Question

The chimney on a particular house is 7m long and acts as an open-open pipe. How many resonant frequencies for this chimney exist between 1000 and 10000 Hz?

A) 5
B) 6
C) 7
D) 8

Answer 1

Using the formula for resonant frequencies of an open-open pipe, we calculate that there are 7 resonant frequencies between 1000 and 10000 Hz for a 7m long chimney acting as an open-open pipe (option C).

Step-by-step explanation:

The chimney in the particular house in question acts as an open-open pipe and resonates at certain frequencies known as resonant frequencies. For an open-open pipe, the resonant frequencies can be found using the formula fn = n(v/2L), where fn is the nth resonant frequency, v is the speed of sound (approximately 343 m/s at room temperature), L is the length of the pipe (7m in this case), and n is a positive integer (1, 2, 3, etc.). To find the number of resonant frequencies between 1000 and 10000 Hz, we can set up inequalities: 1000 <= n(343/14) <= 10000 and solve for n.

The solution gives the range of n values that correspond to the number of resonant frequencies within the given range. Using this method, we find that there are 7 resonant frequencies (n=5 to n=11).

Therefore, the correct answer is C) 7.