A 1.56-m-long rope is stretched between two supports with a tension that makes t

Question

A 1.56-m-long rope is stretched between two supports with a tension that makes the transverse waves have a speed of 70.0 m/s .

Part A

What is the wavelength of the fundamental harmonic?

Express your answer with the appropriate units.

Part B

What is the frequency of the fundamental harmonic?

Express your answer with the appropriate units.

Part C

What is the wavelength of the second overtone?

Express your answer with the appropriate units.

Part D

What is the frequency of the second overtone?

Express your answer with the appropriate units.

Part E

What is the wavelength of the fourth harmonic?

Express your answer with the appropriate units.

Part F

What is the frequency of the fourth harmonic?

Express your answer with the appropriate units.

Explanation / Answer

A) for the funadamental harmonic

l = lamda/2 =

wavelength lamda = 2*l = 2*1.56 = 3.12 m

B) speed is v = lamda*f

frequency f = v/lamda = 70/3.12 = 22.43 Hz

C) second overtone

lamda = (2l/3) = (2*1.56)/3 = 1.04 m

D) frequency f = v/lamda = 70/1.04 = 67.3 Hz

E) Fourth harmonic

l = 2*lamda

lamda = l/2 = 1.56/2 = 0.78 m

F) f = v/lamda = 70/0.78 = 89.74 Hz

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