Question

The frequency of the fundamental mode of vibration of an air column enclosed in a closed-end pipe is 250 Hz. If its length is 33 cm, then find the velocity of sound in the air.
A) 390 m/s
B) 160 m/s
C) 330 m/s
D) 150 m/s

Answer 1

Hint: The frequency is described as the number of waves that pass a fixed place in the given amount of time. It is denoted by the symbol, f and its unit Hertz can also be called cycles per second.

Complete step by step solution:
Frequency = 250 Hz
Length = 33 cm = 0.33m
The velocity of sound in air =?
The fundamental mode of the vibration for a closed-end pipe, $f = \dfrac{v}{{4l}}$
Substituting the value of f and l, we get
$250 = \dfrac{v}{{4 \times 0.33}}$
$ \Rightarrow v = 330m/s$
Thus the velocity of sound in air = 330 ms-1

Hence the correct option is C.

Note:
1. Velocity is defined as the rate of change of the position of the object. It is a vector quantity and thus will have both direction and magnitude. It is a vector expression of the displacement that a particle undergoes concerning time. The unit of velocity is meters per second.
2. The vibration is the oscillations of an object about the equilibrium point. These oscillations may be regular like the motion of a pendulum or oscillations may be random like the movement of a tire on a gravel road.
3. Wave can be defined as the disturbance that travels through a medium and thus transporting the energy from one location to the other location without transporting any matter. Waves consist of alternating compressions and rarefactions in the medium.
4. In simple frequency is the number of the waves that pass a fixed point in unit time. A sound is a form of energy which is produced by the vibrating bodies.