Question 5 (a)
I said the path difference must be a odd number of non integer half wavelengths and the vector sum of the amplitudes must be zero.
The mark scheme says :
either same amplitude / intensity at M
or ratio of amplitudes is 1.28 / ratio of intensities is 1.28^2
Can someone please explain the statements in bold ? How can same amplitudes lead to an intensity of zero ?
My answers would have been :
1. The waves should meet in antiphase at M.(Phase difference = pie)
2. The sources must emit waves having the same amplitudes.
Same amplitudes meaning that their value should be the same but in antiphase.
Example : Amplitude of S1 = 10mm, amplitude of S2 = -10mm.What you said about vector sum should be zero is correct but for amplitude we do not use the term vector. We just say they are equal in amplitude but in antiphase
By ratio of amplitudes, the MS used it in terms of scale drawing. Use pythagoras theorem to find the direct distance from S2 to M. You'll see that it comes out to be 128cm.
Length is directly proportional to the amplitude and also to the square of intensity.
(b) Distance that waves from S1 have to covered is 100cm while those from S2 have to cover 128cm. The difference therefore is 28cm.
Path difference = nV/F
Using the speed of sound and n=1 ----> F
1 = (1 x 330)/0.28 = 1179
Hence F
2 will be (2 x 1179) = 2358 and F
3 = 3(1179) = 3535.
It can be easily seen that F
4 will exceed the limit of 4.0 KHz.
So we'll be having 3 maxima at 1179, 2358 and 3535. This implies that we'll be having only 2 minima.
Hence answer is
2.
Hope it helps
