If L = 1.0 m and v = 340 m/s, what is the third harmonic frequency f3?

If L = 1.0 m and v = 340 m/s, what is the third harmonic frequency f3?

• A. 170 Hz
• B. 510 Hz
• C. 340 Hz
• D. 680 Hz

Answer: (B)

The frequency of a standing wave in a tube or string with both ends fixed is f = n v / (2L), where v is the wave speed and L is the length. The third harmonic uses n = 3, so f3 = 3 v / (2L). Plugging in v = 340 m/s and L = 1.0 m: f3 = 3 × 340 / (2 × 1.0) = 1020 / 2 = 510 Hz. So 510 Hz is the third harmonic. The fundamental would be 170 Hz, the second harmonic 340 Hz, and the fourth harmonic 680 Hz.

The frequency of a standing wave in a tube or string with both ends fixed is f = n v / (2L), where v is the wave speed and L is the length. The third harmonic uses n = 3, so f3 = 3 v / (2L).

Plugging in v = 340 m/s and L = 1.0 m:

f3 = 3 × 340 / (2 × 1.0) = 1020 / 2 = 510 Hz.

So 510 Hz is the third harmonic. The fundamental would be 170 Hz, the second harmonic 340 Hz, and the fourth harmonic 680 Hz.