Question

a wave is represented by the equation y=2sinx (0.5x-700t) where all distances are measured in centimeter and time in seconds. for this wave calculate it. (1) frequency (2)wavelength (3)speed

Answer 1

f = 350/π

λ = 4π

v = 14 m/s

Step-by-step explanation:

y = 2 sin(0.5x - 700t)

y = A sin(kx - ωt), comparing both with each other, we will realise that

A = 2

k = 0.5

ω = 700

A is the amplitude,

k is the phase constant and

ω is the angular frequency

k = 2π/λ, and we know k = 0.5 too, thus

0.5 = 2π/λ

λ = 4π

f = ω/2π

f = 700 / 2π

f = 350 / π

f = 111.39, approximately 111 Hz

v = fλ

v = 350/π * 4π

v = 350 * 4

v = 1400 cm/s

v = 14 m/s

therefore, wavelength is 4π, speed is 14 m/s, and frequency is 350/π

Answer 2

Using y= Asin(kx-wt)

y= 2sinx(0.5x-700t)

By comparison

Omega(w) = 700

But w= 2πf= 700

Frequency= 700/2π= 111.4Hz

2.

K = 2π/ wavelength

So k= 0.5

So wavelength= 2π/0.5= 12.6cm

3.

Speed= wavelength x frequency

= 111.4* 12.6= 1403.6cm/s