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6
votes
5answers
177 views

Why do harmonics occur when you pluck a string?

When you energise a taut string, the following resonant modes of vibration occur: Plotting on the frequency domain, you can see their corresponding frequencies: But what is the underlying ...
2
votes
2answers
466 views

Using $\sin()$ or $\cos()$ for computing SHM?

In simple harmonic motion, you can use either the sin or cos form of the equation but my question is which one do you use when and why? I am having a tough time understanding this, so any help would ...
1
vote
2answers
230 views

A foundational question about harmonic motion : 2 pipes with different length and frequencies [closed]

How to solve the following question? A pipe open only at one end has a fundamental frequency of 256Hz. A second pipe, initially identical to the first pipe, is shortened by cutting off a portion ...
2
votes
1answer
731 views

Harmonics in an open organ pipe

How to solve the following question? An open organ pipe has two adjacent natural frequencies of 500 and 600 Hz. Assume the speed of sound in the air 340m/s. The length of the organ pipe is? What ...
3
votes
1answer
1k views

Why do higher pitches appear to be louder?

It may just be in a few cases, but in the case of a flute, a higher pitch appears to come with a perceived higher volume. Is this simply because you need to put more energy into the flute to get a ...
0
votes
2answers
2k views

Young's Modulus and Vibrating String Harmonics

I was wondering how Young's Modulus effects the resonant harmonics of a vibrating (string instrument) string. I know that the string's fundamental frequency is $$\frac{1}2 \times \text{Length} \times ...
5
votes
1answer
283 views

Boundary conditions from single-valuedness of spherical wavefunctions

This question is a follow-up to David Bar Moshe's answer to my earlier question on the Aharonov-Bohm effect and flux-quantization. What I forgot was that it is not the wavefunction that must be ...
2
votes
1answer
299 views

Where are the harmonics in the radio spectrum?

When I strike a string on my guitar and look at the audio spectrum, I can see the fundamental frequency as a large peak. I can also see the harmonic frequencies as a train of little peaks at ...
2
votes
1answer
228 views

How can Hilbert spaces be used to study the harmonics of vibrating strings?

The overtones of a vibrating string. These are eigenfunctions of an associated Sturm–Liouville problem. The eigenvalues 1,1/2,1/3,… form the (musical) harmonic series. How can Hilbert spaces be ...
5
votes
3answers
408 views

Physics of a guitar

I understand that when you pluck a guitar string, then a bunch of harmonic frequencies are produced rather than just the frequency of the desired note. If this is true, why does C2 sound so different ...
1
vote
1answer
331 views

Open Ended/ Close Ended instruments?

Close ended instruments have twice the wavelength, because the wave must travel twice the distance to repeat itself. Why must a wave reach a lower density medium (air in this case) to repeat? When ...
2
votes
3answers
7k views

When are Maximum Velocity and Acceleration acheived in Simple Harmonic Motion?

Im trying to get my head around SMH out of curiosity because it seems simple yet I'm not getting the concept behind some ideas. For a SMH equation : $$ x=a \sin(\omega t+\phi) $$ Under what ...
0
votes
1answer
4k views

Finding Phase angle of Simple Harmonic Motion?

A sinusoidal oscillator has : $$x=x_{max} \cos(\omega t - \varphi )$$ Period is 2, initial displacement is 100mm initial velocity is 200mm/s What is the phase angle assuming $-\pi < \varphi < ...
-1
votes
1answer
603 views

resonance frequency [closed]

A string has a mass per unit length of 9 10–3 kg/m. What must be the tension in the string if its second harmonic has the same frequency as the second resonance mode of a 2m long pipe open at one end? ...
3
votes
3answers
796 views

Why does an octave on a piano have the divisions of 8 white keys and 5 black keys?

An octave corresponds to a doubling or halving of the frequency. Each octave on a piano and in classical music score is broken downs into 8 white keys and 5 black keys. Is there a physics explanation ...