Respuesta :
Answer
given,
Length of the string, L = 2 m
speed of the wave , v = 50 m/s
string is stretched between two string
For the waves the nodes must be between the strings
the wavelength is given by
[tex]\lambda = \dfrac{2L}{n}[/tex]
where n is the number of antinodes; n = 1,2,3,...
the frequency expression is given by
[tex]f = n\dfrac{v}{2L}[/tex]
now, wavelength calculation
n = 1
[tex]\lambda_1 = \dfrac{2\times 2}{1}[/tex]
λ₁ = 4 m
n = 2
[tex]\lambda_2 = \dfrac{2\times 2}{2}[/tex]
λ₂ = 2 m
n =3
[tex]\lambda_3 = \dfrac{2\times 2}{3}[/tex]
λ₃ = 1.333 m
now, frequency calculation
n = 1
[tex]f = n\dfrac{v}{2L}[/tex]
[tex]f_1 =1\times \dfrac{50}{2\times 2}[/tex]
f₁ = 12.5 Hz
n = 2
[tex]f = n\dfrac{v}{2L}[/tex]
[tex]f_2 =2\times \dfrac{50}{2\times 2}[/tex]
f₂= 25 Hz
n = 3
[tex]f = n\dfrac{v}{2L}[/tex]
[tex]f_3 =3\times \dfrac{50}{2\times 2}[/tex]
f₃ = 37.5 Hz
