Speed of Sound

The speed of Sound is defined as the distance traveled by sound per unit of time. The speed of sound has the same unit as that of speed, i.e., m/s. Since sound waves propagate differently in different media, their speed also varies from one medium to another. Sound waves travel in such a way that there are alternate regions of compression and rarefaction.

Speed of sound is often referred to as the velocity of sound, and the two terms are used interchangeably. The speed of sound depends on the medium through which it propagates. 

Note: The speed of sound in the air at a normal temperature is 343 meters per second (1125 ft/s, 1235 km/h, 767 mph).

Sound Wave

Soundwave is a mechanical wave that travels from the source to the listener through the vibration of particles in a medium. Sound waves are longitudinal in nature, in which particles vibrate in the direction of wave propagation. A sound wave consists of alternate regions of compression and rarefaction.

The speed of sound is defined as the distance traveled per unit time by a sound wave in an elastic medium. It depends on the density and elasticity of the medium. Higher elasticity and lower density result in greater speed; therefore, the speed of sound is maximum in solids and minimum in gases.

Speed of Sound Formula

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

Speed(V) = \frac{Distance(S)}{Time(T)}

The same formula is used to calculate the speed of sound waves. In the case of sound waves, distance is replaced by wavelength, as both represent physical length and have the same unit, the meter (m). The wavelength of a sound wave is defined as the distance between two successive compressions or two successive rarefactions. 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

1. Density of the Medium

The speed of sound depends on the density of the medium. In a densely packed medium where particles are closer together, sound travels faster. That’s why the speed of sound is greatest in solids and lowest in gases.

2. Temperature of the Medium

The speed of sound is directly proportional to the temperature of the medium. As temperature rises, particles move faster, increasing collisions and making energy transfer easier. Consequently, the speed of sound increases with temperature. It has been observed that for each degree Celsius drop in temperature the speed of sound decreases by approximately 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 daily life, when we talk, the medium between the speaker and the listener is air. Therefore, it is important to know the speed of sound in air. The speed of sound is the distance travelled per unit time by a sound wave as it propagates through a medium

At 20 °C, the speed of sound in air is 343.2 m/s. . At this speed, sound travels about one mile in roughly five seconds. Sound travels four times faster in water (1,482 m/s) and around 13 times faster in steel (4,512 m/s).

Speed of Sound in Different Medium

The speed of sound depends on the medium. It is fastest in solids and slowest in gases and increases with temperature. Sound, being a mechanical wave, can only travel through matter.

1. Speed of Sound in Solid

Sound travels fastest in solids because their molecules are closely packed, allowing vibrations to pass quickly. The speed of sound travels at 6000 m/s in solids and 5100 m/s in steel. In diamonds, sound moves 35 times faster than in air.

2. Speed of Sound in Liquid

A liquid's density is higher than a gas's density. 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.

3. Speed of Sound in Gas

The speed of sound in any medium depends on both its elastic properties and density. In gases, it is strongly influenced by temperature and molecular mass, while in liquids and solids, both density and elasticity play major roles.

4. Speed of Sound in Water

Sound travels faster in water than in air. In water, the speed of sound is approximately 1,480 m/s. For purified water, it ranges from 1,450 to 1,498 m/s, while in seawater it is around 1,531 m/s at temperatures between 20 °C and 25 °C.

5. Speed of Sound in Vacuum

Sound cannot travel in a vacuum because there are no particles to transmit vibrations. Therefore, the speed of sound in a vacuum is 0 m/s.

Table for Speed of Sound in Different Mediums

The table shows the speed of sound in different media. Sound travels fastest in solids, slower in liquids, and slowest in gases. In gases, speed depends on the absolute temperature but is mostly unaffected by frequency, strain, or density.

Related Article:

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

Sample Problems

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 travelled 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 travelled 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 a wavelength of 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 = 800

Hz

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

Unsolved Problems

Question 1: A tuning fork produces a sound of frequency 440 Hz. If the speed of sound in air is 343 m/s, calculate the wavelength of the sound.

Question 2: An echo is heard 2 seconds after clapping near a cliff. If the speed of sound is 340 m/s, find the distance of the cliff.

Question 3: The temperature of air increases from 20 °C to 30 °C. How much does the speed of sound increase? (Given: the speed of sound increases 0.6 m/s per °C).

Question 4: A sound wave travels from air into water. If the speed of sound in air is 343 m/s and in water is 1480 m/s, and the frequency of the sound remains the same, find the wavelength of the sound in water if the wavelength in air is 0.85 m.

Question 5: A steel rod transmits a sound wave that covers a distance of 5100 m in 1 second. If a sound wave of frequency 2 kHz is produced in the rod, calculate its wavelength.

Question 6: Ultrasound of frequency 2 MHz is used to detect a flaw in a metal block. If the speed of ultrasound in the metal is 5000 m/s, calculate the wavelength of the ultrasound in the metal.