Question

A wave in a string has amplitude of 2 cm. The wave travels in the +ve direction of x axis with a speed of 128 ms−1 and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is:

• A. (A) y=(0.02)m sin⁡(7.85x+1005t)
• B. (B) y=(0.02)m sin(15.7x−2010t)
• C. (C) y=(0.02)m sin(15.7x+2010t)
• D. (D) y=(0.02)m sin⁡(7.85x−1005t)

Answer 1

Answer: (D)

(D) y=(0.02)m sin⁡(7.85x−1005t)

Answer 2

Explanation:
It is given that the amplitude of the wave in a string is, i.e., A = 2 cmAnd also, the wave is travelling in the positive x-direction.And the velocity v=128 ms−1According to the question 5 complete waves fit in a 4m length of the string, which means that:5λ=4 ----(1)From (1) equation,λ=45And the propagation constant,k=2πλ=2π54=7.85Also, the phase velocity of the wave is given by:v=ωk=128 ms−1⇒ω=v×k=128×7.85=1004.8≈1005 rad/secThe equation of wave can be represented as:y=Asin⁡(kx−ωt)By putting the given values in the above equation we get:y=2sin⁡(7.85x−1005t)⇒y=(0.02)sin⁡ (7.85x−1005t) (amplitude in meter =0.02 m)⇒y=(0.02)m sin(7.85x−1005t)Hence the correct option is (D).