Ruler Music

Classical Mechanics Level 1

Ned is trying to play music using a steel ruler extending beyond the table edge. When he strikes the ruler, a twang sound is produced.

If he wants to produce a higher frequency note, then what should he do?

Strike it softer Strike it harder Decrease the overhang Increase the overhang

9 solutions

Munem Shahriar
Sep 3, 2017

Relevant wiki: Pendulums

. A longer ruler hanging over the edge makes a lower pitch; a shorter ruler gives a higher pitch. A longer ruler vibrates more slowly, so has a lower frequency. A shorter ruler vibrates more quickly so has a higher frequency.

Note that it is hard to see the vibrations as they get very fast when the ruler is very short, so start with the longer ruler and move it gradually slower. But the longer ruler will not produce a higher frequency.

When the ruler is shorter it vibrates more quickly, so makes higher frequency pressure waves, which have a higher pitch.

Hence $\boxed{\text{If he decrease the overhang}}$ it will produce a higher frequency.

Striking the ruler harder or softer will not alter the frequency of vibration only change the its amplitude. And if hypothetically striking the ruler harder were to increase the frequency, saying it might break would in my opinion not justify to rule that answer out.

Kai Ott - 3 years, 9 months ago

Thanks you maybe correct. I have removed that part.

Munem Shahriar - 3 years, 9 months ago

That's the right idea, can you go the extra step and make an argument for why a shorter ruler will have a higher frequency?

Josh Silverman Staff - 3 years, 9 months ago

Make the ruler shorter by decreasing its other end from the edge of the table and try to play again.

Gerald Sipho - 3 years, 9 months ago

But why is it that the larger overhanging vibrates slower?

Agnishom Chattopadhyay - 3 years, 9 months ago

Relate it with sonometer frequency $\nu =1/2l\sqrt (T/\mu )$ . As is visible $\nu$ is inversely proportional to $l$ .Or another way of thinking would be to think of vibrations of the ruler in terms of standing waves with maximum vibration position corresponding to a antinode of a standing wave.When we decrease $'l'$ we actually decrease $\lambda$ and as $v=\nu \lambda$ ,and thereby increase the frequency.

Spandan Senapati - 3 years, 9 months ago

Kai Ott
Sep 4, 2017

Relevant wiki: Pendulums

Frequency of a vibrating object is reciprocally linear to the length in which it is allowed to vibrate. $f = \frac{1}{l}$ so by decreasing the "free" segment of the ruler that is allowed to vibrate $l$ (in this case the overhang, we increase the frequency. Increase/decrease will force the ruler is stroken with will not affect the frequency, only increase/decrease the amplitude of the soundwave (make the same tone louder/more silent).

But why does the frequency and the length behave in this way?

Agnishom Chattopadhyay - 3 years, 9 months ago

Gabriele Manganelli
Sep 4, 2017

Relevant wiki: Pendulums

The frequency of oscillations is inversely proportional to the wavelength estabilished, which depends on the "free" length of the ruler directly.

What is the wave whose wavelength it is that you're referring to?

Josh Silverman Staff - 3 years, 9 months ago

Devdarshan Patra
Sep 7, 2017

The time interval (oscillation) depends on the length of the string ( in case of a pendulum). It does not depend on mass and amplitude. So even if we strike it softer or harder the frequency will remain the same. So there are two options left, one is to increase the overhang and other is to decrease the overhang. When length increases the time interval also increase, which means lesser frequency. If we decrease the overhang the time period will decrease and so we will get the ruler oscillating at a higher frequency. So, the answer to this question is the third option i.e decrease the overhang

Could you explain why changing the length changes the time interval of oscillation?

Pranshu Gaba - 3 years, 9 months ago

Jay Dula
Sep 3, 2017

Distance from table end to the ruler end if shorter makes the frequency,that is cycles per second, rise and the sound is higher pitch

Could you explain why changing the free length of the ruler affects the frequency?

Pranshu Gaba - 3 years, 9 months ago

No comment

Rufus Daodu - 3 years, 9 months ago

Mohammad Khaza
Sep 3, 2017

When you twang a ruler close to the table there is less vibration so the sound frequency is higher.

when you twang it farther away there is more vibration so the sound frequency is lower.

Alexander Groves
Sep 10, 2017

The more vibrations per second the higher the frequency. The shorter the overhang the higher the vibrations per second. Therefore the shorter the overhang the higher the pitch.

Eric Verger
Sep 8, 2017

We can consider that the ruler is a cantilever beam submitted to a vertical force.
the vertical deformation will be : X=FL^3/3EI, where E is young modulus of the material, I quadratic moment, L is the length of the hangover.
If we transform this equation in a spring relation type : F=K*X, K is the rigididity 3EI/L^3
to increase the frequency you need to increase the rigidity : E & I are constant in this problem, so to increase K you need to shorten the L.

Bala Ji B
Sep 8, 2017

decrease the length.. we used to play like this in school days

Ruler Music

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