Frequency, Amplitude and Speed
Dear students, in this article we are going to learn about the frequency, amplitude and speed of wave. We know that the wave is small disturbance travelling through medium. When a wave propagates in the medium, particles of medium vibrates about their mean position. The counting or observations of these vibrations gives us some basic details which explain the various parameters of wave. Let’s learn all the parameters in detail.
Consider that the transverse wave is propagating in the medium like slinky as shown above. During propagation of the wave we can see that the particle starts from mean position reaches to particular height and come back to mean position again. So here we can say that particles got displaced by certain value which is known as amplitude of wave.
Amplitude of wave is defined as the maximum distance travelled by particle from its mean position. SI unit of amplitude is meter. Amplitude decides the intensity of vibration. More is the amplitude; more is intensity of vibration of wave. In case of sound waves, amplitude gives us details about the loudness or presence of noise in sound note.
Another important parameter of wave is termed as frequency of wave. Frequency explains the energy present the wave. Consider a slinky kept on table set up vibrations. Suppose that you are observing the vibrations produced in slinky for 30 seconds and you find that slinky vibrates 60 times in 30 second. So here one can predict that the slinky vibrates 60/30=2 times in one second. The number 2 here is nothing but the frequency of wave.
Frequency of wave is the total number of vibrations completed by particle in given unit time or number of vibrations completed by wave per second. SI unit of frequency is hertz (Hz) or cycles per second (cps). Remember that the frequency is nothing but the reciprocal of period of wave. Period of wave is the time take by particle to complete one set of vibration (T).
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.
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.
Following are some examples which will help us to understand more about the velocity of wave.
Ex:1) Human ear can respond to frequency in ranges from 20 Hz to 20000 Hz. If the speed of sound is 340 m/s. Find the audible range of wavelength for human being.
Ans: Here, f1= 20 Hz, f2= 20000 Hz, v= 340 m/s
∴ Velocity of wave,v = f × λ
∴ λ2 = v/f2
∴ λ2 =340/20000
∴ λ2 = 0.017 m
Human ear can responds to wavelength of range from 0.017 m to 17 m for the given medium.