Question

A rope of length 1.51 m is stretched between two supports with a tension that makes the transverse waves have a speed of 47.6 m/s.

What is the wavelength of the fundamental harmonic?

What is the frequency of the fundamental harmonic?

What is the wavelength of the second overtone?

What is the frequency of the second overtone?

What is the wavelength of the fourth harmonic?

What is the frequency of the fourth harmonic?

Answer 1

Data:

Length, L = 1.51 m

Speed, V = 47.6 m/s

Solution:

(a)

Wavelength, λ = 2L

                       = 2 * 1.51

                       = 2.52 m

Ans: λ = 2.52 m

(b)

Frequency, f = v / λ

                    = 47.6 / 2.52

                    = 18.89 m/s

Ans:

Frequency, f = 18.89 Hz

(c)

For second overtone, L = 3λ/2

Wavelength, λ = 2L/3

                       = 2 * 1.51 / 3

                       = 1.007 m

Ans:

Wavelength, λ = 1.007 m

(d)

Frequency of second overtone, f = v / λ

                                                  = 47.6 / 1.007

                                                  = 47.28 Hz

Ans:

Frequency, f = 47.28 Hz

(e)

For fourth harmonic, L = 4λ/2

                                    = 2λ

Wavelength, λ = L/2

                       =1.51 / 2

                       = 0.755 m

Ans:

Wavelength, λ = 0.755 m

(f)

Frequency of fourth harmonic, f = v / λ

                                                  = 47.6 / 0.755

                                                  = 63.05 Hz

Ans:

Frequency, f = 63.05 Hz