Question

Two waves y1 = A cos( 0.5 πx − 100 πt)
and y2 = A cos( 0.46 πx − 92 πt) are travelling in a pipe placed along x-axis. Find the number of times
intensity is maximum in time interval of 1 sec.
a)4 b)6 c)8 d)10

Answer 1

Answer on Question#38196 – Physics – Other

Two waves $y_1 = A \cos(0.5\pi x - 100\pi t)$ and $y_2 = A \cos(0.46\pi x - 92\pi t)$ are travelling in a pipe placed along x-axis. Find the number of times intensity is maximum in time interval of 1 sec.

a) 4 b) 6 c) 8 d) 10

Solution:

Frequency for the first and second wave:

$$f_1 = \frac{100\pi}{2\pi} = 50\,\mathrm{Hz}; \quad f_2 = \frac{92\pi}{2\pi} = 46\,\mathrm{Hz}$$

Number of times intensity of maximum in time interval of 1 sec:

$$N = (f_1 - f_2) \cdot 1\,\mathrm{sec} = (50\,\mathrm{Hz} - 46\,\mathrm{Hz}) \cdot 1\,\mathrm{sec} = 4$$

Answer: a) 4.