz. If the electromagnetic radiation travels at a speed of 3 × 108 ms−1, what is the wavelength of the radiation?
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Attempt Speed of light / × 108 ms−1
1 2.45
2 2.6
3 2.65
4 2.75
5 2.55

8. A pupil performs an intricate experiment to measure the speed of light through a fibreoptic cable. She attempts the experiment 5 times, obtaining the results shown in the table above. Which of the following should she record as the measured speed?
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