Answer the following questions and provide an explanation for your answer. If th

Question

Answer the following questions and provide an explanation for your answer. If the frequency of a standing wave on a string is doubled with all other factors remaining unchanged, its wavelength is changed by a factor of _____? For full credit, explain your answer. A certain organ pipe is open at both ends. Another organ pipe with the same length is open at one end and closed at the other. Which pipe will have the lower fundamental frequency? Explain. The tube shown here is open at both ends and the displacement of the air molecules from equilibrium is shown at a given instant. In what mode is the system vibrating? Assuming that the velocity of sound in air is about 343 m/s, determine the frequency of this standing wave pattern.

Explanation / Answer

(1) Wavelength become half because both are inversally proportional to each other

(2) For both end open organ pipe

wavelength = length of pipe = L

and for one end open organ pipe

3/2 wavelength = length of pipe,

hence

wavelength =2L/3

now both end open organ pipe has higher wavelength hence it has lower frequency

(3) There are two complete wave for open organ pipe hence it is vibrating in 1st overtone ot 2nd fundamental frequency

From the grapph,

wavelength =20/2=10 cm=0.1 m

frequency = velocity/wavelength=343/0.1=3430 Hz

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