1110. A tuba player plays the note E and sustains the sound...

1110. A tuba player plays the note E and sustains the sound for some time. For a pure E the variation in pressure from normal air pressure is given by $V(t) = 0.2 \sin 80 \pi t$ Where V is measured in pounds per square inch and t is measured in seconds. a) Find amplitude, period, and frequency. b) If the tuba player increases the loudness of the note, how does the equation for V change? c) If the player is playing the note incorrectly and it is a little flat, how does the equation change for V change?

Transcript

00:01 In this problem we have been given that a tuba from brass instrument family is made up of a conical pipe with length of l equals 0 .95 and effective length lf 1 .1 meter.

00:12 So firstly we have been asked is tuba a closed pipe or an open pipe instrument.

00:16 So we can say that given information is lf that is length effective is 1 .1 meters and then we have the value of l as 0 .95 meters.

00:26 So with these kind of values we can say that temperature is 25 degrees celsius.

00:34 So tuba can be thought of as a conical pipe and it is open at the far end or bell but is almost closed at the other end.

00:44 So we can say that it is open at the far end or bell and it is almost open.

00:58 And it is almost closed.

01:00 So it is almost closed at the other end.

01:05 So this is the answer for the first part.

01:07 Now we will look into the answer of the second part.

01:10 So this can be put inside a box.

01:12 So in the second part we have been asked what is the bell diameter d of this tuba? so bell diameter b, bell diameter d of this tuba will be or can be calculated with some kind of formula.

01:27 So let's see what is it.

01:30 So we know that l effective is there.

01:32 So l effective is equal to l plus delta l.

01:35 And then we have the value of delta l to be equals to l effective over, sorry, l effective minus l.

01:44 So l effective is 1 .1 minus 0 .95.

01:49 So this comes around 0 .15 .15 meters.

01:57 So we can say that in correction is delta l and it is equal to delta l equals to 0 .6 r.

02:05 So this will be equal to 0 .3d and we have the value of l already.

02:11 So we have the value of this expression as 0 .15.

02:17 So from here we can say that bell diameter will be equals to this d value, this capital d or small d both are same.

02:25 Okay, so don't get confused like this is capital, this is small.

02:29 So we are also using capital d.

02:31 Otherwise it will be confusing.

02:32 So this is capital d.

02:34 So this will be equals to 0 .5 meter.

02:37 This is the answer for the second part.

02:39 Now we will see how we can calculate the value in the third part.

02:44 So in the third part, we have been asked that what is the speed of sound vt in this tuba? so speed of sound vt in this tuba can be calculated by, some kind of theoretical approach.

02:59 So we can say that v is there equals to 331 .0 plus 0 .6 multiplied tc so tc is in degrees celsius so this will be equals to 331 point sorry 331 plus 0 .6 multiplied 25 degrees celsius is there so this comes around 346 .0 meter per second for the v value.

03:27 That is asked in the third part...

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