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Is speed of sound constant and cannot be varied?

  1. May 30, 2012 #1
    i was wondering that can the speed of sound be lowered than the normal 335m/s in air without changing the air conditions? lets say u spoke in a low voice, will the sound still travel at 335m/s? will all air waves travel at that speed. no matter how weak or strong they are?
  2. jcsd
  3. May 30, 2012 #2
    Interesting question.

    The speed of sound is the same in the same air conditions. When you speak in a low or loud voice the pitch of sound (frequency) is changed. Since the speed of sound is independent of frequency it is the same for all pitches of sound.

    In a non-dispersive medium sound speed is independent of sound frequency, so the speeds of energy transport and sound propagation are the same. For audible sounds, a mixture of oxygen and nitrogen constitutes a non-dispersive medium. But air does contain a small amount of CO2 which is a dispersive medium, and it introduces dispersion to air at ultrasonic frequencies (> 28 kHz).[1]

    In a dispersive medium sound speed is a function of sound frequency, through the dispersion relation. The spatial and temporal distribution of a propagating disturbance will continually change. Each frequency component propagates at its own phase velocity, while the energy of the disturbance propagates at the group velocity. The same phenomenon occurs with light waves; see optical dispersion for a description. (wikipedia)
  4. May 30, 2012 #3


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    the speed of sound varies with the density of the medium
    The amplitude of the sound wave wont ( as far as I'm aware) affect the speed
    only the medium density will

  5. May 30, 2012 #4
    Both the speeds of sound and light varies with density of medium.

    Speed of sound varies directly with density of medium whereas speed of light(or any electromagnetic wave) varies inversely with density of the medium.

    REMEMBER: Speed of light is 3X10^8 only in vacuum and it differs with medium. Thats why refraction takes place.
  6. May 30, 2012 #5
    Speed of any wave is constant for a given medium but varies with change in medium.
  7. May 30, 2012 #6
    This only holds if the temperature is constant. Sound speed varies with change in temperature for the same medium :smile:

    Also, sound speed does not depend on the medium density(for gases), as pressure and density aren't fully independent of each other.
  8. May 31, 2012 #7
    The speed of sound remains constant if provided the temperature remains same, because if the temperature increases, the kinetic energy of the particles of the medium (air here) would increase and the sound waves would travel much faster (sound waves are mechanical waves, they propagate due to the particles of the medium). And if temperature would decrease, the opposite would happen.
    It doesn't depend on how softly you speak (amplitude), or your pitch is high or low (frequency).......Only on the temperature.
  9. May 31, 2012 #8

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    The speed of sound is strongly dependent on temperature and on the constituent gases. The speed of sound in helium at standard temperature and pressure is almost three times the speed of sound in our atmosphere. Even at a constant temperature, the speed of sound is weakly dependent on pressure (or density) because our atmosphere is not quite an ideal gas. These effects are in general rather small.

    The speed of sound is weakly dependent on frequency. However, these frequency dependencies only manifest themselves markedly when the frequency is extremely high. Sound in a gas propagates is a compression wave. When the wavelength gets very short one needs to account for the fact that the continuum model of a gas is no longer valid. A gas is a bunch of particles bouncing off one another. The wavelength needs to be an order of magnitude or so longer than the mean free path for the continuum model to have any validity. Mean free path at standard temperature and pressure is about 68 nanometers, or a frequency of about 5 gigahertz. Sound above 200 or so megahertz or so propagates weirdly because the wavelength is on an order or two of magnitude times the mean free path.

    Loudness also plays a role. At low volumes the pressure varies sinusoidally for a pure tone. At 194 decibels the low pressure in that sinusoid because zero. This sinusoid gets clipped at for extremely loud sounds as there is no such thing as negative absolute pressure. Sounds over 194 dB propagate as shock waves rather than as sound waves.

    These effects are small and only manifest themselves at extremely high frequencies, extremely high volumes. For the most part it is fair to say that the speed of sound does not depend on frequency or loudness. It of course does depend on temperature and chemical composition.
  10. Jun 1, 2012 #9


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    I like to think of the variation of the speed of sound with temperature as follows:
    In an ideal gas, you can treat the molecules as very small billiard balls so they take no time to transfer their energy from one to another. The time for the pressure to be communicated from one molecule to the other depends just on how long it takes to get from one collision to the next. If the time is related to the 1/velocity then the speed of the sound will be proportional to the velocity of the molecules - however densely they are packed, because the actual collisions take no time. Their average velocity, then, would be proportional to the root of the Mean Kinetic Energy (mvrms2/2), which is proportional to the square root of the temperature.
    You'd expect this to be the dominating factor - and I believe it is.
  11. Jun 1, 2012 #10
    It is NOT ONLY density that has an influence on the speed of sound.... the temperature also has an effect. Higher temp.... faster speed
  12. Jun 1, 2012 #11


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    It is important not to imply that density differences due to differences in pressure is what counts, though. What counts is the speed of the molecules which, in turn, is governed by the molecular mass - because the temperature is the average KE of all the molecules. The speed of the molecules of a gas is not dependent, primarily, upon the pressure (except at high pressure where the internal energy has a significant Potential Energy component). The speed of the molecules depends upon the molecular mass (bigger means slower for the same KE) so relative density of a gases at the same pressure would also be the relative factor in speed of sound.

    See this wiki link.
  13. Jun 1, 2012 #12
    exactly what i put across
  14. Jun 1, 2012 #13


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    Not really. You can change the density of a gas very easily by changing the pressure and that will have no effect on the speed of sound. You didn't make that clear.
  15. Jun 1, 2012 #14
    My students seem to find it easy to accept that density changes due to pressure changes are not important. They realise very quickly that it is molecular SPEED that is important and it follows easily that TEMPERATURE is the important physical quantity.
    I will state that now but I find it strange that some basic information needs to be given in post 13 !! Of a topic
  16. Jun 1, 2012 #15


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    You make a zee joke? This is PF. Some of the threads run into dozens of posts before someone injects some proper sense.
    PS You must have a very gifted set of students if they do not need that density thing to be spelled out to them. Lucky you. :smile:
  17. Jun 2, 2012 #16
    You are correct, I do have bright students but that is neither here nor there. I don't think I have the monopoly on bright students.
    From early days students are taught that speed of molecules is related to temperature and it causes no problems. When kinetic theory of gases is met, again it is the speed of molecules that is important in the analysis.
    Density is an unimportant quantity in its own right, it is a convenient combination of other physical quantities that turn up in the analysis. Density is a very difficult concept for students to be comfortable with...ton of feathers, ton of lead syndrome.
    Again the speed of molecules is directly related to temperature and it is no surprise that the speed of sound for a gas depends only on the temperature.
    I can imagine someone seeing c^2 = 3P/ρ and forming the (wrong) conclusion that the speed of sound depends on pressure and density.
    There are several posts above that state that the speed in a gas depends on density.
    None of my text books back that up. (this is not to confused with the fact that the speed is different in different gases)
  18. Jun 2, 2012 #17
    It is temperature that is important.
    Density does not appear in the equations to calculate molecular speeds. Mass of a molecule does but not density.
    Last edited: Jun 2, 2012
  19. Jun 2, 2012 #18
    "the relative density of gases at the same pressure would be a relative factor in the speed of sound" is true for DIFFERENT GASES but not for A gas.
    If the pressure of a particular gas is kept constant and its density becomes different then its volume has changed.... this is achieved by changing the temperature.
    This equation c^2 = 3P/ρ causes so many problems for those without a deeper understanding of the physics and the relationship between P, V, T and ρ.
  20. Jun 2, 2012 #19


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    I agree with all of that. My only point is that many of the people who read these posts would assume that density of a gas depends on pressure as much as anything else and could jump to unwarranted conclusions. Some things need to be spelled out and we can't expect all readers to be a smart as your students (they don't all have your tender care either). This is a 'Comprehensive' forum.

    Common experience is that the speed of sound is lower at high altitude. There is less pressure at high altitude - hence the possible, erroneous conclusion that speed relates to pressure / density. We just need to close these routes to possible misconception when we can.
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