Chap -4

 

Wave

“A wave is a vibratory disturbance that travels through medium which carries energy from one place to another.”When a pebble is thrown
in a lake, it creates a disturbance and forms ripples which travel together as
water wave. In propagating of wave, particles of medium do not leave their position. They execute simple harmonic motion about mean points. A few examples of waves are:  water wave, light wave, electromagnetic wave, sound wave, seismic wave (earthquakes).

Distinguish between mechanical and non mechanical wave

            We can distinguish wave in two parts on the basis of requirement of medium for propagation.

Mechanical wave	Non mechanical (Electromagnetic Wave)
1.      Those waves which require a medium for their propagation are called mechanical waves.	Those waves which do not require a medium for their propagation are called non mechanical waves or electromagnetic waves.
2.      Mechanical waves can be transverse or longitudinal.	Electromagnetic waves are always transverse wave.
3.      These waves travel in the form of crest and troughs or compression and rarefaction.	These wave travel in the form of electric and magnetic field.
4.      Speed is less in compare to an electromegnic wave.	Electromagnetic waves travel in vacuum with speed of 3 x 108 m/s.

Distinguish between transverse and longitudinal wave

            We can distinguish wave in two parts on the basis of direction of particles’ vibration in medium.

Transverse Wave	Longitudinal Wave
1.      A wave in which the particles of the medium vibrate perpendicular to the direction of propagation of wave is called a transverse wave.	A wave in which the particles of the medium vibrate parallel to the direction of propagation of wave is called a longitudinal wave.
2.
3.      This wave travels in the form of crest and troughs.	This wave travels in the form of compressions and rarefactions.
4.      While passing through the medium this wave change shape of the medium.	While passing through the medium this wave change volume (density and pressure) of the medium.
5.      This wave is possible in solid medium only.	This wave is possible in all kinds of medium.
6.      This type of wave can be polarised.	This wave cann’t be polarised.
7.      Vibration in string, Electromegnetic waves are some of the example of transevese wave.	Sound wave, wave in spring, Primary wave in earthquack are some of the example of longitudinal wave.

Wave anatomy

            A simple wave has a number of characteristics, which are shown as follows.

Crest: The highest points on the wave are known as crests.

Trough: The lowest points on the wave are known as troughs.

Amplitude: The maximum displacement of the particle from the mean position is called amplitude.

Wavelength (): The distance between two consecutive particles having phase difference 2Π is called wavelength of the wave. OR The distance between two consecutive crests or troughs is called wavelength. Wavelength gives us length of one complete wave.

Periodic time (T): The time taken by particle to complete one vibration or oscillation is called periodic time or time period of wave.

Frequency (f): The number of oscillations or vibrations completed by particle in one second is called frequency of the wave.

Unit of frequency is s^-1 or hertz (Hz).

5.1.3 Relation between velocity, frequency and wavelength

We know that distance travelled by wave per unit time is called velocity of wave.

Velocity of wave=(distance travelled by wave)/time

v=d/t

We have known that time taken for one complete oscillation of particle on wave is called time period (T) and in this time wave travelled as much distance as wavelength (λ).

So, velocity 

v=λ/T

But, frequency f=1/T

v=fλ

Numerical 1: Calculate the wavelength and the time period of a tuning fork of frequency 256 Hz which is set to vibrate. Velocity of sound in air is 330 m/s.

Solution: 

Frequency of the tuning fork (f) = 256 Hz

Velocity of sound (v) = 330 m/s

We know that the formula for velocity of sound,     v=fλ

so, wavelength  λ= v/f

∴ λ = 330/256 = 1.29 m

And time period T = 1/f  = 1/256 = 0.0039 s

Numerical 2:  What is the wavelength of sound, whose frequency is 512 Hz? Velocity of sound in air is 330 m/s.

Solution:    

Speed of the sound wave (v) = 330 m/s

Frequency of the sound wave (f) = 512 Hz

So, wavelength  λ = v/f

∴  λ = 330/512 = 0.644 m

Numerical 3:  Radio waves of speed 3X108 ms-1 are reflected by an asteroid and received by earth station. The time elapsed between the sending of the signal and receiving it back at the earth station is 10 s. What is the distance of the asteroid from the earth?

Solution:    

Here distance travelled by wave from earth to asteroid is d and asteroid to earth is also d then total distance travelled by radio wave is 2d.

Speed v=2d/t

∴ Distance d = (v×t )/2  = (3 X 〖10〗^8  X 10)/2   = 15 X 108 m

Numerical 4:  A sound wave of wave length 0.33 m has a time period of 10-3 s. If the time period is decreased to 10-4 s. Calculate the wave length and frequency of the new wave.

Solution:    

Here wave length of wave λ = 0.33 m

And time period of wave, T = 10-3 s

Velocity of sound  v=λ/T

∴ v  =   0.33/〖10〗^(-3)  = 0.33 X 103 = 330 m/s

Time period of new wave, T = 10-4 s

Therefore wavelength of new wave  λ = v X T = 330 x 10-4 = 0.033 m

Frequency of new wave f =   1/T  = 1/〖10〗^(-4)  = 104 Hz

Numerical 5:  A sound wave has a frequency of 3250 Hz and a wavelength of  0.1 m then find out  its velocity.

Solution:    

Frequency of the sound wave (f) = 3250 Hz.

wavelength of the sound (λ) = 0.1 m

We know that the formula for velocity of sound,     v=fλ = 3250 X 0.1 = 325 m/s

Numerical 6: A sound wave travels with a velocity of 330 m/s and has a frequency of 500 Hz.  What is its wavelength?

Solution:    

Speed of the sound wave (v) = 330 m/s

Frequency of the sound wave (f) = 500 Hz

So, wavelength  λ = v/f

∴  λ = 330/500 = 0.66 m