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If a string vibrates according to the equation y(x,t)=0.04sin(3pi x)cos(20pi t)

If a string vibrates according to the equation (in SI units_ y(x,t)=0.04sin(3pi x)cos(20pi t)

i)What type of wave is this? (longitudinal, transverse, progressive, stationary, etc)
ii) What is the frequency of this vibration?
iii) How many nodes are exhibited?
iv) The wave is formed by the superposition of two travelling waves. What are their amplitudes?
(edited 3 years ago)
Original post by Becca.D
If a string vibrates according to the equation (in SI units_ y(x,t)=0.04sin(3pi x)cos(20pi t)

i)What type of wave is this? (longitudinal, transverse, progressive, stationary, etc)
ii) What is the frequency of this vibration?
iii) How many notes are exhibited?
iv) The wave is formed by the superposition of two travelling waves. What are their amplitudes?


Can you explain what is your difficulty(ies)?

(i) We can determine whether the wave is progressive or stationary by "looking" at y(x,t)=0.04sin(3pi x)cos(20pi t.
(ii) The frequency is deduced from 20pi.
(iii) I thought there is only one note associate with one frequency.. Or the question is asking "nodes" instead of "notes".
(iv) 2A = 0.04 where A is the amplitude of the "original" travelling waves.
Where is this question from? I am unfamiliar with doing questions like this from A-level Maths or Physics.
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Becca.D
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Original post by Eimmanuel
Can you explain what is your difficulty(ies)?

(i) We can determine whether the wave is progressive or stationary by "looking" at y(x,t)=0.04sin(3pi x)cos(20pi t.
(ii) The frequency is deduced from 20pi.
(iii) I thought there is only one note associate with one frequency.. Or the question is asking "nodes" instead of "notes".
(iv) 2A = 0.04 where A is the amplitude of the "original" travelling waves

Apologies, I meant to delete i) when I copied the question over.
For ii) This is not the equation I was taught so I was unsure how to get the frequency, however I've just realised omega is angular frequency not acceleration woops.
Yes iii) was supposed to be nodes not notes, autocorrect. Im just not sure how you're supposed to figure out nodes from that equation.
For iv) again its not the equation I'm used to but I see what youve done now, so would the standard equation to compare it to be y(x,t)=2Asin(kx)cos(omega t)? And then just relate the two from there?
From your writing, it seems that you have obtained for (ii).

Original post by Becca.D
…Yes iii) was supposed to be nodes not notes, autocorrect. Im just not sure how you're supposed to figure out nodes from that equation.


Nodes occur when sin(3πx) = 0. So you need to solve the trigonometric equation.

Original post by Becca.D
… For iv) again its not the equation I'm used to but I see what youve done now, so would the standard equation to compare it to be y(x,t)=2Asin(kx)cos(omega t)? And then just relate the two from there?


Yes
y(x,t)=2A sin(kx) cos(ωt) is one of the standing wave expressions that we can write.

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