Calculating Clicks: Spoke Card Oscillations and Rotational Motion

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SUMMARY

The discussion focuses on calculating the required rotational speed of a wheel with 32 spokes to produce a musical note at 440 Hz using a thin card. The key formula involved is ω = 2πƒ, where ω represents angular velocity in radians per second. To convert this to revolutions per minute (rpm), the result must be multiplied by 60. The correct calculation reveals that the wheel must rotate at 825 rpm to achieve the desired frequency, factoring in the number of spokes that generate a sound with each contact.

PREREQUISITES
  • Understanding of angular velocity and its relationship to frequency
  • Familiarity with the formula ω = 2πƒ
  • Basic knowledge of rotational motion concepts
  • Ability to convert between radians per second and revolutions per minute
NEXT STEPS
  • Study the relationship between frequency and angular velocity in rotating systems
  • Learn how to calculate revolutions per minute from angular velocity
  • Explore the physics of sound generation through mechanical disturbances
  • Investigate the effects of varying the number of spokes on sound frequency
USEFUL FOR

Physics students, educators, and anyone interested in the principles of rotational motion and sound generation in mechanical systems.

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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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