Calculating Clicks: Spoke Card Oscillations and Rotational Motion

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Homework Help Overview

The problem involves a rotating wheel with spokes producing a musical note when a card is held against them. The goal is to determine the necessary rotation speed in revolutions per minute to achieve a specific frequency of sound (440 Hz).

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to relate the frequency of sound to the angular velocity of the wheel, expressing uncertainty about incorporating the number of spokes into their calculations. Some participants suggest that the frequency of sound is linked to the disturbances caused by the spokes hitting the card, questioning the need for wavelength or speed of sound in the solution.

Discussion Status

Participants are exploring different interpretations of how to connect the rotational motion of the wheel with the sound frequency produced. There is acknowledgment of a potential discrepancy between the original poster's calculations and the expected answer, prompting further inquiry into the role of the spokes in generating sound.

Contextual Notes

The original poster notes a specific expected answer from a textbook, which raises questions about the assumptions made in their approach. There is also a mention of the need to clarify how the number of spokes influences the frequency of sound produced.

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Homework Statement



A thin card produces a musical note when it is held lightly against the spokes of a rotating wheel. If the wheel has 32 spokes, how quickly must it rotate, in revolutions per minute, in order to produce the A above middle C (i.e. 440 Hz)?

Homework Equations



ω=2πƒ; ƒ=1/T; ϑ=ƒλ

The Attempt at a Solution



Knowing that the speed of sound is about 340 m/s in the air, we can find the wavelength of the sound produced by the spoke card at 440 Hz frequency: λ(=ϑ/ƒ)=0.773 m. The problem is that I can't figure out what formula should include the number of spokes and how to put together sound wave motion and rotational motion of a wheel to find it's angular velocity ω. Any help is appreciated
 
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Hello and welcome to PF!

The frequency of the sound is determined by the source of the sound. In this case, the frequency of the sound is determined by the frequency that the source disturbs the air. There is a disturbance of the air each time a spoke hits the card. You don't need to use the wavelength or speed of sound.
 
TSny said:
Hello and welcome to PF!

The frequency of the sound is determined by the source of the sound. In this case, the frequency of the sound is determined by the frequency that the source disturbs the air. There is a disturbance of the air each time a spoke hits the card. You don't need to use the wavelength or speed of sound.

Hi! Thank you for your help. Unfortunately, I still haven't solved the problem. I could just substitute frequency of the sound into the equation ω=2πƒ and multiply it by 60 to get the angular velocity in rpm, but the answer I get is different from the answer given in my book (should be 825 rpm). That makes me conclude that my approach is wrong. Also I still can't see the way I can use the number of spokes to solve this problem
 
As each spoke contacts the card and then breaks contact the card is first deflected and then released . This action causes an audible 'click' .

If the wheel has X number of spokes and is rotating at N rotations/second how many clicks are generated in one second ?
 
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