Zainab Ilyas

· 11 Dec 2021

Follow Following

What is the speed of sound?

A sound wave is a pressure wave that moves across a medium via particle-to-particle contact. When one particle is disturbed, it exerts a force on the next nearby particle, causing that particle to be disturbed and the energy to be transported across the medium. The speed of a sound wave, like any other wave, relates to how quickly the disturbance is conveyed from particle to particle. While frequency refers to the number of vibrations made by a single particle per unit of time, speed relates to the distance travelled per unit of time by the disturbance. Always remember to distinguish between the two frequently mistaken numbers of speed (how rapidly...) and frequency (how often..).

Because the speed of a wave is defined as the distance travelled per unit of time by a point on the wave (such as a compression or rarefaction), it is commonly given in meters per second (abbreviated m/s). This is what it looks like in equation form.

speed = distance/time

A sound wave will cover more space in the same amount of time if it travels quicker. If a sound wave travels 700 meters in 2 seconds, the speed of the wave is 350 meters per second. A slower wave would cover less distance in the same amount of time - possibly 660 meters - and hence have a speed of 330 meters per second. Waves that travel faster cover more ground in the same amount of time.

Factors Affecting Wave Speed

Any wave's speed is determined by the qualities of the medium through which it travels. Wave speed is often influenced by two types of qualities: inertial properties and elastic properties. When a force or stress is applied to a material, its elastic qualities are those that pertain to the material's inclination to keep its shape and not deform. When a stress is applied to a material like steel, it will suffer a very tiny deformation of shape (and dimension). Steel is a stiff, elastomer-rich material. A rubber band, on the other hand, is a highly flexible material that deforms or changes shape rapidly when a force is applied to stretch it. The rubber band deforms dramatically when it is subjected to a modest amount of force .A rubber band is considered a flexible material, whereas steel is considered a stiff or hard substance. A stiff or unyielding substance is defined at the particle level by atoms and/or molecules that have significant attraction to one another. When a force is given to the material in an attempt to stretch or deform it, the material's strong particle interactions prevent the material from deforming and assist it keep its shape. Steel and other rigid materials are thought to have a high flexibility. (The technical phrase is elastic modulus.) The elastic characteristics of the medium are greatly influenced by the phase of matter. Solids have the most powerful particle interactions, followed by liquids, and finally gases. As a result, longitudinal sound waves in solids move quicker than they do in liquids and gases. Despite the fact that the inertial factor favors gases, the elastic component has a stronger impact on wave speed (v), resulting in this overall pattern.
vsolids > vliquids > vgases

Inertial qualities refer to a material's tendency to be slow in response to changes in its state of motion. An example of an inertial property is the density of a medium. The greater the inertia (i.e., mass density) of individual medium particles, the less sensitive they are to interactions between surrounding particles, and the slower the wave. As previously established, sound waves move quicker in solids than in liquids than in gases. Within a single phase of matter, however, the inertial attribute of density is the one that has the largest influence on sound speed. In a less dense medium, a sound wave travels quicker than in a more dense substance. As a result, a sound wave in Helium travels roughly three times quicker than in air.

The Speed of Sound in Air

The speed of a sound wave in air is determined by the air's qualities, most notably temperature and, to a lesser extent, humidity. The presence of water vapor in the air causes humidity. Water, like any other liquid, has a propensity to evaporate. Particles of gaseous water become intermingled in the air as a result of this. This increased substance will have an impact on the air's mass density (an inertial property). The strength of particle interactions is affected by temperature (an elastic property). The temperature dependence of the speed of a sound wave through dry air is approximated by the following equation at normal atmospheric pressure:

v = 331 m/s + (0.6 m/s/C)•T
where T is the temperature of the air in degrees Celsius. Using this equation to determine the speed of a sound wave in air at a temperature of 20 degrees Celsius yields the following solution.

v = 331 m/s + (0.6 m/s/C)•T
v = 331 m/s + (0.6 m/s/C)•(20 C)

v = 331 m/s + 12 m/s

v = 343 m/s

(For temperatures between 0 and 100 Celsius, the preceding equation relating the speed of a sound wave in air to temperature offers generally accurate speed figures.) The equation has no theoretical foundation; it is merely the result of looking at temperature-speed data for this temperature range. Other equations based on theoretical reasoning exist, and they offer precise data for all temperatures. Nonetheless, for our purposes as beginning Physics students, the equation above will suffice.)

Using Wave Speed to Determine Distances

A sound wave will move at roughly 343 m/s under normal atmospheric pressure and a temperature of 20 degrees Celsius, which is approximately 750 miles per hour. While this speed appears quick by human standards (the fastest people can sprint at 11 m/s and highway speeds are around 30 m/s), the speed of a sound wave is modest when compared to the speed of a light wave. Light flows through air at a speed of 300,000,000,000,000 m/s, or about 900,000,000 times the speed of sound. As a result, during a storm, people may sense a discernible temporal delay between thunder and lightning. The light wave from the lightning strike arrives in such a short amount of time that it is almost imperceptible. The arrival of the sound wave from the place of the lightning strike, on the other hand, takes significantly longer. The time difference between the arrival of the light wave (lightning) and the arrival of the sound wave (thunder) allows a person to estimate their distance from the storm. For example, if thunder is heard 3 seconds after lightning is seen, sound (at a speed of 345 m/s) has travelled a distance of 345 meters.
distance = v • t = 345 m/s • 3 s = 1035 m

The storm is 0.65 miles distant when this figure is converted to miles (division by 1600 m/1 mi).

An echo is a phenomena that is connected to the sense of time delays between two occurrences. A human may frequently detect a temporal delay between the generation of a sound and the arrival of a distant barrier's reflection of that sound. Perhaps you've heard an echo of your holler off a distant canyon wall if you've ever made a holler within a canyon. The time between the holler and the echo corresponds to the time it takes the holler to travel the round-trip distance from the canyon wall to the other side. A person may estimate the one-way distance to the canyon wall by measuring this time. For example, if you hear an echo 1.40 seconds after hollering, you may calculate the distance to the canyon wall as follows:

distance = v • t = 345 m/s • 0.70 s = 242 m

The distance between you and the canyon wall is 242 meters. You may have observed that the equation uses a time of 0.70 seconds. The one-way distance to the canyon wall equates to one-half the time delay because the time delay relates to the time it takes the sound to travel the round-trip distance to the canyon wall and back.

While an echo is of minor value to humans, echolocation is a crucial skill for bats. Bats must utilize sound waves to travel and hunt since they are nocturnal creatures. They emit brief bursts of ultrasonic sound waves that bounce off nearby objects and return to them. A bat's ability to discern the time delay between transmitting and receiving pulses helps it to estimate the distance to nearby objects. Some bats, known as Doppler bats, can determine the speed and direction of moving objects by observing variations in the frequency of reflected pulses. The physics of the Doppler effect, which was addressed in a previous lesson, is being used by these bats. A bat may explore and hunt using this echolocation technique.

The Wave Equation Revisited

A sound wave, like any other wave, has a speed that is mathematically proportional to its frequency and wavelength. The mathematical link between speed, frequency, and wavelength is described by the equation below, as discussed in a prior section.

Speed = Wavelength • Frequency
Using the symbols v, λ, and f, the equation can be rewritten as

v = f • λ
The above equation can be used to solve mathematical issues involving the connection between speed, frequency, and wavelength. However, the equation may communicate one key misunderstanding. The wave speed is not reliant on the frequency or wavelength, despite the fact that they are used to compute it. A change in wavelength has no effect on (or change in) wave speed. Rather, a change in wavelength has the opposite effect on frequency. The frequency is halved when the wavelength is doubled, but the wave speed remains same. A sound wave's speed is determined by the qualities of the medium through which it travels, and the only method to modify the speed is to change the medium's properties.

#speed
#sound
#wavelength