Calculating Clicks: Spoke Card Oscillations and Rotational Motion

[Aboramou]

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

 

[TSny]

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.

 

[Aboramou]

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

 

[Nidum]

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 ?