Question

derive the relation between wave speed , frequency and wavelength of a progressive wave

Answer 1

The equation for progressive wave is written as -

                              $y =rsin[kx-\omega t]$

    Here y = instantaneous  displacement

             k = propagation constant

             x = the direction of propagation

        $\omega\ =\ angular\ frquency$

        $The\ propagation\ constant\ k\ =\frac{2\pi}{\lambda}$

$and\ angular\ frequency\ \omega\ =\frac{2\pi}{T}$

Here  T = time period

        $\lambda =\ wavelength$

    The speed of a progressive wave is calculated as-

                                          $v=\frac{\omega}{k}$

                                                 $=\frac{2\pi/T}{2\pi/\lambda}$

                                                 $=\frac{\lambda}{T}$

                                                 $=f\lambda$

Here f is the frequency and frequency is the reciprocal of time period.

Hence relation between speed, frequency and wavelength for a progressive is -

                          $v=f\lambda$

                                                 

   

       

Answer 2

Answer:

Wave speed : 1he distance covered by a progress

Ive wave per unit time is called the wave speed.

(2) Frequency : The number ot waves that pass per

unit time across a given point of the medium is

called the frequency of the wave.

INote : t is equal to the number of vibrations per unit

time made by a particle of the medium.]

3) Wavelength: Wavelength is the distance between

consecutive particles of the medium which are

moving in exactly the same way at the same time

and have the same displacement from their equili-

brium postions.

INote : Such particles are said to be in the same phase

(the same state ot vibration).

Amplitude: The magnitude of the maximum dis-

placement of a particle of the medium from its

equilibrium position is called the amplitude of the

wave.

5) Period: The time taken for a complete wave

(one wavelength long) to pass a given point in the

medium is called the period of the wave.

INote: It is equal to the periodic time of the vibrational

motion of a particle of the medium.

6) Wave number: The number of waves present per

unit distance is called the wave number.