Exercise 15.38 A 1.45-m-long rope is stretched between two supports with a tensi

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Exercise 15.38

A 1.45-m-long rope is stretched between two supports with a tension that makes the transverse waves have a speed of 64.0 m/s .

Part A

What is the wavelength of the fundamental harmonic?

Express your answer with the appropriate units.

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Part B

What is the frequency of the fundamental harmonic?

Express your answer with the appropriate units.

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Part C

What is the wavelength of the second overtone?

Express your answer with the appropriate units.

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Part D

What is the frequency of the second overtone?

Express your answer with the appropriate units.

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Part E

What is the wavelength of the fourth harmonic?

Express your answer with the appropriate units.

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Part F

What is the frequency of the fourth harmonic?

Express your answer with the appropriate units.

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PHY 2048 Section 981 Fall 2015

Signed in as Rohan Wadera

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Exercise 15.38

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Exercise 15.38

A 1.45-m-long rope is stretched between two supports with a tension that makes the transverse waves have a speed of 64.0 m/s .

Part A

What is the wavelength of the fundamental harmonic?

Express your answer with the appropriate units.

Explanation / Answer

a)

wavelength, lambdaf, of fundamental harmonic, in terms of L distance between supports, is given by
lambdaf /2 = L or lambdaf = 2L = 2*1.45 = 2.9 m

b)

Frequencyf = 64 / 2.9 = 22.07 Hz

c)

3(lambda2H/2) = L or lambda2H = 2L/3 = 2.9/3 = 0.967 m

d)

Frequency2H = 64/0.967 = 66.18 Hz

e)

5(lambda2H/2) = L or lambda2H = 2L/5= 2.9/5 = 0.58 m

f)

Frequency4H = 64/0.58 = 110.34 Hz

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