Question

A wave on a string has the formula y = 0.6sin (0.5x – 2.5t + π/2). Find the wavelength, frequency, period, phase constant, and speed of the wave? The string has a linear density μ = 0.2 kg/m. What is the tension in the string?

Answer 1

(1) Time period T= 2π/ω = 2π/3 sec

general equation of wave

y( x,t ) = A sin ( kx−ωt )

frequency f = 1/T = 3/2π Hz

Answer 2

The general equation of wave is y(x,t)=Asin(kx−ωt+ϕ).

where,

A= amplitude

k= wave number = 2π/λ

ω=anuglar frequency= 2π/T

Phase constant = ϕ

Speed of wave(v) =ω/k

The speed of the wave is also, (v)= √μ/T  ( where μ = linear density and T = tension)

1. so the wave length =

k= 2π/λ

λ=2π/k

Given, k= 0.5

λ=4π

2. Frequency(f)=2πf=ω

Given, ω=2.5

f=2π/ω

f=0.8π

3. time period= 1/f

                         =5/4π

4. phase constant= π/2

5. wave speed (v)= ω/k

                           =2.5/0.5

                          =5m/s

6. Tension =

v=√μ/T

v= 5m/s

Given, μ = 0.2kg/m

T= μ/v²

T=0.2/5²

T= 0.08 N