Question
formula for frequency of standing wave on string fixed at both ends
Answers
GPT-4o mini
The frequency of a standing wave on a string fixed at both ends can be determined using the following formula:
\[
f = \frac{n}{2L} \sqrt{\frac{T}{\mu}}
\]
Where:
- \( f \) is the frequency of the standing wave,
- \( n \) is the mode number (an integer representing the number of half-wavelengths in the string, with possible values \( n = 1, 2, 3, \ldots \)),
- \( L \) is the length of the string,
- \( T \) is the tension in the string,
- \( \mu \) is the linear mass density of the string (mass per unit length).
The values of \( n \) relate to the harmonic mode of the standing wave:
- For \( n = 1 \), it is the fundamental frequency (first harmonic),
- For \( n = 2 \), it is the second harmonic,
- For \( n = 3 \), it is the third harmonic, and so on.
This formula allows you to calculate the frequencies of the different harmonics of a standing wave formed on a string that is fixed at both ends.
\[
f = \frac{n}{2L} \sqrt{\frac{T}{\mu}}
\]
Where:
- \( f \) is the frequency of the standing wave,
- \( n \) is the mode number (an integer representing the number of half-wavelengths in the string, with possible values \( n = 1, 2, 3, \ldots \)),
- \( L \) is the length of the string,
- \( T \) is the tension in the string,
- \( \mu \) is the linear mass density of the string (mass per unit length).
The values of \( n \) relate to the harmonic mode of the standing wave:
- For \( n = 1 \), it is the fundamental frequency (first harmonic),
- For \( n = 2 \), it is the second harmonic,
- For \( n = 3 \), it is the third harmonic, and so on.
This formula allows you to calculate the frequencies of the different harmonics of a standing wave formed on a string that is fixed at both ends.