Speed of sound, sound waves and frequency



Sound waves

Sound waves can be modeled with that example: By throwing a stone into a pond, it is observed that there is a multitude of waves in rings moving from the place where the stone fell towards outer circles. Carefully observing the water surface it is easy to see that the waves floating in it up and down.  This happens because when we throw the stone, the energy on the surface is being transferred. This movement is called wave motion.

What about the relationship between sound velocity, wavelength and frequency? What is the influence of humidity and temperature?


Speed ​​of sound

Speed of sound is not as fast as light. If you are far away from the stage at a live concert, you can see the drumsticks on a drum beat before you hear the bang. 100 meters distance is already a time delay of about 1/3 second. That is very obvious. Sound we hear is vibrating in the air. Noise can also be propagated by, for example metal, wood, or water. The speed of sound is dependent on the carrier material. the more rigid the material is, the higher is the speed. In gases lighter-than-air such as helium, the speed of sound is also higher, so your voice is higher if you have inhaled a helium balloon. In air, the speed of sound is around 344m/sec, in steel it is approximately 5800m/sec, in rubber 60m/sec, in the timber (depending on the type and in which direction) + / – 3800m/sec.

The speed of sound depends on:

  • The medium (air, metal, wood, etc.): higher density, higher speed.
  • Temperature: higher temperature,higher speed.
  • Humidity (air, wood)

The calculator below shows the effect of temperature:

c * = 20 √ (273 + T), T is the temperature in degrees Celsius; c is the speed of sound in meters / sec.

Speed of sound in water,air and steel:

In dry air at 20 °(68° F)

m / s

km / h












18 000


Wavelength and frequency of sound waves

Sound in air has a velocity of 20 ° C (c) of 344m/sec (= 1238 km / h = Mach 1). On this basis you can calculate the corresponding wavelength λ at each frequency f . This wavelength is equal to the distance which the sound travels through which the complete vibration has taken place.


  • c = λ xf
  • λ = c / f
  • f = c / λ

Distance, speed, time

Assuming a sound speed c = 344m/sec find calculate the distance the sound travels in a given time, or the time it needs to make. The speed of sound can be determined by measuring the time required for the waves to be transmitted via a known distance.


  • d = cxt
  • t = d / c

As a concrete wall at a distance of 30m from the sound source, the first echo to the sound source has a distance of: 2×30 = 60m . That’s after 0.174 sec.

If you hear the thunder 10 seconds after the lightning flash then the distance is  10x344m = 3440m (3.4 km);

The lowest note of a piano has a wavelength of 12.5 meters, a maximum of 8.2 cm. The highest observable tone (if you have very good ears at least) of 20 KHz has a wavelength of 1.7 cm.


Frequencies of musical notes and instruments


Speed of sound, sound waves and frequency



Characteristics of sound: Intensity, Quality (timbre), Loudness

Intensity:  It allows us to perceive a sound as “weak” or “strong”. It is related to the amount of energy transferred by sound waves, e.g. by pressing a guitar string, it transfers energy propagating in the air by longitudinal waves. The greater the amount of energy that spreads, the greater the intensity of the sound perceived .

The amount of energy carried by a wave is greater the higher the amplitude: Lightly pressing guitar string, the amplitude of oscillation is small and there is a low intensity sound. Instead, pressing harder the string causes the amplitude of oscillation to produce greater sound.

In short, the sound intensity is dependent on the amplitude of the sound waves.

However, the perception of sound intensity in humans is subjective and bears no direct proportion to the intensity of physical quantity. Due to this reason, it is customary to specify the levels of sound intensity with the unit of bel (usually expressed in decibels).

Tone:  allows to distinguish the bass (bass) of the treble (treble) and is related to the frequency of vibration. The musicians relate the different tones with musical notes; different notes are differentiated by tone.

Quality (timbre) is related to the shape of the sound wave. You can identify the sound of a flute, piano or violin with it even issuing the same note at the same time.

Loudness is the subjective perception of the magnitude of a sensation of sound and takes into account psychological aspects of sound that is not directly related to the intensity measured in decibels.

However, scientists (physiologists and physicists) have defined a sound unit ,the  sone ,in order to study the effects of the sound in the human being.


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