A string 2.0 m long has a mass of 2.4  10^-² kg. When fixed at both ends, it vibrates with a fundamental frequency of 150 Hz. The frequency of the third harmonic of this fundamental is A) 50 Hz. B) 75 Hz. C) 0.15 kHz. D) 0.45 kHz. E) 1.1 kHz.

Question

Quizplus · Accepted Answer

We can use the formula $f_n = n \cdot \frac{v}{2L}$, where $f_n$ is the frequency of the $n$th harmonic, $v$ is the speed of the wave, and $L$ is the length of the string. Solving for $v$, we get $v = 2L\cdot f_n / n$.

Using the fundamental frequency, we can find the speed of the wave:
$$v = 2L\cdot f_1 = 2(2.0	ext{ m})\cdot 150	ext{ Hz} = 600	ext{ m/s}$$

Now we can use this speed to find the frequency of the third harmonic:
$$f_3 = 3 \cdot \frac{v}{2L} = 3\cdot\frac{600	ext{ m/s}}{2(2.0	ext{ m})} = 450	ext{ Hz} = 0.45	ext{ kHz}$$

Therefore, the answer is D.

A String 2