A wave is represented by the equation y = 0.5 sin 0.4π(X - 60t), where the distance (X) is measured in centimetres and time (t) in seconds. What is the wavelength of the wave?

sundaykingsley123

4 months ago

i don't understand why 0.4π changed to 4π in the answer

AyanfeOba.Dudu

1 year ago

The wave equation is given as:

𝑦
=
0.5
sin
⁡
(
0.4
Ω
(
𝑋
−
60
𝑡
)
)
y=0.5sin(0.4Ω(X−60t))
A standard wave equation is:

𝑦
=
𝐴
sin
⁡
(
𝑘
𝑋
−
𝜔
𝑡
)
y=Asin(kX−ωt)
where:

𝑘
k is the wave number, given by
𝑘
=
2
𝜋
𝜆
k=
λ
2π
​
, where
𝜆
λ is the wavelength.

𝜔
ω is the angular frequency.

By comparing the given equation with the standard form, we identify:

𝑘
=
0.4
Ω
k=0.4Ω
Since
𝑘
=
2
𝜋
𝜆
k=
λ
2π
​
, we equate:

0.4
Ω
=
2
𝜋
𝜆
0.4Ω=
λ
2π
​

Solving for
𝜆
λ:

𝜆
=
2
𝜋
0.4
Ω
λ=
0.4Ω
2π
​

Approximating
𝜋
≈
3.14
π≈3.14:

𝜆
=
6.28
0.4
λ=
0.4
6.28
​

𝜆
=
10.0
 cm
λ=10.0 cm
Thus, the correct answer is:

𝐸
.
 
10.0
 
𝑐
𝑚
E. 10.0 cm

Ebere333

2 years ago

please who can solve this oh....