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?
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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?
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(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
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