Question

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 1

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

`\lambda = (2L)/(n)`

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

the frequency expression is given by

`f = n(v)/(2L)`

now, wavelength calculation

n = 1

`\lambda_1 = (2* 2)/(1)`

λ₁ = 4 m

n = 2

`\lambda_2 = (2* 2)/(2)`

λ₂ = 2 m

n =3

`\lambda_3 = (2* 2)/(3)`

λ₃ = 1.333 m

now, frequency calculation

n = 1

`f = n(v)/(2L)`

`f_1 =1* (50)/(2* 2)`

f₁ = 12.5 Hz

n = 2

`f = n(v)/(2L)`

`f_2 =2* (50)/(2* 2)`

f₂= 25 Hz

n = 3

`f = n(v)/(2L)`

`f_3 =3* (50)/(2* 2)`

f₃ = 37.5 Hz