Question

Standing waves are excited in a 1 m long pipe open at one end, closed at the other. Take the speed of the wave as 340 m/s and calculate the frequency of the first overtone (i.e. the first harmonic above the fundamental frequency).

(a) 170 Hz
(b) 340 Hz
(c) 510 Hz
(d) 680 Hz

Answer 1

The frequency of the first overtone in a 1 m long pipe open at one end and closed at the other is 340 Hz.Option B is the correct answer.

Step-by-step explanation:

To find the frequency of the first overtone in a 1 m long pipe open at one end and closed at the other, we need to determine the frequency of the fundamental frequency and then calculate the frequency of the second harmonic. The fundamental frequency is determined by the length of the pipe and the speed of the wave. Since the pipe is closed at one end, the fundamental frequency is given by:

fundamental frequency = (speed of wave) / (2 * length of pipe)

Plugging in the values, we get: fundamental frequency = 340 m/s / (2 * 1 m) = 170 Hz

The frequency of the first overtone (second harmonic) is twice the fundamental frequency:

first overtone frequency = 2 * fundamental frequency = 2 * 170 Hz = 340 Hz