The displacement of particles in a string stretched in the x-direction is represented by y. Among the following expressions for y, those describing wave motion are?
A.
coskxsinωt
B.
k2 ω2-ω2 t2
C.
cos2 (kx+ωt)
D.
cos2 (k2 x2-ω2 t2)
Answer: Option A
Explanation:
y= coskxsinωt is the only equation of standing wave. The conditions for a function of x and t to represent a wave is (∂2 y)/∂x2 = constant×(∂2 y)/∂t2 Only first expression satisfies this condition.
A tube closed at one end and containing air produces, when excited, the fundamental note of frequency 512Hz. If the tube is open at both ends, the fundamental frequency that can be excited is (in Hz).
A.
1024
B.
512
C.
256
D.
128
Answer: Option A
Explanation:
Fundamental frequency of a closed pipe, γ=v/4L=512Hz Fundamental frequency of open pipe γ‘=v/4L=2γ=2×512=1024Hz.
