wiz-icon
MyQuestionIcon
MyQuestionIcon
22
You visited us 22 times! Enjoying our articles? Unlock Full Access!
Question

A composite string is made by joining two strings of different masses per unit length μ and 4μ. The composite string is under the same tension. A transverse wave pulse. y=(6 mm)sin(5t+40x), where 't' is in seconds and 'x' is in meters, is sent along the lighter string towards the joint. The joint is at x=0. The equation of the wave pulse reflected from the joint is y=(2 mm)sin(5t40x+π). The percentage of the power transmitted to the heavier string through the joint is approximately

A
33%
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
89%
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
67%
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
75%
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 89%
We know that,
wave speed on a stretched string is given by
v=Tμ
On the lighter string,
v1=Tμ
On the heavier string,
v2=T4μ
Clearly, we can say that, v2<v1
and, v2=v12 ..........(1)
Amplitude of the reflected wave Ar=v1v2v1+v2Ai(ArAi)2=v1v2v1+v22
1(ArAi)2=4v1v2(v1+v2)2

Substituting (1) in the above equation, we get

1(ArAi)2=89

Since, IA2 we can say that, PA2 where, P is the power transmitted.

Power of incident wave Pi=Pr+Pt
where Pr and Pt are the powers of reflected and transmitted waves.

Thus, fraction of power transmitted to the heavier string is given by

PiPrPi×100=A2iA2rA2i×100
(1A2rA2i)×100=89×10089%

flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon