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0.5 Longitudinal waves  (Page 2/3)

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Wavelength and amplitude

Wavelength
The wavelength in a longitudinal wave is the distance between two consecutive points that are in phase.

The wavelength in a longitudinal wave refers to the distance between two consecutive compressions or between two consecutive rarefactions.

Amplitude
The amplitude is the maximum displacement from equilibrium. For a longitudinal wave which is a pressure wave this would be the maximum increase (or decrease) in pressure from the equilibrium pressure that is cause when a peak (or trough) passes a point.
Wavelength on a longitudinal wave

The amplitude is the distance from the equilibrium position of the medium to a compression or a rarefaction.

Period and frequency

Period
The period of a wave is the time taken by the wave to move one wavelength.
Frequency
The frequency of a wave is the number of wavelengths per second.

The period of a longitudinal wave is the time taken by the wave to move one wavelength. As for transverse waves, the symbol T is used to represent period and period is measured in seconds (s).

The frequency f of a wave is the number of wavelengths per second. Using this definition and the fact that the period is the time taken for 1 wavelength, we can define:

f = 1 T

or alternately,

T = 1 f

Speed of a longitudinal wave

The speed of a longitudinal wave is defined as:

v = f · λ

where

  • v = speed in m · s - 1
  • f = frequency in Hz
  • λ = wavelength in m

The musical note “A” is a sound wave. The note has a frequency of 440 Hz and a wavelength of 0,784 m. Calculate the speed of the musical note.

  1. f = 440 Hz λ = 0 , 784 m

    We need to calculate the speed of the musical note “A”.

  2. We are given the frequency and wavelength of the note. We can therefore use:

    v = f · λ
  3. v = f · λ = ( 440 Hz ) ( 0 , 784 m ) = 345 m · s - 1

  4. The musical note “A” travels at 345 m · s - 1 .

A longitudinal wave travels into a medium in which its speed increases. How does this affect its... (write only increases, decreases, stays the same ).

  1. period?
  2. wavelength?

  1. We need to determine how the period and wavelength of a longitudinal wave change when its speed increases.

  2. We need to find the link between period, wavelength and wave speed.

  3. We know that the frequency of a longitudinal wave is dependent on the frequency of the vibrations that lead to the creation of the longitudinal wave. Therefore, the frequency is always unchanged, irrespective of any changes in speed. Since the period is the inverse of the frequency, the period remains the same.

  4. The frequency remains unchanged. According to the wave equation

    v = f λ

    if f remains the same and v increases, then λ , the wavelength, must also increase.

Sound waves

Sound waves coming from a tuning fork are caused by the vibrations of the tuning fork which push against the air particles in front of it. As the air particles are pushed together a compression is formed. The particles behind the compression move further apart causing a rarefaction. As the particles continue to push against each other, the sound wave travels through the air. Due to this motion of the particles, there is a constant variation in the pressure in the air. Sound waves are therefore pressure waves. This means that in media where the particles are closer together, sound waves will travel quicker.

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Source:  OpenStax, Physics - grade 10 [caps 2011]. OpenStax CNX. Jun 14, 2011 Download for free at http://cnx.org/content/col11298/1.3
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