Two waves of amplitude 2A and A of same frequency and velocity propogate in same direction with same phase. Then resultant amplitude is
Resultant amplitude
\[ R= \sqrt{A^{2}+(2A)^{2}+ 2A.2A cos\theta} \]
As ΞΈ = 0ΒΊ
R= A+2A=3A
Two waves of intensity I1 and I2 propagate in a medium in same direction. Then sum of maximum and minimum intensity is
\[ I _{max= }\left( \sqrt{I_{1}} +\sqrt{I_{2}}\right)^{2} \]
\[ I _{min = }\left( \sqrt{I_{1}} - \sqrt{I_{2}}\right)^{2} \]
\[ I _{max} + I _{min} = 2(I_{1} + I_{2})\]
Two waves of intensity ratio 9 : 1 produce interference then
\[ \frac{I _{max}}{I _{min} } = \]
A source of sound gives five beats per second when sounded with another source of frequency 100 sβ1. The second harmonic of the source together with a source of frequency 205 sβ1 gives five beats per second. What is the frequency of the source ?
Ten tuning forks are arranged in increasing orderof frequency in such a way that any two nearest tuning forks produce 4 beats/sec. The highest frequency is twice of the lowest. Possible highest and the lowest frequencies are
Two coherent sources of different intensities send waves which interfere. The ratio of the maximum intensity to the minimum intensity is 25. The intensities are in the ratio
The equations of two interferring waves are \(Y_1 = b cos \omega t\) and \(Y_2 = b cos (\omega t+\phi)\) respectively. Destructive interference will take place at the point of observation for the following value of \(\phi\) :β
For destructive interference to occur, the phase difference between the two interfering waves must be an odd multiple of \(pi\) (i.e., \(180^0\), \(540^0 \), etc.). From the options, \(180^0 \) is correct.
Two waves having the intensities in the ratio of 9 : 1 produce interference. The ratio of maximum to minimum intensity is equal to:
The ratio of maximum to minimum intensity is given by \(frac{I_{\text{max}}}{I_{\text{min}}} = \left(\frac{\sqrt{I_1/I_2} + 1}{\sqrt{I_1/I_2} - 1}\right)^2\). Substituting \(\frac{I_1}{I_2} = 9\) yields \(\left(\frac{3 + 1}{3 - 1}\right\)^2 = 4\), which is \(4:1\).
Assertion (A): If two waves of same amplitude produce a resultant wave of same amplitude, then the phase difference between them will be \(120^\circ\).
Reason (R): The resultant amplitude of two waves is equal to sum of amplitude of two waves.
For two waves of amplitude \(A\) and phase difference \(phi\), the resultant amplitude is \(A_r = 2A \cos(\frac{\phi}{2})\). Given \(A_r = A\), so \(A = 2A \cos(\frac{\phi}{2})\), which means \(cos(\frac{\phi}{2}) = \frac{1}{2}\). Thus \(\frac{\phi}{2} = 60^\circ\), so \(\phi = 120^\circ\). Hence (A) is true. The resultant amplitude is the sum only if \(\phi = 0\). So (R) is false.
Assertion (A): Interference is position dependent phenomenon.
Reason (R): Beats is time dependent phenomenon.
Interference describes the variation of intensity with position due to superposition of waves, so (A) is true. Beats describe the periodic variation in intensity with time at a point due to superposition of two waves with slightly different frequencies, so (R) is true. (R) does not explain (A).