The speed of propagation of a transverse wave on a 2.0-m long string fixed at both ends is 200 m/s Which one of the following is not a resonant frequency of this string?
A) 25 Hz
B) 100 Hz
C) 200 Hz
D) 50 Hz

Question

The speed of propagation of a transverse wave on a  2.0-m long string fixed at both ends is  200 m/s Which one of the following is not a resonant frequency of this string?
A)  25 Hz
B)  100 Hz
C)  200 Hz
D)  50 Hz

Quizplus · Accepted Answer

The resonant frequencies of a string fixed at both ends are given by $f_n = n\frac{v}{2L}$, where $v$ is the speed of the wave, $L$ is the length of the string, and $n$ is a positive integer (1, 2, 3, ...). For a string of length 2.0 m and speed 200 m/s, the fundamental frequency ($n=1$) is $f_1 = \frac{200}{2*2} = 50$ Hz. The second harmonic ($n=2$) is $100$ Hz, the third harmonic ($n=3$) is $150$ Hz, and so on. Thus, 25 Hz is not a resonant frequency because it does not fit the formula for any value of $n$.

The Speed of Propagation of a Transverse Wave on a