Final answer:
In this case, the frequency of the next higher harmonic is 165.5 Hz. To find the frequency of the next higher harmonic of a pipe closed at one end, you can use the formula f = nv/2L, where n is the harmonic number, v is the speed of sound, and L is the length of the pipe. By calculating the length of the pipe, we can determine the frequency of the next higher harmonic.
Step-by-step explanation:
An open-pipe resonator has a fundamental frequency of 250 Hz. By changing its length, we can find the frequency of the next higher harmonic. The fundamental frequency is given by the formula f = nv/2L, where f is the frequency, n is the harmonic number (1 for fundamental), v is the speed of sound, and L is the length of the resonator. Solving for L, we can then substitute in the values for the next harmonic and find the new length. Rearranging the formula, we have L = nv/2f. Plugging in the values for n=2, v=331 m/s, and f=250 Hz, we can calculate:
- L = 2 * 331/2 * 250
- L = 663/500
- L = 1.326 m
Hence, the frequency of the next higher harmonic of the pipe is obtained by using the formula f = nv/2L. Since the length of the pipe is now 1.326 m, we can calculate the frequency of the next higher harmonic (n=3) as:
- f = 3 * 331/2 * 1.326
- f = 165.5 Hz
Therefore, the correct answer is option c. 165.5 Hz.