A 2-m long string is stretched between two supports with a tension that produces a wave speed equal to vw=50.00m/s. What are the wavelength and frequency of the first three modes that resonate on the string?

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

where n is the number of antinodes; n = 1,2,3,...

the frequency expression is given by

now, wavelength calculation

      n = 1

                    λ₁ = 4 m

      n = 2

                   λ₂ = 2 m

      n =3

                    λ₃ = 1.333 m

now, frequency calculation

      n = 1

                    f₁ = 12.5 Hz

      n = 2

                    f₂= 25 Hz

      n = 3

                    f₃ = 37.5 Hz

force tends to be low and long diustance masses are high