a 0.303 kg clothesline is stretched with a tension of 53.4 n between two poles 6.60 m apart.

part a
what is the frequency of the fundamental harmonic?
$f_1 =$ hz

part b
what is the frequency of the second harmonic?
$f_2 =$ hz

Question

a 0.303 kg clothesline is stretched with a tension of 53.4 n between two poles 6.60 m apart.

part a
what is the frequency of the fundamental harmonic?
$f_1 =$ hz

part b
what is the frequency of the second harmonic?
$f_2 =$ hz

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Wave Speed on a String", "Tension in a Wire", "Fundamental Frequency" ], "new_concepts": [], "current_concepts": [ "Wave Speed on a String", "Tension in a Wire", "Fundamental Frequency", "Standing Waves in Pipes" ] } ## Calculate the wave speed on the clothesline $$ \begin{aligned} m &= 0.303\text{ kg}\ L &= 6.60\text{ m}\ T &= 53.4\text{ N}\ \mu &= \frac{m}{L} = \frac{0.303}{6.60} \approx 0.045909\text{ kg/m}\ v &= \sqrt{\frac{T}{\mu}} = \sqrt{\frac{53.4}{0.045909}} \approx 34.105\text{ m/s} \end{aligned} $$ ## Calculate the fundamental frequency (Part A) $$ \begin{aligned} f_1 &= \frac{v}{2L} = \frac{34.105}{2 \times 6.60} \approx 2.5837\text{ Hz} \approx 2.58\text{ Hz} \end{aligned} $$ ## Calculate the frequency of the second harmonic (Part B) $$ \begin{aligned} f_2 &= 2 \times f_1 = 2 \times 2.5837 \approx 5.1674\text{ Hz} \approx 5.17\text{ Hz} \end{aligned} $$ ## Question 1 $f_1 =$ 2.58 Hz ## Question 2 $f_2 =$ 5.17 Hz { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Natural Science", "Physics", "Wave Speed on a String" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the wave speed on the clothesline

Calculate the fundamental frequency (Part A)

Calculate the frequency of the second harmonic (Part B)

Answer:

Question 1

Question 2