Respuesta :
Answer:
283.33 Hz
Explanation:
For an organ pipe open at both ends, the harmonics are based on the pipe supporting standing waves that have nodes at the ends. The wavelength of the nth harmonic in such a pipe can be expressed as:
[tex]\lambda_n=\dfrac{2L}{n}[/tex]
Where:
- 'L' is the length of the pipe
- 'n' is the harmonic number
The frequency (f_n) of the nth harmonic can be found using the relationship between speed (v), wavelength (λ), and frequency (f), given by:
[tex]f_n=\dfrac{v}{\lambda_n}[/tex]
Substituting the expression for 'λ_n' gives:
[tex]\Longrightarrow f_n=\dfrac{v}{\dfrac{2L}{n}}=\dfrac{nv}{2L}[/tex]
Given the length of the pipe (L) is 1.80 meters, the speed of sound (v) is 340 m/s, and we are interested in the third harmonic (n = 3), we can substitute these values into the formula to find the frequency of the third harmonic:
[tex]\Longrightarrow f_3=\dfrac{(3)(340 \text{ m/s})}{2(1.80 \text{ m})}\\\\\\\\\therefore f_2 \approx \boxed{283.33 \text{ Hz}}[/tex]
Thus, the frequency of the third harmonic for an organ pipe open at both ends is approximately 283.33 hertz.
Final answer:
Using the formula for the third harmonic of an organ pipe open at both ends, the frequency is approximately 283.33 Hz, based on a 1.80 m length organ pipe and the velocity of sound in air at 340 m/s.
Explanation:
The question pertains to the calculation of the frequency of the third harmonic in an organ pipe open at both ends. Using the given length of the pipe (1.80 m) and the velocity of sound in air (340 m/s), we can determine the frequency of the third harmonic. For an organ pipe open at both ends, the harmonics are formed at frequencies that are multiples of the fundamental frequency. The fundamental frequency (first harmonic) is determined by the formula f1 = v / (2L), where v is the velocity of sound and L is the length of the organ pipe.
The third harmonic will be three times the frequency of the fundamental. Thus, the frequency of the third harmonic, f3, is 3 times f1, giving us f3 = 3(v / (2L)). If we plug in the values (v = 340 m/s and L = 1.80 m), the calculation yields:
f3 = 3(340 m/s) / (2 * 1.80 m) = 3 * 340 m/s / 3.60 m = 3 * 94.44 Hz = 283.33 Hz.
Therefore, the frequency of the third harmonic in the organ pipe is approximately 283.33 Hz.
