ip two violinists, one directly behind the other, play for a listener directly in front of them. both violinists sound concert a (440 hz).

part a
what is the smallest separation between the violinists that will produce destructive interference for the listener?
$d =$ m

part b
does this smallest separation increase or decrease if the violinists produce a note with a higher frequency?
( ) increases
( ) decreases

Question

ip two violinists, one directly behind the other, play for a listener directly in front of them. both violinists sound concert a (440 hz).

part a
what is the smallest separation between the violinists that will produce destructive interference for the listener?
$d =$   m

part b
does this smallest separation increase or decrease if the violinists produce a note with a higher frequency?
( ) increases
( ) decreases

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Wave Speed Formula", "Wave Interference", "Path Difference", "Constructive Interference" ], "new_concepts": [ "Destructive Interference Condition" ], "current_concepts": [ "Wave Speed Formula", "Wave Interference", "Path Difference", "Destructive Interference Condition" ] } ## Calculate the wavelength of the sound wave $$ \begin{aligned} &v = 343\text{ m/s} \quad (\text{speed of sound in air at } 20^\circ\text{C})\ &f = 440\text{ Hz}\ &\lambda = \frac{v}{f} = \frac{343}{440} \approx 0.7795\text{ m} \end{aligned} $$ ## Determine the smallest separation for destructive interference $$ \begin{aligned} &d = \frac{\lambda}{2}\ &d = \frac{0.7795}{2} \approx 0.390\text{ m} \end{aligned} $$ ## Analyze the effect of a higher frequency on the separation $$ \begin{aligned} &f \uparrow \implies \lambda = \frac{v}{f} \downarrow\ &d = \frac{\lambda}{2} \downarrow \implies \text{decreases} \end{aligned} $$ ## Question 1 $d = 0.390$ m ## Question 2 increases

decreases

{ "subject": "Natural Science", "question_type": "Multi-part", "knowledge_point": [ "Natural Science", "Physics", "Wave Interference" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the wavelength of the sound wave

Determine the smallest separation for destructive interference

Analyze the effect of a higher frequency on the separation

Answer:

Question 1

Question 2