Question
Two waves passing through a region are represented by
y = 1.0 cmsin [ (3.14 cm−1) x − (157 s−1)t]
and y = 1.5 cmsin [ (1.57 cm−1)x − (314 s−1) t]
Find the displacement of the particle at x = 4.5 cm at time t = 5.0 ms.
y = 1.0 cmsin [ (3.14 cm−1) x − (157 s−1)t]
and y = 1.5 cmsin [ (1.57 cm−1)x − (314 s−1) t]
Find the displacement of the particle at x = 4.5 cm at time t = 5.0 ms.
Answer: Option D
:
D
According to the principle of superposition, each wave produces its disturbance independent of the other and the resultant disturbance is equal to the vector sum of the individual disturbances. The displacements of the particle at x = 4.5 cm at time t = 5.0 ms due to the two waves are,
y1=(1.0cm)sin(3.14cm−1)(4.5cm)−(157s−1)(5.0×10−3s)
=(1.0cm)sin[4.5π−π4]
=(1.0cm)sin[4.5π−π4]=1.0cm√2
and
y2=(1.5cm)sin[(1.57cm−1)(4.5cm)−(314s−1)(5.0×10−3s)]
= (1.5cm)sin[2.25π−π2]
= (1.5cm)sin[2π−π4]
= −(1.5cm)sinπ4=−1.5cm√2
The net displacment is
y=y1+y2=−0.5cm√2=−0.35cm
Was this answer helpful ?
:
D
According to the principle of superposition, each wave produces its disturbance independent of the other and the resultant disturbance is equal to the vector sum of the individual disturbances. The displacements of the particle at x = 4.5 cm at time t = 5.0 ms due to the two waves are,
y1=(1.0cm)sin(3.14cm−1)(4.5cm)−(157s−1)(5.0×10−3s)
=(1.0cm)sin[4.5π−π4]
=(1.0cm)sin[4.5π−π4]=1.0cm√2
and
y2=(1.5cm)sin[(1.57cm−1)(4.5cm)−(314s−1)(5.0×10−3s)]
= (1.5cm)sin[2.25π−π2]
= (1.5cm)sin[2π−π4]
= −(1.5cm)sinπ4=−1.5cm√2
The net displacment is
y=y1+y2=−0.5cm√2=−0.35cm
Was this answer helpful ?
More Questions on This Topic :
Latest Videos
Latest Test Papers
Submit Solution