Sound WavesHard
Question
A wave disturvance in a medium is described by
y(x,t) = 0.02 cos
cos(10π)
where x and y are in meters and t is in seconds
y(x,t) = 0.02 cos
cos(10π)where x and y are in meters and t is in seconds
Options
A.A node occurs at x = 0.15 m
B.An antinode occurs at x = 0.3 m
C.The speed of wave is 5 ms-1
D.The wavelength of wave is 0.2 m
Solution
It is given that y(x,t) = 0.02 coscos(10πx)
A cos(ωt + π/2) cos kx
Node occurs when kx =
etc.
10 πx =
⇒ x = 0.05 m, 0.15 m option (a)
Antinode occurs when kx = π, 2π 3π etc.
10πx = π, 2π 3π
⇒ x = 0.1m, 0.2m, 0.3m option (b)
Speed of wave is given by
v =
= 
= 5 m/s option (c)
Wavelength is given by
λ =
m = 0.2m option (d)
cos(10πx) A cos(ωt + π/2) cos kx Node occurs when kx =
etc. 10 πx =
⇒ x = 0.05 m, 0.15 m option (a)
Antinode occurs when kx = π, 2π 3π etc.
10πx = π, 2π 3π
⇒ x = 0.1m, 0.2m, 0.3m option (b)
Speed of wave is given by
v =
= = 5 m/s option (c)Wavelength is given by
λ =
m = 0.2m option (d)Create a free account to view solution
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