Wave speed proof - schoolphysics



Proof of the formula for wave speed

We start with the simple formula for speed:

Speed = distance/time in other words speed is the distance travelled in one second.

The frequency (f) of w a wave is how any vibrations per second the wave makes at a particular point

The wavelength (λ) of a wave is the distance between ‘similar’ points on the wave. That is, for example, crest-to-crest or trough-to-trough.

Now if f waves move past appoint in one second the distance travelled by the wave is f whole wavelengths. (See Figure 1 (a) and (b))

But the distance travelled in one second is the speed and so:

-----------------------

3λ

Speed = frequency (f) x wavelength (λ)

Figure 1(a)

Figure 1(b)

P

P

P

In Figure 1(a) the wavelength of the wave is 1.5 cm and three waves pass the point P every secoࠀ਀ਂఈఊಆಈಊಌಢತದನಬ೴೶೸೼ഔഖമരഴശഺ഼ീ฀᐀ᙔᚂᚄᛂᛄᜂᜄᜲ᜴ᝂᝄᝎnd. This means that the frequency of the wave is 3 Hz and the speed of the wave is 3x1.5 = 4.5 cm/s.

In Figure 1(b) the wavelength of the wave is 0.75 cm and four waves pass the point P every second. This means that the frequency of the wave is 4 Hz and the speed of the wave is 4x0.75 = 3 cm/s.

Wave Starting position

Wave position one second later

Wave position one second later

Wave starting position

1.5 cm

3 cm

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