Speed of Sound
Dear students, in this article we are going to learn about the speed of sound. Before proceeding with speed of sound we need to recall few definitions, viz. Speed is distance travelled by object in unit time.
Frequency of wave is the total number of vibrations completed by particle in given unit time.
Wavelength of wave is the distance travelled by vibrating particle in one complete oscillation.
Period of wave is the time take by particle to complete one set of vibration.
Now when we find the speed of sound, first we need to recall that, sound is longitudinal wave which requires material medium for its propagation. When longitudinal wave propagates in medium it divides itself into alternate compressions and rarefactions. At compressions the pressure of particles of medium increases and at rarefaction pressure of particles decreases. This continuous change in pressure of medium transfers the energy throughout the medium so that we can get sensation of listening.
To find speed of sound, consider that the tuning fork produces sound wave in which particle is vibrating such that the direction of propagation of particle is parallel to direction of propagation as shown in fig. below.
Let ‘T’ be the period of wave i.e. time taken to complete one set of compression and rarefaction.
Let ‘λ’ be the wavelength of wave i.e. distance travelled in one complete set of vibration.
Velocity of wave is defined the distance covered by vibrating particle in given unit time.
For any wave,
Distance covered in one vibration= wavelength of wave= λ
Time taken to complete one vibration= period of wave= T
Then the velocity of wave is given as,
But we know that, frequency, f= 1/T
∴ v = f × λ
Therefore, velocity of wave can defined as the product of frequency and wavelength of wave.
Velocity of wave depends upon factors like, temperature of medium, density of medium etc. Velocity of wave is independent of pressure of medium.
Following are some examples which will help us to understand more about the velocity of wave.
Ex:1) A radio channel emits the sound of frequency 15000 Hz and wavelength of 1.5 m in air. Find the velocity of sound by with which it reaches to listener.
Ans: Here, f = 15000 Hz, λ = 1.5 m
∴ Velocity of wave, v = f × λ
∴ v = 15000 × 1.5
∴ v = 22500 m/s
Ex:2) The sound travels at speed of 380 m/s in water. If the frequency of sound is 10000 Hz. Find the wavelength of sound in water.
Ans: Here, f= 10000 Hz, v=380 m/s
∴ Velocity of wave, v = f×λ
∴ λ = v/f
∴ λ = 380/10000
∴ λ = 0.038 ≈ 0.04 m = 4 cm