CGPET 2021 Solved Paper

Given, equation of wave,
y(x,t)=(0.01)[sin(62.8m−1).x][cos(628s−1).t]
and π=3.14
Compare with standard equation given below,
we get
y(x,t)=(2a)sin(kx),cosωt
ω=628s−1,
k=62.8m−1
Since, k=

2π

λ

⇒ λ=

2π

k

=

2×3.14

628

∴ λ=

1

10

m
(A) According to the problem, string is vibrating in its fifth harmonic frequency, so there are 5 complete loops as shown in the figure.Thus, total number of nodes =6

(B) The length of the string for 5 harmonics,
l=

5λ

2

=

5

2

×

1

10

∴ l=0.25 m
(C) The fundamental frequency, nf=

v

2l

⇒ nf=

ω

k

.(2l)(∵v=

ω

k

)
=

628

628

.

1

2×0.25

=20Hz
(D) The fifth harmonic frequency, n5=5(

v

2l

)
=5(20)=100Hz