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The displacement of a medium in a sound ...

The displacement of a medium in a sound wave is given by the equation `y_(1)=Acos(ax+bt)` where A, a and b are positive constants. The wave is reflected by an obstacle situated at x=0. the intensity of the reflected wave is 0.64 times that of the incident wave.
(i) What are the wavelength and frequency of incident wave ? ________ (ii) Write the equation for the reflected wave. _________ (iii) In the resultant wave formed after reflection, find the maximum and minimum values of the particle speeds in the medium. ____________ (iv) Express the resultant wave as a superposition of a standing wave and a traveling wave. What are the positions of the antinodes of the standing wave ? What is the direction propagation of traveling wave?__________

A

y=0.8A Cos(bt – ax)

B

y=0.4A Sin(bt - ax)

C

y=-0.8A Cos(bt -ax)

D

y=0.4A Sin(bt + ax)

Text Solution

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The correct Answer is:
C
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The displacement of the medium in a sound wave is given by the equation y_(1) = A cos(ax + bt) where A , a and b are positive constants. The wave is reflected by an obstacle situated at x = 0 . The intensity of the reflected wave is 0.64 times that of the incident wave. (a) What are the wavelength and frequency of incident wave? (b) Write the equation for the reflected wave. ( c ) In the resultant wave formed after reflection, find the maximum and minimum values of the particle speeds in the medium. (d) Express the resultant wave as a superposition of a standing wave and a travelling wave. What are the positions of the antinodes of the standing wave ? What is the direction of propagation of travelling wave?

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