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# Speed of Sound in Different Mediums

Aug 20, 2022

## Key Concepts

1. Speed of sound
2. Speed of sound in different mediums
3. Sonic boom

## Introduction:

Sound propagates from the source of sound to its destination by propagating through a medium. It propagates through a medium at a particular speed. This speed depends on various factors linked to the medium. In this section, we will be throwing some light on this.

## Explanation:

### Speed of sound:

The speed of sound is defined as the distance covered by a point on a sound wave, such as a compression or a rarefaction per unit time. Any point can be considered to observe the speed of sound. However, we can usually consider the points of compression, rarefaction and mean value as shown by the red dots.

We know that,

The speed of a moving body

= distance traveled by the body/time taken to cover that distance.

A sound wave travels a distance equal to its wavelength in a time equal to its time period.

Therefore, the speed of a sound wave is given by,

Speed, v =wave length / time period

Or, v =𝛌/𝐓

The frequency (ν) of a sound wave is related to its time period (T) as,

ν =1/T

Therefore, the speed of a sound wave is given by,

Speed, v =𝛌

The speed of sound remains the same for all frequencies in the same medium and under identical physical conditions.

### Speed of sound in different mediums:

The sound of thunder is generally heard after the lightning is seen. This indicates that sound travels with a much lesser speed as compared to light. The speed of sound in a particular medium depends on various properties of the medium such as,

1. Temperature
1. Density

The speed of sound depends upon the temperature of the medium of propagation. As the temperature of the medium increases, the speed of sound in it also increases. For example, the speed of sound in air at 0 degree Celsius is 331 m/s. However, at 22 degrees Celsius, it is 344 m/s.

The speed of sound depends upon the density of the particles of the medium. As the density of the medium increases, the speed of sound in it also increases at a particular temperature. For example, the speed of sound in air at a particular temperature is 331 m/s. However, it is 1498 m/s in water and in aluminum, it is 6420 m/s.

### Sonic Boom:

When the speed of motion of any object exceeds the speed of sound, it is said to be traveling at a supersonic speed. Bullets and jet aircrafts often travel at supersonic speeds. When a sound producing object moves at a supersonic speed, it produces shock waves in the air. The air pressure variation associated with these shock waves produces a sharp and loud sound called the “sonic boom”. The shock waves generally carry a huge amount of energy. The shock waves generated by supersonic jets is enough to damage buildings and shatter window glasses.

1. A sound wave of wavelength 25 cm has a frequency of 1 kHz. What is its speed? How long will it take to travel a distance of 2.5 km?

Given that,

The wavelength of sound (λ) = 25 cm = 0.25 m

The frequency of sound (ν) = 1 kHz = 1000 Hz

Distance traveled by it = 2.5 km

Now, the speed of a sound wave is given by,

Speed, v =λν

v = 0.25 x 1000

v = 250 m/s

Thus, the speed of the sound wave is 250 m/s.

Now, the speed of a sound wave is given by,

Speed, v = distance/time

Therefore, time = distance/speed

t = 2500 / 250

t = 10 s

Thus, the sound will take 10 seconds to travel a distance of 2.5 km.

1. A sound wave traveling at a speed of 330 m/s has a frequency of 1 kHz. What is its wavelength?

Given that,

The speed of sound (v) = 330 m/s

The frequency of sound (ν) = 1 kHz = 1000 Hz

Now, the speed of a sound wave is given by,

Speed, v =λν

330 =λ x 1000

λ= 330/1000 = 0.33 m

Thus, the wavelength of the sound wave is 0.33 m.

### Summary:

1. The speed of sound is defined as the distance covered by a point on a sound wave, such as a compression or a rarefaction per unit time.
2. The speed of sound is given by, v =λ/T=λv.
3. The speed of sound in a particular medium depends on various properties of the medium such as, temperature, density etc.
4. As the temperature of the medium increases, the speed of sound in it also increases.
5. As the density of the medium increases, the speed of sound in it also increases at a particular temperature.
6. When the speed of motion of any object exceeds the speed of sound, it is said to be traveling at a supersonic speed.
7. When a sound producing object moves at a supersonic speed, it produces shock waves in the air.
8. The air pressure variation associated with these shock waves produces a sharp and loud sound called the sonic boom.

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