Two waves, each having a frequency of 100 Hz and a wavelength of 2 0 cm, are travelling in the same direction on a string. What is the phase difference between the waves (A) if the second wave was produced 0 015 s later than the first one at the same place, (B) if the two waves were produced at the same instant but the first one was produced a distance 4 0 cm behind the second one? (C) If each of the waves has an amplitude of 2 0 mm, what would be the amplitudes of the resultant waves in part (A) and (B)?

Question

Philoid · Accepted Answer

A. 3π B. 4π

C. zero, 40 mm

Wave speed = wave length × wave frequency

So, in 0.015 seconds, the path travelled by wave is,

Now, we know that, phase difference,

(A)

Now, given, path difference,

Putting in the equation, we get,

(B)

If two waves have same frequency and wavelength, the must have same amplitude too.

Using this concept, we get,

So,

Or,

So, final resulting amplitude is,

Now, putting the values of r, we get,

A=0 for

A=4 mm for (C)