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Question 1137253: The frequency of a sound wave is called its pitch. The pitch p of a musical tone and its wavelength w are related by the equation p=v/w, where v is the velocity of sound through air. Suppose a sound wave has a velocity of 1056 feet/second.
a.) Graph the equation p=v/w. What lines are close to the maximum values for the pitch and the wavelength?
b.) What happens to the pitch of the tone as the wavelength decreases?
c.) If the wavelength is doubled, what happens to the pitch of the tone?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! p = v / w.
p is the pitch.
v is the velocity of sound through air.
w is the wavelength.
assume the velocity is 1056 feet per second.
then you get p = 1065 / w
the value of w is shown by the value on the x-axis.
the value of p is shown by the value on the y-axis.
the maximum value for the pitch is plus infinity.
this occurs when w approaches 0.
the maximum value for w is plus infinity.
this occurs when the pitch approaches 0.
the graph looks like this.
the graph has positive and negative value of w and positive and negative values of p.
however, since wavelength has to be positive, you can ignore the part of the graph where the wavelength is negative.
if you were drawing the graph by hand, you would only draw the part of the graph where the wavelength is oositive.
the domain of the function is 0 <= w <= plus infinity.
the range of the graph is 0 <= p <= plus infinity.
the maximum value for p is plus infinity.
the maximum value for w is plus infinity.
as the wavelength gets smaller, the pitch gets higher.
this can be seen by taking two values for the wavelength and then determining what the pitch would be according to the fomula.
when the wavelength is 100, the pitch is 1065 / 100 = 10.65.
when the wavelength is 10, the pitch is 1065 / 10 = 106.5.
if the wavelength is doubled, the pitch becomes half of what it was.
this can be seen by taking two values for the wavelength where one of the values of of the wavelength is double the other value ofthe wavelength and then determine what the value of the pitch would be according to the formula.
when the wavelength is 100, the pitch is 1065 / 100 = 10.65.
when the wavelength is doubled to 200, the pitch is 1065 / 200 = 5.375 which makes it half of what it was.
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