Question

A rope of length 1.40 m is stretched between two supports with a tension that makes the transverse waves have a speed of 47.9 m/s .

Part A

What is the wavelength of the fundamental harmonic?

Part B

What is the frequency of the fundamental harmonic?

Part C

What is the wavelength of the second overtone?

Part D

What is the frequency of the second overtone?

Part E

What is the wavelength of the fourth harmonic?

Part F

What is the frequency of the fourth harmonic?

Answer 1

given

L = 1.4 m

v = 47.9 m/s

A)

lamda1 = 2*L

= 2*1.4

= 2.80 m

B) f1 = v/lamda1

= 47.9/2.8

= 17.1 Hz

C) lamda3 = 2*L/3 (second overtone = third harmonic)

= 2*1.4/3

= 0.933 m

D) f3 = v/lamda3 (second overtone = third harmonic)

= 47.9/0.933

= 51.3 Hz

E) lamda4 = 2*L/4

= 2*1.4/4

0.7 m

F) f4 = v/lamda4

= 47.9/0.7

= 68.4 Hz