xercise 15.40 A rope of length 1.41m is stretched between two supports with a te

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xercise 15.40

A rope of length 1.41m is stretched between two supports with a tension that makes the transverse waves have a speed of 49.0m/s .

Part A

What is the wavelength of the fundamental harmonic?

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Part B

What is the frequency of the fundamental harmonic?

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Part C

What is the wavelength of the second overtone?

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Part D

What is the frequency of the second overtone?

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Part E

What is the wavelength of the fourth harmonic?

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Part F

What is the frequency of the fourth harmonic?

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xercise 15.40

A rope of length 1.41m is stretched between two supports with a tension that makes the transverse waves have a speed of 49.0m/s .

Part A

What is the wavelength of the fundamental harmonic?

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Part B

What is the frequency of the fundamental harmonic?

? = m

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Part C

What is the wavelength of the second overtone?

f = Hz

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Part D

What is the frequency of the second overtone?

? = m

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Part E

What is the wavelength of the fourth harmonic?

f = Hz

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Part F

What is the frequency of the fourth harmonic?

? = m

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f = Hz

Explanation / Answer

A) Wavelenth of fundamental harmonic, lamda1 = 2*L

= 2*1.41

= 2.82 m

B) the frequency of the fundamental harmonic, f1 = v/lamda1

= 49/2.82

= 17.4 Hz

C)What is the wavelength of the second overtone, lamda3 = 2*L/3

= 2*1.41/3

= 0.94 m

d) the frequency of the second overtone, f3 = v/lamda3

= 49/0.94

= 52.12 Hz

e) What is the wavelength of the fourth harmonic, lamda4 = 2*L/4

= 2*1.41/4

= 0.705 m

f) the frequency of the second overtone, f3 = v/lamda3

= 49/0.705

= 69.5 Hz

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