Speed of Sound

Speed of Sound as the name suggests is the speed of the sound in any medium. We know that sound is a form of energy that is caused due to the vibration of the particles and sound travels in the form of waves. A wave is a vibratory disturbance that transfers energy from one point to another point without the actual transfer of matter. Hence, when we speak the sound from our vocal cords reaches to listener’s ear in the form of a wave.

Since the sound travels from the source point to the destination point within a time period, this encourages us to calculate the speed of the sound with which it travels. Also, we know that Sound is a mechanical wave hence its speed of propagation varies in different materials. In this article, we will learn, what is sound, what is the definition of Speed of Sound and the Speed of Sound with which it propagates in different media.

What is a Sound Wave?

Sound Wave is defined as a mechanical wave that travels from source to destination via the vibration of the particles of the medium between the source and the listener. The nature of sound waves is longitudinal. In a longitudinal wave, the particle vibrates in the direction of propagation of waves. A sound wave comprises compression and rarefaction in an alternate manner. In the region of compression, the particles are densely packed, and in the region of rarefaction, the particles are larger distances.

The distribution in a medium may be used to investigate some of the medium’s properties. The speed of sound is defined as the distance travelled per unit of time by a sound wave propagating across an elastic medium. The speed of sound in a given medium is determined by its density and elasticity. According to mechanics, the greater the speed of sound, the greater the elasticity, and the lower the mass. Therefore, the speed of sound is maximum in solids and minimum in solids.

Read more about Waves.

What is Speed of Sound?

Speed of Sound is defined as the distance travelled by sound per unit of time. The speed of sound has the same unit as that of speed i.e. m/s. Since, we know that sound waves propagate differently in different media, hence the speed of sound waves varies in different media. Sound waves travel in a manner that there is an alternate zone of compression and rarefaction.  

Speed of Sound is synonymous with the Velocity of Sound, hence the two terms must not be confused. Speed of Sound depends on the media in which it is propagating. 

Note: Speed of sound in air at normal temperature is 343 metres per second (1,125 ft/s; 1,235 km/h; 767 mph).

Learn more about Speed and Velocity.

Speed of Sound Formula

We know that the speed of an object is given by distance divided by time.

Speed(v) = Distance(s)/Time(T)

The same formula will be used to calculate the speed of sound waves. In the case of sound waves, the distance is replaced by wavelength which has the same physical dimension of distance. Both wavelength and distance are physical ‘Length’ and have the same unit ‘meter’. The wavelength of a wave is defined as the distance between a successive crest and a trough. Wavelength is represented by λ.

Hence, the formula for the Speed of Sound is given as:

Speed of Sound = Wavelength/Time

v = λ/T

We can rewrite the formula as v = λ×1/T

Here, 1/T is called Frequency(f). Frequency of sound is defined as the number of oscillations in one unit of time. Frequency is given as the reciprocal of the time period, hence its unit is s^-1 or Hertz(Hz).

Hence, the speed of sound in terms of frequency is given as follows

Speed of Sound = Wavelength × Frequency

v = λ × f

The unit of Speed of Sound is m/s.

Factors Affecting the Speed of Sound

As we know that sound wave needs a medium to travel. Hence, they are affected by the properties of the medium through which they travel. The speed of sound is affected by two factors:

• Density of the Medium
• Temperature of the Medium

Density of the Medium

Since sound waves need a medium to travel the speed of sound is dependent on the density. In a densely packed medium where the intermolecular space is minimum, the speed of sound is larger. Hence, the speed of sound is greatest in solids because of high density and lowest in gas because of low density and large intermolecular space. Thus we can say that the speed of sound increases with the density of the medium. 

Temperature of the Medium

The speed of the sound is directly proportional to the temperature of the medium. This is because as the temperature rises there is an increase in the rate of collision among the particles of the medium, thus making the transfer of sound energy easy.  As a result, as the temperature rises, so does the speed of sound. When temperature decreases the speed of sound also decreases. It has been observed that for each degree of temperature decreased, the speed of sound reduces by 0.6 m/s.

Note: It should be noted that at a constant temperature, the speed of sound is not affected by the pressure.

Speed of Sound in Air

In our daily life when we talk, the medium between the speaker and the listener is air. Hence, it becomes important to know with what speed sound travels in the air. The speed of sound is an important parameter in many fields of physics. The distance traveled per unit time by a sound wave propagating through a medium is referred to as the speed of sound. 

At 20 °C, the speed of sound in air is 343.2 m/s, which corresponds to 1,236 km/h. At this rate, sound will travel one mile in around five seconds. Sound travels 4 times faster in water (1,482 meters per second) and around 13 times faster through steel (4,512 meters per second).

Speed of Sound in Different Medium

The speed of sound depends on the properties of the medium through which it travels. The speed of sound decreases when we go from a solid to a gaseous state. In any medium, as we increase the temperature, the speed of sound increases. Sound waves are mechanical waves that can only pass through matter. The medium is the matter in which the waves pass. Let’s learn what is the speed of sound in different mediums.

Speed of Sound in Solid

Sound is nothing more than a vibration caused by particle collisions; one molecule colliding with the next, and so on. Solids are much denser than liquids or gases. This suggests that in solids, molecules are closer to each other than in liquids, and in liquids, molecules are closer to each other than in gases. Because of their near proximity due to mass, they will collide very easily. It takes less time for a stable molecule to collide with its neighboring molecule. Because of this advantage, the speed of sound in a solid is greater than that of a gas. The speed of sound in solid is 6000 m/s, while the speed of sound in steel is 5100 m/s. Another fascinating finding about sound speed is that sound moves 35 times faster in diamonds than in the air.

Speed of Sound in Liquid

A liquid’s density is higher than a gas’s density. As a result, the distances between molecules in liquids are greater than in solids but smaller than in gases. As a result, the speed of sound in liquids is intermediate between the speeds of sound in solids and gases.

Speed of Sound in Gas

When sound approaches a liquid or solid, the speed of sound is independent of the density of the medium. Since gases expand to fill a given vacuum, their density is very uniform regardless of the type of gas. This is obviously not the case for solids and liquids.

Speed of Sound in Water

The speed of sound in water exceeds that of air. Alternatively, sound moves quicker in water than in air. In water, the speed of sound is 1480 m/s. It’s also worth noting that the speed of purified water will range from 1450 to 1498 m/s, while the speed of seawater ranges from 1531 m/s while the temperature is between 20 °C and 25 °C.

Speed of Sound in Vacuum

Since there are no particles in a vacuum, the speed of sound is zero meters per second. When there are ions for the propagation of these sound waves, they fly through a medium. Sound waves do not propagate in the vacuum since it is an empty space.

Table for Speed of Sound in Different Mediums

The table below shows the speed of sound in various media. In general, sound waves move the fastest through solids, then liquids, and finally gases. In gases, the speed of sound is equal to the square root of the absolute temperature (measured in Kelvin), but it is unaffected by the frequency of the sound wave, strain, or density of the medium. However, none of the gases we encounter in everyday life are ideal gases, and as a result, their properties vary slightly.

Speed of Sound in Different Media at 25 ºC
State	Substance	Speed(in m/s)
Solids	Aluminum	6420
	Nickel	6040
	Brass	4700
	Iron	5950
Liquids	Water(Sea)	1531s
	Water(distilled)	1498
	Ethanol	1207
	Methanol	1103
Gases	Hydrogen	1248
	Helium	965
	Air	346
	Oxygen	316

Read More

• Production and Propagation of Sound
• Refraction of Sound
• Noise Pollution

Sample Problems on Sound Waves

Problem 1: An echo is heard after 4 s. What is the distance of the reflecting surface from the source given that the speed of sound is 284 m/s?

Solution:

Given,

Speed of sound (v) = 284 m/s and

Echo returns in time (t) = 4 s

Therefore,

The distance traveled by sound:

d = v × t 

⇒ d = 284 m/s × 4 s 

⇒ d = 1136 m

Since, Sound has to travel a distance that is twice the distance of the reflecting surface and the source.

Hence, the distance of the reflecting surface from the source, 

D = 1136 m / 2  

⇒ D = 568 m

Problem 2: A person clapped his hands near a cliff and heard the echo after 3 s. What is the distance of the cliff from the person if the speed of the sound is taken as 348 m/s?

Solution:

Given,

Speed of sound, v = 348 m/s and

Time taken for hearing the echo, t = 3 s.

Distance traveled by the sound,  

d = v × t 

⇒ d = 348 m/s × 3 s 

⇒ d = 1044 m 

In 2 s sound has to travel twice the distance between the cliff and the person.

Hence, the distance between the cliff and the person,

D = 1044 m / 2 

⇒ D = 522 m

Problem 3: Explain how defects in a metal block can be detected using ultrasound.

Solution:

Ultrasound waves have a high frequency. They can travel in mediums even with obstacles. Ultrasound waves can be transmitted through a metal block, if a defect is present then either its speed will change due to the defect or the wave will reflect back completely and will be detected by the detector. If no defect is found then the sound comes out at the expected velocity.

Problem 4: A sound wave has a frequency of 4 kHz and wavelength 35 cm. How long will it take to travel 2.5 km?

Solution:

Given,

Frequency (ν) = 4 kHz = 4000 Hz

Wavelength (λ) = 35 cm = 0.35 m

We know that, 

The speed of the wave = wavelength × frequency

v = λ ν 

⇒ v = 0.35 m × 4000 Hz 

⇒ v = 1400 m/s

The time taken by the wave to travel a distance of 2.5 km,

t = 2500 / 1400 

⇒ t =1.78 s

Thus, the sound will take 1.78 s to travel a distance of 2.5 km.

Problem 5: A body is vibrating 48000 times in one minute. If the velocity of sound in air is 360 m/s, find:

(a) Frequency of vibration in hertz,

(b) Wavelength of the wave produced.

Solution:

(a) Given,

Number of vibration in one minute = 48000

Number of vibrations in one sec =48000/60 = 800Hz

Therefore, Frequency (f)= 800 Hz

(b) Given,

Velocity of speed in air (v) = 360 m/s

Frequency (f) = 800 Hz

v = f λ

or λ = v / f

⇒ λ = 360 / 800 

⇒ λ = 0.45 m

FAQs on Speed of Sound

1. What is the Speed of Sound in MPH?

The Speed of Sound in mph is 767mph.

2. What is the Speed of Sound in Kilometers per Hour?

The Speed of Sound Kilometers per Hour is 1,235 kmph.

3. How Fast does Sound Travel per Second?

As the speed of Sound is 1236 km/h at 20°C in air, thus per second sound travels 1236/3600 ≈ 0.343 Kilometers or 343.33 meters.

4. What is the Formula for Speed of Sound?

The formula for speed of sound is wavelength/time or wavelength × frequency.

5. In which medium, Sound travel fastest?

Sound travels fastest in Solid.

6. What is the Nature of Sound Wave?

Sound Wave is a mechanical wave and is longitudinal in nature.

7. What are the Factors on which the Speed of Sound Wave depends?

Speed of Sound Wave depends on the density and the temperature of the medium.

8. How does the Speed of Sound depend on the Density of the Medium?

The Speed of Sound increases with an increase in the density of the material.

9. How does the Speed of Sound depend on the Temperature of the Medium?

The speed of sound is directly proportional to the temperature of the material.

10. What is the Speed of Sound in Vacuum?

The speed of sound in vacuum is 0 because there is an absence of matter.

11. How does the Speed of Sound depend on the Elasticity of the Medium?

The Speed of Sound is directly proportional to the square root of the elasticity of the material. It is given as v √(B/ρ) where B is the Bulk Modulus of Elasticity and ρ is the density of the material.